Category: Reasoning

“The role of analogy is to aid understanding rather than to provide justification.” To what extent do you agree with this statement?

Human beings share a strong intuition that analogical justification forces us to better understand and interpret the situations that we face in our everyday lives. These analogies are widely recognized as playing an important role as a mental shortcut that allows people to solve problems and make judgments quickly and efficiently. Analogies provide insight and formulate possible solutions to problems. According to a pioneer in chemistry and electricity, Joseph Priestley said that analogy is our best guide in philosophical investigations (Bartha). Due to their heuristic role, analogies and analogical reasoning have been a massive focus in artificial intelligence and other various research (Helman). In order to examine the question proposed, it is important first to establish the meaning of a few keywords. An analogy is a comparison between two objects, or system of objects, that highlights respects in which they are thought to be similar (Bartha). Furthermore, an analogical argument is an explicit representation of a form of analogical reasoning that cites accepted and justified similarities between two systems to support the conclusion (Bartha). This essay will argue that analogies serve as justifications rather than simply a way to better understand concepts. The knowledge question formulated here, therefore, is “what justification can be given for a claim that analogical arguments deliver a plausible conclusion?” In order to explore this question, examples will be examined through the two areas of knowledge, Natural Sciences, and Human Sciences.

Analogies become fundamental elements in the process of learning, based on concepts, relations, and images that are accessible to students, as they allow students to use what is familiar to them in order to understand what is not so familiar (Koszowski). The use of analogies has been shown to be especially relevant in the case of learning sciences that involve abstract concepts, in this case chemistry, which is often difficult from the students’ point of view. For this reason, literature extensively defends the teaching of chemistry and other sciences (such as physics, biology, and geography) through the use and drawing of analogies aimed at facilitating students’ understanding, acquisition of new knowledge, and modification of alternative conceptions (Rosaria). The core of analogies is called mapping and has been the main focus of analogy research. At a first level, the mapping process consists of finding how two situations are similar and then bringing across further inferences from the better-known situation (the base, or source ) to the less familiar one (the target) (Canale and Tuzet). What distinguishes analogy from other kinds of similarity is that for two situations to be analogical, they must be similar in their relational structure. Analogy research has largely agreed on a set of principles laid out by Dedre Gentner in 1983, in a theory called structure mapping. According to structure mapping theory, analogical mapping requires aligning the two situations based on their commonalities – particularly their common relational structure – and projecting inferences from the base to the target, according to this alignment. Thus, if two similar objects are compared to one another through mapping, then the concept can be justified through analogical reasoning (Lo).

Many teachers use analogies to aid students for a better understanding and give justification to a concept being discussed. An analogy can allow new material to be more easily absorbed with the student’s prior knowledge. This enables the students who do not readily think in abstract terms to develop a clear understanding of the concepts (Rosaria). A popular analogy that I came across when I was studying chemistry was that Lego bricks are often used to represent atoms. Atoms are the basic building blocks for all matter around us. By combining atoms in different ways new materials are formed, just as new structures can be created from combining Lego bricks (RSC). The mapping process in this example is a complex concept, atoms, are brought across a more familiar situation, the Lego bricks. This example does provide justification and delivers a plausible conclusion that if Lego blocks do makeup everything, so does atoms. Thus, justification of analogical reasoning is validated to deliver a plausible conclusion.

However, in some cases analogical reasoning does not provide justification in a concept being discussed. For instance, in physics, a ‘solider’ analogy is used by many teachers to explain how light refracts. The soldiers are marching on a normal ground to a mud which slows them down. The soldiers that reach the mud first are slowed down first and the row bends. This explanation of the line of the marching soldiers bending is closely correlated to how a light refracts through different mediums (The Dangers of Analogies). However, anyone who has been in a marching band will find that this argument is rather unconvincing. Marching bands are usually trained to maintain a constant stride in order to be symmetrical. Does this analogy give any correct insight about the underlying mechanism of light refraction? If the marching band crossed a curved interface, would the ranks focus to a point, or diverge in many directions? Does the analogy work for reflection? (Simanek) Many questions are created by the analogy if it is taken to the literally. The explanation expects the reader to assume that the necessary adjustments will be made to maintain perpendicularity between ranks and files. Therefore, this analogy does not provide justification to deliver plausible conclusions of how light refracts. If the analogical reasoning is not taken to this level of analysis, then this analogy could provide meaning and justification to the student.

On the contrary, analogical arguments in human sciences, more specifically legal cases, provide justification to a problematic topic being discussed and delivers plausible conclusions. Analogies in law are used to argue that one disputed situation is indistinguishable from another situation where the merits are relatively clear (Lamond). In other words, attorneys use analogies, that are similar to the case, to justify an argument in order to convince the judge. Moreover, the judge also uses analogical reasoning in legal cases. For instance, a well-known description of analogical reasoning in legal cases is from Edward Levi. Levi says that a judge reasoning by analogy studies the facts and outcomes of a case she deems similar to the case before her. The judge then formulates the rule “inherent” in the prior case and uses it to decide her case. This practice of reasoning by analogy is on the basis of its epistemic and institutional advantages (Sherwin). These advantages are that the analogical arguments produce a plethora of data for decision-making. For instance, an advantage that analogical arguments produce is that they demonstrate the collaborative effort of the judges over time and also correct any biases that might guide judges to discount for their prior decisions (Ashley). Furthermore, it exerts a conservative force in law, holding the development of law to a gradual pace. Eminently, these points of interest do not reply upon the rational power of analogical reasoning, rather, author contends that, as open-ended reasoning and analogical reasoning alike may sometimes result in incorrect decisions, these qualities of analogical reasoning make it a desirable method of deciding legal disputes (Sherwin). When a judge is defied with an agitated inquiry, the judge overviews past decisions, recognizes manners by which these choices are similar and different, and develops a principle that captures the similarities and differences the judge thinks is important. This principle in return gives premise to the judge’s very own decision (Ashley).

However, there is also limitations to the argument that analogies do provide justification in legal cases. The most notable criticism comes from Larry Alexander. Alexander says that analogical reasoning originates with the prior decisions of others rather than the subject’s own perceptions and instincts. Since judges are fallible, a portion of judges made prior that are potentially wrong (Sherwin). Thus, the data is flawed and decision-making by analogy will simply entrench the errors of the past. A judge’s ethical reasoning may be flawed. However, if the judge feels obliged to seek analogies, they have incentive to sift more carefully through reported opinions. The practice of analogical reasoning from past decisions has procedural benefits that go beyond the rational force it carries in any case (Sherwin). Thus, the analogical reasoning in legal situations are justified, and also give plausible conclusions.

In conclusion, analogical reasoning does give justification and deliver plausible conclusions to a complex concept or topic being studied. In the area of natural sciences, we see that analogies in both chemistry and physics are used to aid understanding and give justification and the complex topics. Analogies provide insight and formulate possible solutions to problems that otherwise would have been difficult to interpret and solve by one individual. The analogies are a fundamental process of learning as they allow students to use that which is familiar to them in order to understand that which is not familiar. Furthermore, in legal cases, analogical arguments are used to argue that one disputed situation is indistinguishable from another situation where the merits are relatively clear, giving justification. Thus, analogies are a useful tool in understanding abstract concepts in a more tangible form. As exemplified with natural sciences and human sciences, the more tangible analogies such as Lego blocks in understanding chemistry as well as the marching band to understand refraction theory displays that these concepts are not only easily understood they are justified through the explication. Finally, in the case of law, judges often use analogies to justify their reasoning. Therefore, analogies are used as justifications.

Bibliography

1. Ashley, Kevin D. “Arguing by Analogy in Law: A Case-Based Model.” Analogical Reasoning: Perspectives of Artificial Intelligence, Cognitive Science, and Philosophy, edited by David H. Helman, Springer Netherlands, 1988, pp. 205–24. Springer Link, doi:10.1007/978-94-015-7811-0_10.
2. Bartha, Paul. “Analogy and Analogical Reasoning.” The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Spring 2019, Metaphysics Research Lab, Stanford University, 2019, https://plato.stanford.edu/archives/spr2019/entries/reasoning-analogy/.
3. Canale, Damiano, and Giovanni Tuzet. “Analogical Reasoning and Extensive Interpretation.” Analogy and Exemplary Reasoning in Legal Discourse, edited by Hendrik Kaptein and Bastiaan van der Velden, Amsterdam University Press, 2018, pp. 65–86. JSTOR, JSTOR, https://www.jstor.org/stable/j.ctv62hfhb.7.
4. Helman, D. H., editor. Analogical Reasoning: Perspectives of Artificial Intelligence, Cognitive Science, and Philosophy. Springer Netherlands, 1988. www.springer.com, doi:10.1007/978-94-015-7811-0.
5. KOSZOWSKI, MACIEJ. “Multiple Functions of Analogical Reasoning in Science and Everyday Life.” Polish Sociological Review, no. 197, 2017, pp. 3–19.
6. Lamond, Grant. “Precedent and Analogy in Legal Reasoning.” The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Spring 2016, Metaphysics Research Lab, Stanford University, 2016. Stanford Encyclopedia of Philosophy, https://plato.stanford.edu/archives/spr2016/entries/legal-reas-prec/.
7. Lo, Norva. [U08] Analogical Arguments. https://philosophy.hku.hk/think/value/analogy.php. Accessed 4 Jan. 2020.
8. Rosaria, Justi. Science Teachers’ Analogical Reasoning. https://link-springer-com.proxy.lib.sfu.ca/content/pdf/10.1007/s11165-012-9328-8.pdf. Accessed 5 Jan. 2020.
9. rsc. Developing and Using Models – Analogies in Chemistry – Core Idea – Further Examples of Commonly Used Analogies. https://www.rsc.org/cpd/resource/RES00001452/analogies-in-chemistry/RES00001448?cmpid=CMP00003577. Accessed 5 Jan. 2020.
10. Sherwin, Emily. “A Defense of Analogical Reasoning in Law.” The University of Chicago Law Review, vol. 66, no. 4, 1999, pp. 1179–97. JSTOR, JSTOR, doi:10.2307/1600365.
11. Simanek, Donald. The Dangers of Analogies. https://www.lockhaven.edu/~dsimanek/scenario/analogy.htm. Accessed 5 Jan. 2020.

Chapter one: Introduction

Calculus is the study of variation, and it is also the central subject in mathematics (Boyer, 1959; Goldstine, 2012; Tall, 1990). The concept of calculus is applied in statistics, science, economics, and engineering to study the concepts of gravity, speed, velocity, variations, growth or decay function, and maximum or minimum of profit and cost function (Boyer, 1959, Goldstine, 2012; Tall, 1992). Many of scientific and technological growth since 1900s to the current time are linked with the idea of calculus (Boyer, 1959; Goldstine, 2012). However, the core concepts of calculus: infinitesimals, variations, rates of change, derivatives, and integrals are difficult for students to learn (Bezuidenhout, 1998; Burns, 2014; Carlson et al., 2002; Castillo-Garsow, 2012; Orhun, 2012, Park 2015; Tall, 1992; Thompson & Carlson, 2017). In this study, I seek to investigate the mathematical reasoning that undergird the concept of variation, rate of change, and derivative.

The concept of variation is fundamental for understanding the main idea of calculus and it has different mathematical meanings from elementary school to higher-level mathematics studies (Akgün & Özdemir, 2006; Gray, Loud, & Sokolowski, 2007; Jacobs, 2008; Kaput & Roschelle, 2013; National Governors Association (NGA), 2010; Philipp, 1992; Stephens, 2005). For example, within mathematics, variables have many meanings and it has a meaning of a fixed number or value, unknown values of an equation, an algebraic symbol, and varying quantities (Akgün & Özdemir, 2006; Ely & Ellis, 2018; Philipp, 1992; Stephens, 2005; Thompson & Carlson, 2017). The concepts of variation and infinitesimal variation are the foundation and main source of the development of the idea of constant rate of change, rate of change, function, derivative, and advanced concepts of calculus (Gray, Loud, & Sokolowski, 2007; Kaput, 1994; Meletiou, 2000; Philipp, 1992; Schoenfeld, Arcavi, 1988; Stephens, 2005). For instance, the concept of average rate of change is built on the quotient of two simultaneously varying quantities. However, the concept of variation is not well studied or it is often neglected in mathematics learning, despite its importance in the development of the fundamental concept of calculus (Akgün & Özdemir, 2006; Schoenfeld & Arcavi, 1988; Thompson & Carlson, 2017).

The concept of rate of change is first introduced in early middle school mathematics as connected to the concept of ratio, slope, and proportion (NGA, 2010). In elementary school, students discuss the concept of fractions, ratios, and proportions as they progressively learn the concept of whole numbers, integers, decimal numbers, and the rational number system in connection with the elementary mathematical operations (NGA, 2010). Similarly, the concept of rate of change is used to describe the relationship between two or more varying quantities in different fields, such as physics (e.g., speed and velocity which is used to describe the relationship between position and time), statistics (e.g. average and mean which is used to describe the distribution of data points), and economics (e.g., interest rate and percentage change which is used to describe the amount of money change in relation to a particular time interval). Within mathematics, the concept of rate of change has many meanings among high school, undergraduate, and graduate students (e.g., slope, rise over run, average rate of change, and derivative which is used to describe the relationship between two simultaneously changing quantities) (Bezuidenhout, 1998; Byerley, Hatfield, & Thompson, 2012; Ehlke & Hajra, 2017; Johnson, 2015; Musgrave & Carlson, 2016; Tyne, 2014, 2017; Weber, 2013). The fundamental concepts of calculus (e.g. functions, derivatives, integrals, and differential calculus) are founded on the conceptual understanding of the rate of change (Johnson, 2012; Thompson, 1994; Thompson & Carlson, 2017; Thompson & Thompson, 1992; Thompson & Thompson, 1994). However, many calculus students have weak or unproductive understanding towards the concept and idea of rate of change (Johnson, 2015; Musgrave & Carlson, 2016; Tyne, 2014, 2017; Thompson & Carlson, 2017).

The concept of derivative in calculus is deeply rooted in the ideas and concepts of variation and rate of change (Park, 2013; Thompson, 1994). The concept of derivative can be developed from the idea of constant rate of change or average rate of change to a continuously varying rate of change function, or an instantaneously varying rate of change function (Carlson et al., 2002; Thompson & Ashbrook, 2016; Thompson & Carlson, 2017). In calculus, the concept of derivative is typically introduced in a post-secondary school level or after a pre-calculus course using the concept of a limit of the average rate of change function (Hart, 2019; Stewart, 2015; Tan, 2018). Student’s conceptual understanding of integrals, differential equations, and advanced calculus concepts is founded on the idea and the concept of derivative function (Burns, 2014; Dufour, 2015; Firouzian, 2013; Habre & Abboud, 2006; Park, 2012; Park, 2013; Thompson & Carlson, 2017; Wagner, Roundy, Dray, Monogue & Weber, 2015). However, many students when joining their post-secondary school exhibited underdeveloped conceptual understanding to the concepts of derivative (Byerley, Hatfield & Thompson, 2012; Park, 2012; Park, 2013; Dorko & Weber, 2013).

The conceptual understanding of variation, rate of change, and the derivative are deeply founded on the students’ clear and sound mathematical reasoning abilities (Carlson et al., 2002; Gray, Loud, & Sokolowski, 2007; Moore, 2010; Thompson & Carlson, 2017). Mathematical reasoning is defined as “a capacity to think logically about the relationship among concepts and situations” (NRC, 2001, p.129). This idea of mathematical reasoning that focused on the students’ logical thinking ability about two or more covarying quantities is currently promoted in calculus learning (Carlson et al., 2002; Castillo-Garsow, 2012; Engelke, 2007; Gray, Loud, & Sokolowski, 2007; Moore, 2010; Thompson & Carlson, 2017). Researchers in calculus are currently investigating mathematical reasoning abilities like variational reasoning, quantitative reasoning, covariational reasoning, continuous covariational reasoning, and smooth continuous covariational reasoning, which are foundational to advanced calculus learning (Carlson, Larsen, & Jacobs, 2001; Carlson et al., 2002; Castillo-Garsow, 2012; Engelke, 2007; Gray, Loud, & Sokolowski, 2007; Moore, 2010; Moore& Paoletti, 2013; Thompson & Carlson, 2017; Weber & Carlson, 2010). Most study results in calculus showed that students’ learning of the foundational ideas of calculus like the rate of change, derivative, and integrals rely on their clear and explicit covariational reasoning capability (Carlson et al., 2002; Castillo-Garsow, 2012; Engelke, 2007; Gray, Loud, & Sokolowski, 2007; Moore, 2010; Moore & Paoletti, 2013; Moore & Paoletti, 2015; Thompson & Carlson, 2017; Weber & Carlson, 2010).

The notion of covariational reasoning means a student has an image of two quantities varying together within specified intervals (Carlson et al., 2002; Castillo-Garsow, 2012; Thompson & Carlson, 2017). According to Thompson (2011, p.46), “the mathematical reasoning of variation or covariation involves imagining a quantity whose value varies.” Additionally, Thompson (1996, p.1) indicated that “mathematical reasoning at all levels is firmly grounded in imagery.” Imagining for a student could mean someone visualizes mentally how “the volume and height of water are varying as the bottle is being filled with water without actually filling the bottle with the water” (Castillo-Garsow, Johnson & Moore, 2013; Thompson, 1994). Further discussion will be included about imagery and the idea of mathematical reasoning from the views of Thompson (1996) and Piaget (1967) in Chapter 2. The quote below gives an illustration to what it means to imagine how a quantity varies over certain given interval of time.

“An elementary school student might envision a situation in which one tree is three times as tall as another. What she will find difficult is to imagine this relationship holding over time as the trees grow—imagining that the taller tree is always three times as tall as its neighbor as each of them grow. The two instances reveal a stark contrast between two ways of thinking. In the first instance, “three times as tall” is a description of a static relationship. In the second instance, “three times as tall” is an invariant relationship between two quantities whose values vary. The second instance involves a way of thinking that is foundational for the concepts of variable and function in calculus” (Thompson, 2011, p.46).

Researchers in calculus are investigating numerous ways to improve students’ mathematical reasoning, for example, in several studies in calculus researchers are focused on developing and investigating students’ quantitative reasoning, continuous variational reasoning, and covariational reasoning. This study is similarly focused on investigating and understanding the students’ mathematical reasoning, especially students’ smooth continuous covariational reasoning ability, since covariational reasoning ability is viewed as a key mathematical reasoning ability that will help students to understand the central concept of calculus. Thompson and Carlson (2017) indicated that covariational reasoning is a foundational reasoning ability in mathematics, particularly in calculus, to advance students’ conceptual understanding of the concept of function, rate of change, and derivatives. There are two distinct views among researchers and educators regarding how students develop covariational reasoning. The two distinct views emerged from the continuous covariational reasoning view: (1) chunky continuous covariational reasoning view and (2) smooth continuous covariational view. More detailed discussion of these views will occur in the next section and chapter 2.

Background for the Study

Students’ variational and covariational reasoning have critical roles in conceptual understanding of the foundational concepts of rate of change, derivatives, integrals, and advanced calculus concepts (Castillo-Garsow, 2010, 2012; Castillo-Garsow et al., 2013; Ely & Ellis, 2018; Thompson & Carlson, 2017). Conflicted theoretical constructs on how students develop variational, covariational, and other related reasoning types exist among the major researchers like Saldanha and Thompson (1998), Carlson et al. (2002), Confrey and Smith (1994), and others. For example, for Confrey and Smith (1994) covariation means coordinating the change from y_m to y_(m+1) with the change from x_m to x_(m+1)without considering the change in-between the intervals. That is, covariation have a meaning of chunky by moving or adding values continuously between the start and the end values of one variable with successive values of change with the other variable. This equally means that chunky reasoning is the ability of coordinating a completed change in the first variable value with a completed change in the second variable (i.e., coordinating a complete ∆x with a complete ∆y)( Castillo-Garsow, 2012; Confrey & Smith, 1994; Saldanha &Thompson, 1998; Thompson & Carlson, 2017). On the other hand, Saldanha and Thompson (1998) viewed covariation in terms of imagining one quantity’s values varying continuously and then imagining the second quantity’s values varying simultaneously. For Saldanha and Thompson (1998) covariation has a meaning of continuous covariation where students imagining two quantities values moving together. That is, students imagining one quantity values varying by different values continuously as it passes all the way through the given interval and then imagining the second quantity simultaneously moving continuously at the beginning and end of the interval (Castillo-Garsow, 2012; Thompson, 2008; Thompson & Carlson, 2017). In continuous covariational reasoning there is an imagination of how quantities’ values vary within an interval (i.e., there is an imagination of change within ∆x). The continuous covariation reasoning proposed by Saldanha and Thompson (1998) could entail two reasonings chunky continuous covariation and smooth continuous covariation reasoning. For example, for the hypothetical problem “imagine a bottle filled with liquid. How do you think about the volume of the liquid as it changes relative to the height of the liquid in the bottle?” (Castillo-Garsow et al.,2013, p.31) For this kind of problem two ways of thinking are possible. One possible mathematical reasoning is filling the volume of the bottle smoothly and continuously by some amount of water. That is, it might have a mental image of change in progress (e.g., filling a bottle with a hose) which is a smooth reasoning. Another possible mathematical reasoning is filling the volume of the bottle in a discrete amount that is, it might entail images of change as occurring in discrete chunks (e.g., filling a bottle with successive cups of water) which is chunky reasoning. Therefore, chunky continuous covariation reasoning has a meaning of imagining a two covarying quantities changing their values continuously by adding the same amount of values at the end of the interval but not imagining variation within the interval. This type of reasoning can go with the covariational reasoning proposed by Confrey and Smith (1994). While smooth continuous covariation reasoning has a meaning of imagining two quantities covarying simultaneously; and at the same time thinking the two quantities varying continuously in a bit or vary smoothly and continuously in all in-between values over the interval, which is currently proposed by Carlso-Garwall (2012). The basic distinction between the two reasoning lays on their views of variation or change that is, in chunky reasoning there is starting and ending values (complete change) but in smooth reasoning there is starting but not ending values (keep moving or change in progress). When Thompson’s refuted Confrey’s idea (i.e. Confrey has chunky thinking towards two covarying quantities) he described the following statement which supported his idea of smooth continuous covariation. “Continuous variation in Confrey’s way of thinking about multiplicative change is very hard to imagine. If the underlying idea is that all multiplicative change happens by a split, then I do not know how to imagine the value of 2^x varying smoothly as I smoothly vary the value of x” (Thompson, 2008, p.39). The above quote shows that Thompson’s ideas of continuous covariation has smooth continuous reasoning but not chunky continuous reasoning. Though the two reasonings are co-related, since they emerge from continuous reasoning, nonetheless they are distinct in nature and they will produce two different mathematics. In the following section, I will discuss the two types of covariational reasoning.

Chunky Continuous Covariational Reasoning

Chunky continuous covariational reasoning is an imagination of change that focuses on how the change is happening at the start and end of the interval, or it is mathematical reasoning that happens by coordinating two end values (Carlso-Garwall, 2010, 2012; Confrey, 1991; Confrey and Smith, 1994; Thompson & Carlson, 2017). Figure 1 illustrates the nature of chunky continuous covariational reasoning.

Figure 1. Example of Chunky Continuous Covariational Reasoning

Figure 1 illustrates that changes in one variable x by 1 will coordinately increase the value of y by 2 (the left table of figure 1), or change by a factor of 3 (the right table of figure1). Confrey and Smith (1994) concluded that students who built their reasoning coordinately, as illustrated in figure 1, can produce a functional relationship between the two co-varying quantities. However, this type of reasoning was not helpful for students when students asked to think about what happens in between the endpoint of the interval (Carlso-Garwall, 2012; Thompson & Carlson, 2017).

For example, in Carlso-Garwall’s (2012, p.12) study for the per-capital policy problem, when two students were asked “to graph the first two seconds of a bank account under the given policy, beginning with an investment of $500”, the two students’ produced two different solutions to the problem. One of the subjects (i.e., Tiffany) produced an incorrect solution when she was asked what happened between the intervals because of her “completed chunks” reasoning. For instance, Tiffany had an imagination that the second value of the variable should be higher than the first variable value, but she didn’t think the variable values can continuously vary within the interval, due to this reasoning she produced incorrect curve or graph (see figure 2). “How do we fill in what goes on in-between points” (Carlso-Garwall, 2012, p.12), is what the researcher asks in order understand her reasoning for a very small chuck size value, and Tiffany repeated her chunk continuous process on a small scale and she described a process of finding the next value by using the first value (i.e., for any 1s chunk size length if she asked what goes on in-between 1s size length and she will definitely produce another 0.5s chunk size length interval within 1s chunk size length interval).

Philosophy is a perspective about the world, the universe, and society. It works by posing fundamental inquiries about the idea of human idea, the nature of the universe, and the associations between them. The thoughts in reasoning are regularly broad and dynamic. However, this doesn’t imply that way of thinking isn’t about this present reality. Morals, for instance, gets some information about how to be great in our everyday lives. Mysticism gets some information about how the world functions and what it is made of. Reasoning is the investigation of people and the world by intuition and posing inquiries. It is a science and a craftsmanship. Theory attempts to address significant inquiries by concocting answers about genuine articles and asking ‘why?’

Here and there, reasoning attempts to respond to indistinguishable inquiries from religion and science. For instance in his work Kant posed after inquiries:

1. What would i be able to state?
2. What will I do?
3. What might I venture to trust?
4. What is man?

The responses to these inquiries give the various areas or classes of theory.

What is Theory?

Theory is the investigation of general and crucial issues, for example, those associated with presence, information, values, reason, psyche, and language. Reasoning is the objective endeavor to plan, comprehend, and answer basic inquiries.

As per well known scholar more than everything else, theory is thinking. The principle instrument that rationalists use in leading their examinations is the human personality. They don’t attempt to take care of philosophical issues by directing logical, exact research. They watch, think, comprehend, and attempt to address key inquiries intelligently. has very much stated, Reasoning is a thorough, trained and monitored examination of some most troublesome issues which man has ever confronted.

In his book’ Thales to Dewey’ composes, reasoning is thought to have really started under Socrates, an antiquated Greek thinker who is viewed as the most well known and significant rationalist ever. He built up the Socratic Strategy, a general method for taking a gander at philosophical issues dependent on definition, investigation, and combination.

Etymological

The inference of ‘reasoning’ from the Greek is proposed by the accompanying words and word-pieces.

Meanings Of theory

Characterizing reasoning is as troublesome as attempting to characterize love. The word theory isn’t a lot of assistance. Reasoning is a blend of two Greek words, philein sophia, which means admirer of knowledge. In antiquated occasions an admirer of insight could be identified with any zone where knowledge was communicated. This could be ready to go, legislative issues, human relations, or carpentry and different aptitudes. Theory had a ‘wholeness’ way to deal with life in ancient times. As opposed to this, some cutting edge definitions limit reasoning to what can be known by science or the investigation of language.

As indicated by various scholars

• Reasoning is the science and analysis of cognizance’
• Reasoning is the study of learning’ (Fichte).
• Reasoning is totally bound together information—the generalizations of theory grasping and solidifying the vastest speculations of science’ (Herbert Spencer).
• Theory is the unification of all information got by the exceptional sciences in a steady entire’ (Wundt).
• Theory goes for the information of the endless, of the fundamental idea of things’ (Plato).
• Reasoning isn’t a panacea for the issues of men, yet is what develops out of the techniques utilized by them to take care of their issues’ (John Dewey).
• Reasoning is an expanding exertion to find the general truth that lied behind the specific actualities to perceive and furthermore the truth that lies behind appearance’ (Raymont).

By taking a gander at these definitions we can say that there is, maybe, nobody single feeling of ‘reasoning.’ Inevitably numerous journalists desert the endeavor to characterize theory and, rather, go to the sorts of things savants do. Since the first significance of the word, theory, doesn’t give us much for explicit substance, we will go to spellbinding definitions. An expressive meaning of theory is that it tries to portray its capacities, objectives, and purposes behind presence.

What theory includes is depicted by the London Times in an article The incredible excellence of reasoning is that it instructs not what to think, however how to think. It is the investigation of significance, of the standards hidden lead, thought and learning. The aptitudes it sharpens are the capacity to examinations, to address orthodoxies and to express things plainly. The capacity to detail questions and pursue contentions is the pith of reasoning.

Nature Of Philosophy

Theory … has no other topic than the idea of this present reality, as that world lies around us in regular daily existence, and falsehoods open to onlookers on each side. Be that as it may, if this is all in all, it might be approached what capacity can stay for theory when each bit of the field is plundered out and encased by masters? Theory professes to be the study of the entire; be that as it may, in the event that we get the learning of the parts from the various sciences, what is there left for reasoning to let us know? To this it is adequate to answer commonly that the union of the parts is something more than that itemized information of the parts in division which is picked up by the man of science. It is with a definitive union that way of thinking concerns itself; it needs to demonstrate that the topic which we are for the most part managing in detail truly is an entire, comprising of explained individuals

• As an Action

Dr. Levision expresses that Way of thinking is the above all else an action of a particular kind and just optionally a topic comprising of an unequivocal collection of writing. In its genuine sense, theory is a psychological movement which includes the issues of human life, its tendency, and purposes.

• As a Lifestyle

The determination of the word expresses that way of thinking means love of knowledge. Insight is viewed as learning for the direct of life and reasoning is esteemed as a lifestyle. Huxely properly says, Man live as per their ways of thinking of life, their origination of the world. This is genuine even of the most neglectful.

• As a science

In the cutting-edge time frame, we regularly accept that we are living in the Time of science; it may be known as the period of request. Both way of thinking and science enquire with truth. As per John Brubacher , Theory is the study of sciences. It has been called mother of sciences in light of the fact that the autonomous controls of today were an essential piece of reasoning at one or his different occasions of past years.

Theory Endeavors to Build up a Thorough Origination or Anxiety of the World.

Theory looks to coordinate the learning of the sciences with that of different fields of concentrate to accomplish some sort of steady and intelligible world view. Savants would prefer not to bind their thoughtfulness regarding a piece of human experience or learning, yet rather, need to think about existence as a totality. In talking about this specific capacity, Charlie says:Its item is to assume control over the consequences of the different sciences, to add to them the aftereffects of the strict and moral encounters of humankind, and after that to think about the entirety. The expectation is that, by this implies, we might have the option to arrive at some broad resolutions with regards to the idea of the universe, and as to our position and prospects in it

Reasoning Examinations and Fundamentally Assesses Our Most Profoundly Held Convictions and Frames of mind (specifically, those which are regularly held uncritically).

Scholars have a frame of mind of basic and sensible keenness. They drive us to see the importance and outcomes of our convictions, and once in a while their irregularities. They examine the proof (or absence of it) for our most cherished convictions, and look to expel from our points of view each corrupt hint of obliviousness, bias, superstition, daze acknowledgment of thoughts, and some other type of silliness.

Reasoning Examines The Standards And Guidelines Of Language, And Endeavors To Explain The Significance Of Ambiguous Words And Ideas.

Reasoning inspects the job of language in correspondence and thought, and the issue of how to distinguish or guarantee the nearness of significance in our utilization of language. It is a technique training – which tries to uncover the issues and disarrays which have results from the abuse of language, and to explain the importance and utilization of dubious terms in logical as well as regular talk.

Fundamentally performs three sorts of capacities:-

• Standardizing

The word ‘Standardizing’ alludes to the ‘standards’ or ‘benchmarks’. So the regularizing elements of Theory means setting of standards, objectives, standards, guidelines, and so on. As educator V.R. Taneja composes When man is looked with the troubles, strains and stresses, conflicting circumstances, unexpected conditions and interesting issues, reasoning empowers him to consider the ‘masters’ and ‘cons’ and land at right arrangement.

• Theoretical

In this capacity, Reasoning strikes a union inside the variety of certainties and bits of information assembled from different sources. It drives the man from good judgment way to deal with discerning and point of view approach.

3. Basic

In this capacity, it arranges ideas, test speculation, builds up consistency, presents solidarity of viewpoint, and moves consistent thinking. A basic capacity assesses the marvel or procedure and contrasts it and the way of thinking’s sentiment, that is, as the name infers – condemns, reaches inferences and gives a resolution. The master assessment of theory is more extensive than in different sciences and is guided by different criteria, which for some different controls don’t bode well.

Significance

As per Barron.

• The investigation of Theory empowers us to contemplate significant issues.
• In contemplating Theory, we figure out how to make a stride once again from our regular deduction and to investigate the more profound, greater inquiry which supports our idea.
• The center in the investigation of Reasoning is to realize not what to accept, yet how to think.
• Studying theory hones your systematic capacities, empowering you to recognize and assess the qualities and shortcomings in any position.
• It empowers you to build and lucid contentions.
• It prompts you to work crosswise over disciplinary limits and to ponder issues
• It empowers to think consistently and discover the purposes for anything.
• It educates to research before thinking anything.
• People can explain what they accept and why they accept.

Reasoning has had tremendous on our regular daily existences. The very language we talk utilizes groupings got from reasoning. For instance, the characterizations of thing and action word include the thoughtful thought that there is a distinction among things and activities. On the off chance that we ask what the thing that matters is, we are beginning a scholarly request).

Each organization of society depends on logical thoughts, regardless of whether that establishment is the law, government, religion, the family, marriage, industry, business or instruction. Thoughtful contrasts have prompted the topple of governments, extraordinary changes in laws and the change of whole financial frameworks. Such changes have happened in light of the fact that the individuals included held certain convictions about what is significant, genuine, genuine, and noteworthy and about how life ought to be requested.

Epistemology

1. The philosophical investigation of the idea of information and how it identifies with so much ideas as truth, conviction, and defense,
2. Different issues of wariness,
3. The sources and extent of learning and legitimized conviction
4. The criteria for learning and legitimization.

It thought about the hypothesis of learning, particularly as to its techniques, legitimacy, and scope, and the differentiation between legitimized conviction and sentiment. Epistemology is characterized as the investigation of the nature and extent of information and supported conviction. It investigates how the idea of information identifies with comparable thoughts, for example, truth, conviction and avocation. It additionally manages the methods for generation of information, just as doubt about various learning claims. It is basically about issues having to do with the creation and dispersal of learning specifically regions of request. Epistemology is considered by certain specialists as one of the ‘center regions’ of theory. It is worried about the nature, sources and points of confinement of information.

Metaphysics

it is characterized as the investigation of the most broad highlights of the real world, for example, presence, time, the connection among psyche and body, objects and their properties, wholes and their parts, occasions, procedures, and causation. It is communicated as the investigation of the idea of the real world, of what exists on the planet, what it resembles, and how it is requested. It is the investigation of ‘reality’ that is past the logical or scientific domains. The expression ‘power’ itself actually signifies ‘past the physical.’ It is the investigation of presence and the idea of presence. It is investigation of what exists and the structure inside which the items that make up the world work. This incorporated the ideas of being, presence, everlasting status, God, profound creatures, time, personality, cognizance, cause, substance, space, steadiness and so forth., by and large way. It is the investigation of nature of an individual, which means of truth, presence of God, presence of psyche, the response of brain and body, impact of one occasion to other. It talks about the presence of God, the spirit, and existence in the wake of death. It assesses the importance of time, nature of the real world. It is the investigation of the world completely, and the investigation of being.

Logic:

It is characterized as the examination of terms, suggestions, and the standards of thinking. It is the standards (both formal and casual) of explanation. It is investigation of ‘conceptual representative thinking.’ It is the investigation of ‘right thinking.’ It is the device scholars use to contemplate other philosophical classifications. Great rationale incorporates the utilization of good reasoning aptitudes and the shirking of rationale false notions. It is the investigation of the nature and structure of contentions.

Rationale is the precise investigation of the principles for the right utilization of these supporting reasons, rules we can use to recognize great contentions from terrible ones. The vast majority of the extraordinary scholars from Aristotle to the present have been persuaded that rationale pervades every other part of theory. The capacity to test contentions for coherent consistency, comprehend the intelligent outcomes of specific suspicions, and recognize the sort of proof a scholar is utilizing are fundamental for ‘doing’ theory.

Significance of Contemplating Rationale/Thinking

• Reasoning makes us progressively reasonable
• When we reason well we are probably going to land at a legitimate truth.
• By getting to truth, we procure learning. – Thinking great causes us in the obtaining of information.
• Reasoning causes us to maintain a strategic distance from dubiousness and uncertainty.
• Logic empowers us to be exact in our appearances and interchanges and that spares time. Thinking great causes us to stay away from superfluous clashes.
• Reasoning causes us to convey consistently.

Axiology

Definition:

Axiology is the investigation of ‘Qualities’, axiology looks to comprehend the idea of qualities and worth judgment. It is likewise called hypothesis of significant worth. The term was presented toward the start of the twentieth century when it turned into a perceived piece of theory. As an order unmistakable from science, axiology was now and again even compared with the entire of reasoning, particularly in Germany.

Morals

It thought about the examination of the idea of profound quality and ethics. It is the investigation of right activity. It manages the topic of how individuals should act with respect to themselves, other individuals, and the world, qualities, and basic leadership process. It is the investigation of activity, investigation of ‘virtue,’ ‘good and bad.’ It associated with putting an incentive to individual activities, choices, and relations. The investigation of morals frequently concerns what we should do and what it is ideal to do. In battling with this issue, bigger inquiries regarding what is great and right emerge. Morals or ‘good way of thinking,’ is characterized as the part of axiology that reviews great and terrible, good and bad. The essential examination of morals or ethical quality is given as the most ideal approach to live. Morals or good way of thinking is communicated as the part of theory that includes systematizing, shielding, and prescribing ideas of good and bad direct.

Esthetics

Feel is a part of theory that manages the idea of workmanship, magnificence and taste, with the creation or valuation for excellence, with hypotheses and originations of excellence or craftsmanship and with tastes for and ways to deal with what is satisfying to the faculties and particularly locate.

Style considers how craftsmen envision, make and perform masterpieces; how individuals use, appreciate, and scrutinize craftsmanship; and what occurs in their psyches when they see depictions, tune in to music, or read verse, and comprehend what they see and hear. It likewise examines how they feel about craftsmanship, why

They like a few works and not others, and how craftsmanship can influence their states of mind, convictions, and frame of mind toward life.

All the more extensively, researchers in the field characterize feel as ‘basic reflection on craftsmanship, culture and nature’. In present day English, the term tasteful can likewise allude to a lot of standards fundamental crafted by a specific craftsmanship development or hypothesis

Conclusion

Albeit numerous individuals are unconvinced that that way of thinking is significant, I think there are valid justifications to think it is significant. Theory can help improve basic reasoning abilities, however it can help furnish us with learning of rationale that can significantly help improve basic reasoning. By contemplating theory, individuals can explain what they accept and they can be animated to consider extreme inquiries. Theory can make an individual full man-refined, refined and balanced. It gives him the capacity to blend, scrutinize, systematize and assess an assortment and enormous mass of learning. So Theory and investigation of reasoning is similarly significant like some other order.

In addition to conditional reasoning, the other key type of deductive reasoning is syllogistic reasoning, which is based on the use of syllogisms. Syllogisms are deductive arguments that involve drawing conclusions from two premises (Maxwell, 2005; Rips, 1994, 1999). All syllogisms comprise a major premise, a minor premise, and a conclusion.

Categorical syllogism comprise of two premises and a conclusion. the premises state something about the category memberships of the terms. In fact, each term represents all, none, or some of the members of a particular class or category.

As with other syllogisms, each premise contains two terms. One of them must be the middle term, common to both premises. The first and the second terms in each premise are linked through the categorical membership of the terms. That is, one term is a member of the class indicated by the other term. However the premises are worded, they state that some (or all or none) of the members of the category of the first term are (or are not) members of the category of the second term. To determine whether the conclusion follows logically from the premises, the reasoner must determine the category memberships of the terms.

• For example, All cognitive psychologists are pianists.
• All pianists are athletes.
• Therefore, all cognitive psychologists are athletes.

Logicians often use circle diagrams to illustrate class membership. The conclusion for this syllogism does in fact follow logically from the premises. This is shown in the circle diagram in this figure by Strenberg & Strenberg (2011):

However, the conclusion is false because the premises are false. For the preceding categorical syllogism, the subject is cognitive psychologists, the middle term is pianists, and the predicate is athletes. In both premises, we asserted that all members of the category of the first term were members of the category of the second term.

There are four kinds of premises (See also in the table below by Sternberg & Sternberg,2011)

1. Statements of the form “All A are B” sometimes are referred to as universal affirmatives, because they make a affirmative statement about all members of a class (universal).
2. Universal negative statements make a negative statement about all members of a class (e.g., “No cognitive psychologists are flutists.”).
3. Particular affirmative statements make a positive statement about some members of a class (e.g., “Some cognitive psychologists are left-handed.”).
4. Particular negative statements make a negative statement about some members of a class (e.g., “Some cognitive psychologists are not physicists.”).

In categorical syllogisms, in particular, we cannot draw logically valid conclusions from categorical syllogisms with two particular premises or with two negative premises.

• For example, Some cognitive psychologists are left-handed.
• Some left-handed people are smart.

Based on these premises, one cannot conclude even that some cognitive psychologists are smart. The left-handed people who are smart might not be the same left-handed people who are cognitive psychologists. We just don’t know. Consider a negative example:

• No students are stupid.
• No stupid people eat pizza.

We cannot conclude anything one way or the other about whether students eat pizza based on these two negative premises. As you may have guessed, people appear to have more difficulty (work more slowly and make more errors) when trying to deduce conclusions based on one or more particular premises or negative premises (Strenberg & Strenberg, 2011).

How do people solve syllogisms? Many theories have been proposed as to how people solve categorical syllogisms. One of the earliest theories was the atmosphere bias (Begg & Denny, 1969; Woodworth & Sells, 1935). There are two basic ideas of this theory:

1. If there is at least one negative in the premises, people will prefer a negative solution.
2. If there is at least one particular in the premises, people will prefer a particular solution. For example, if one of the premises is “No pilots are children,” people will prefer a solution that has the word no in it.

Other researchers focused attention on the conversion of premises (Chapman & Chapman, 1959). Here, the terms of a given premise are reversed. People sometimes believe that the reversed form of the premise is just as valid as the original form. The idea is that people tend to convert statements like “If A, then B” into “If B, then A.” They do not realize that the statements are not equivalent. These errors are made by children and adults alike (Markovits, 2004).

A more widely accepted theory is based on the notion that people solve syllogisms by using a semantic (meaning-based) process based on mental models (Ball & Quayle, 2009; Espino et al., 2005; Johnson-Laird & Savary, 1999; Johnson-Laird & Steedman, 1978). This view of reasoning as involving semantic processes based on mental models may be contrasted with rule-based (“syntactic”) processes, such as those characterized by formal logic (Strenberg & Strenberg, 2011).

A mental model is an internal representation of information that corresponds analogously with whatever is being represented (see Johnson-Laird, 1983). Some mental models are more likely to lead to a deductively valid conclusion than are others. In particular, some mental models may not be effective in disconfirming an invalid conclusion (Strenberg & Strenberg, 2011).

For example, in the Johnson-Laird study, participants were asked to describe their conclusions and their mental models for the syllogism, “All of the artists are beekeepers. Some of the beekeepers are clever. Are all artists clever?”

One participant said, “I thought of all the little . . . artists in the room and imagined they all had beekeeper’s hats on” (Johnson-Laird & Steedman, 1978, p. 77). The figure below by Strenberg & Strenberg (2011), shows two different mental models for this syllogism.

As the figure shows, the choice of a mental model may affect the reasoner’s ability to reach a valid deductive conclusion. Because some models are better than others for solving some syllogisms, a person is more likely to reach a deductively valid conclusion by using more than one mental model (Strenberg & Strenberg, 2011).

In the figure, the mental model shown in (a) may lead to the deductively invalid conclusion that some artists are clever.

By observing the alternative model in (b), we can see an alternative view of the syllogism. It shows that the conclusion that some artists are clever may not be deduced on the basis of this information alone. Specifically, perhaps the beekeepers who are clever are not the same as the beekeepers who are artists.

The difficulty of many problems of deductive reasoning relates to the number of mental models needed for adequately representing the premises of the deductive argument (Johnson-Laird, Byrne, & Schaeken, 1992). Arguments that entail only one mental model may be solved quickly and accurately.

However, to infer accurate conclusions based on arguments that may be represented by multiple alternative models is much harder (Strenberg & Strenberg, 2011). Such inferences place great demands on working memory (Gilhooly, 2004).

In these cases, the individual must simultaneously hold in working memory each of the various models (Strenberg & Strenberg, 2011). Only in this way can he or she reach or evaluate a conclusion. Thus, limitations of working-memory capacity may underlie at least some of the errors observed in human deductive reasoning (Johnson-Laird, Byrne, & Schaeken, 1992).

In two experiments, the role of working memory was studied in syllogistic reasoning (Gilhooly et al., 1993). In the first, syllogisms were simply presented either orally or visually. Oral presentation used a higher load on working memory because participants had to remember the premises. In the visual presentation condition, participants could just only look at the premises. As predicted, performance was lower in the oral-presentation condition. In a second experiment, participants needed to solve syllogisms while at the same time performing another task. Either the task drew on working-memory resources or it did not. The researchers found that the task that drew on working-memory resources interfere with syllogistic reasoning.

Other factors also may contribute to the ease of forming appropriate mental models. People seem to solve logical problems more accurately and more easily when the terms have high imagery value (Clement & Falmagne, 1986).

Aids and Obstacles to Deductive Reasoning

In deductive reasoning, as in many other cognitive processes, we engage in many heuristic shortcuts. These shortcuts sometimes lead to inaccurate conclusions. In addition to these shortcuts, we often are influenced by biases that distort the outcomes of our reasoning (Strenberg & Strenberg, 2011).

Heuristics in Deductive Reasoning

Heuristics in syllogistic reasoning include overextension errors. In these errors, we overextend the use of strategies that work in some syllogisms to syllogisms in which the strategies fail us (Strenberg & Strenberg, 2011).

For example, although reversals work well with universal negatives, they do not work with other kinds of premises. We also experience foreclosure effects when we fail to consider all the possibilities before reaching a conclusion. In addition, premise-phrasing effects may influence our deductive reasoning (Strenberg & Strenberg, 2011). For example, the sequence of terms or the use of particular qualifiers or negative phrasing. Premise-phrasing effects may lead us to leap to a conclusion without adequately reflecting on the deductive validity of the syllogism.

Biases in Deductive Reasoning

Biases that affect deductive reasoning generally relate to the content of the premises and the believability of the conclusion. They also reflect the tendency toward confirmation bias. In confirmation bias, we seek confirmation rather than disconfirmation of what we already believe. Suppose the content of the premises and a conclusion seem to be true. In such cases, reasoners tend to believe in the validity of the conclusion, even when the logic is flawed (Evans, Barston, & Pollard, 1983).

Confirmation bias can be detrimental and even dangerous in some circumstances (Strenberg & Strenberg, 2011). For instance, in an emergency room, if a doctor assumes that a patient has condition X, the doctor may interpret the set of symptoms as supporting the diagnosis without fully considering all alternative interpretations (Pines, 2005). This shortcut can result in inappropriate diagnosis and treatment, which can be extremely dangerous.

Other circumstances where the effects of confirmation bias can be observed are in police investigations, paranormal beliefs, and stereotyping behaviour (Ask & Granhag, 2005; Biernat & Ma, 2005; Lawrence & Peters, 2004). To a lesser extent, people also show the opposite tendency to disconfirm the validity of the conclusion when the conclusion or the content of the premises contradicts the reasoner’s existing beliefs (Evans, Barston, & Pollard, 1983; Janis & Frick, 1943).

Enhancing Deductive Reasoning

To enhance our deductive reasoning, we may try to avoid heuristics and biases that distort our reasoning (Strenberg & Strenberg, 2011). We also may engage in practices that facilitate reasoning.

For example, we may take longer to reach or to evaluate conclusions. Effective reasoners also consider more alternative conclusions than do poor reasoners (Galotti, Baron, & Sabini, 1986). In addition, training and practice seem to increase performance on reasoning tasks. The benefits of training tend to be strong when the training relates to pragmatic reasoning schemas (Cheng et al., 1986) or to such fields as law and medicine (Lehman, Lempert, & Nisbett, 1987). The benefits are weaker for abstract logical problems divorced from our everyday life (see Holland et al., 1986; Holyoak & Nisbett, 1988).

One factor that affects syllogistic reasoning is mood or emotions. When people are in a sad mood, they tend to pay more attention to details (Schwarz & Skurnik, 2003). People tend to do better in syllogistic reasoning tasks when they are in a sad mood than when they are in a happy mood (Fiedler, 1988; Melton, 1995). People in a neutral mood tend to show performance in between the two extremes.

Improving your deductive reasoning skills

From: Cognitive Psychology 6th Edition by Sternberg & Sternberg, 2011

Even without training, you can improve your own deductive reasoning through developing strategies to avoid making errors. For example, an unscrupulous politician might state, “We know that some suspicious-looking people are illegal aliens. We also know that some illegal aliens are terrorists. Therefore, we can be sure that some of those people whom we think are suspicious are terrorists, and that they are out to destroy our country!” The politician’s syllogistic reasoning is wrong. If some A are B and some B are C, it is not necessarily the case that any A are C. This is obvious when you realize that some men are happy people and some happy people are women, but this does not imply that some men are women.

Make sure you are using the proper strategies in solving syllogisms. Remember that reversals only work with universal negatives. Sometimes translating abstract terms to concrete ones (e.g., the letter C to cows) can help. Also, take the time to consider contrary examples and create more mental models. The more mental models you use for a given set of premises, the more confident you can be that if your conclusion is not valid, it will be disconfirmed. Thus, the use of multiple mental models increases the likelihood of avoiding errors.

The use of multiple mental models also helps you to avoid the tendency to engage in confirmation bias. Circle diagrams also can be helpful in solving deductive-reasoning problems.

The reasoning is the process where the information is given and is compared with the known information or knowledge and come up with a reasoned conclusion. Reasoning skills can help in decision making, distinguishing situations and problems solving. To have agents involved in reasoning, they have to equipped with higher-level cognitive functions. For examples, beliefs and goals, actions, perception, plan coordination, the mental states of other agents and collaborative task execution.

The belief-desire-intention (BDI) model is an approach that contains various types of mental attributes and relationships. BDI model is a philosophical theory of the practical reasoning that is basically proposed by Bratman. This model consists of two steps: deliberation and means-ends reasoning (BDI4JADE, n.d.). Deliberation means that a set of desires is chosen and then to be carried out according to the current condition of the agent’s beliefs. The output of deliberation is intentions. Means-ends reasoning is the step that how the earlier step to be determined and can be accomplished according to the agent’s available choices and thus results in the specific goals.

BDI4JADE (n.d.) states that the BDI model has three parts of mental attitudes: beliefs, desires, and intentions. Beliefs means the information about the world or the knowledge of the world. After the perception of every operation and the execution of intentions, the environment characteristics are updated subsequently. Beliefs can be represented as the informative unit of the system. Desires represent the objectives to be accomplished also known as goals. They correspond to the tasks assigned to the agent. Desires is responsible to accomplish a belief, and to test a condition, and expressed a situation formula. The data of the goals to be accomplished is stored in this part. The motivational state of the system can also be represented in this stage. Intentions mean that the current processing plan is chosen to achieve the desire of the agent. The deliberation step is done in this stage as intentions are the output of deliberation.

According to BDI4JADE (n.d.), there are seven main components in a BDI agent:

• Beliefs. It is a set of current beliefs that contain the information of current environment that is possessed by the agent.
• Belief revision function. This function establishes a new set of beliefs based on the perceptual input and the current belief.
• Option generation function. This function helps to decide the desires based on the current beliefs that contain the current environment and current intentions.
• Desires. It is a set of current desires which represent the agent’s available actions that are based on the possible courses.
• Filter function. Based on the current beliefs, desires, and intentions, this function helps in deciding the intentions of the agent.
• Intentions. It is a set of current intentions. It contains the current focus which is ready to be tried to carry out.
• Action selection function. This function references the current intentions so that to help deciding performable action.

BDI agents can also be used to solve problems with partial information in a complex and dynamic environment. For example: The OASIS (Optimal Aircraft Sequencing using Intelligent Scheduling) air-traffic management system (Innocentini, 2017).

According to Innocentini (2017), The OASIS is tested successfully at Sydney Airport in 1995. It is implemented using PRS (Procedural Reasoning Systems). It uses multiple agents. Each agent tracks the sub-problems and communicates between each other by using asynchronous messages. The list of agents is: SEQUENCER Agent, AIRCRAFT Agent, and WIND MODEL Agent. The possible BDI example int this scenario: 1) belief (the position of the plane); 2) desire (decrease the speed of aircraft); 3) intention (adopted plan). If there are changes in the environment, the intentions are reassessed.