From Logic Programming to Human Reasoning:: How to be Artificially Human

Results of psychological experiments have shown that humans make assumptions, which are not necessarily valid, that they are influenced by their background knowledge and that they reason non-monotonically. These observations show that classical logic does not seem to be adequate for modeling human reasoning. Instead of assuming that humans do not reason logically at all, we take the view that humans do not reason classical logically. Our goal is to model episodes of human reasoning and for this purpose we investigate the so-called Weak Completion Semantics. The Weak Completion Semantics is a Logic Programming approach and considers the least model of the weak completion of logic programs under the three-valued Łukasiewicz logic. As the Weak Completion Semantics is relatively new and has not yet been extensively investigated, we first motivate why this approach is interesting for modeling human reasoning. After that, we show the formal correspondence to the already established Stable Model Semantics and Well-founded Semantics. Next, we present an extension with an additional context operator, that allows us to express negation as failure. Finally, we propose a contextual abductive reasoning approach, in which the context of observations is relevant. Some properties do not hold anymore under this extension. Besides discussing the well-known psychological experiments Byrne’s suppression task and Wason’s selection task, we investigate an experiment in spatial reasoning, an experiment in syllogistic reasoning and an experiment that examines the belief-bias effect. We show that the results of these experiments can be adequately modeled under the Weak Completion Semantics. A result which stands out here, is the outcome of modeling the syllogistic reasoning experiment, as we have a higher prediction match with the participants’ answers than any of twelve current cognitive theories. We present an abstract evaluation system for conditionals and discuss well-known examples from the literature. We show that in this system, conditionals can be evaluated in various ways and we put up the hypothesis that humans use a particular evaluation strategy, namely that they prefer abduction to revision. We also discuss how relevance plays a role in the evaluation process of conditionals. For this purpose we propose a semantic definition of relevance and justify why this is preferable to a exclusively syntactic definition. Finally, we show that our system is more general than another system, which has recently been presented in the literature. Altogether, this thesis shows one possible path on bridging the gap between Cognitive Science and Computational Logic. We investigated findings from psychological experiments and modeled their results within one formal approach, the Weak Completion Semantics. Furthermore, we proposed a general evaluation system for conditionals, for which we suggest a specific evaluation strategy. Yet, the outcome cannot be seen as the ultimate solution but delivers a starting point for new open questions in both areas

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

Human reasoning and cognitive science

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain

The Resemblance Structure of Natural Kinds: A Formal Model for Resemblance Nominalism

278 p.The aim of this thesis is to better understand the ways natural kinds are related to each other by species-genus relations and the ways in which the members of the kind are related to each other by resemblance relations, by making use of formal models of kinds. This is done by first analysing a Minimal Conception of Natural Kinds and then reconstructing it from the ontological assumptions of Resemblance Nominalism. The questions addressed are:(1) What is the external structure of kinds' In what ways are kinds related to each other by species-genus relations'(2) What is the internal structure of kinds' In what sense are the instances of a kind similar enough to each other'According to the Minimal Conception of Kinds, kinds have two components, a set of members of the kind (the extension) and a set of natural attributes common to these objects (the intension). Several interesting features of this conception are discussed by making use of the mathematical theory of concept lattices. First, such structures provide a model for contemporary formulations of syllogistic logic. Second, kinds are ordered forming a complete lattice that follows Kant's law of the duality between extension and intension, according to which the extension of a kind is inversely related to its intension. Finally, kinds are shown to have Aristotelian definitions in terms of genera and specific differences. Overall this results in a description of the specificity relations of kinds as an algebraic calculus.According to Resemblance Nominalism, attributes or properties are classes of similar objects. Such an approach faces Goodman's companionship and imperfect community problems. In order to deal with these, a specific nominalism, namely Aristocratic Resemblance Nominalism, is chosen. According to it, attributes are classes of objects resembling a given paradigm. A model for it is introduced by making use of the mathematical theory of similarity structures and of some results on the topic of quasianalysis. Two other models (the polar model and an order-theoretic model) are considered and shown to be equivalent to the previous one.The main result is that the class of lattices of kinds that a nominalist can recover uniquely by starting from these assumptions is that of complete coatomistic lattices. Several other related results are obtained, including a generalization of the similarity model that allows for paradigms with several properties and properties with several paradigms. The conclusion is that, under nominalist assumptions, the internal structure of kinds is fixed by paradigmatic objects and the external structure of kinds is that of a coatomistic lattice that satisfies the Minimal Conception of Kinds

Metalogic and the psychology of reasoning.

The central topic of the thesis is the relationship between logic and the cognitive psychology of reasoning. This topic is treated in large part through a detailed examination of the recent work of P. N. Johnson-Laird, who has elaborated a widely-read and influential theory in the field. The thesis is divided into two parts, of which the first is a more general and philosophical coverage of some of the most central issues to be faced in relating psychology to logic, while the second draws upon this as introductory material for a critique of Johnson-Laird's `Mental Model' theory, particularly as it applies to syllogistic reasoning. An approach similar to Johnson-Laird's is taken to cognitive psychology, which centrally involves the notion of computation. On this view, a cognitive model presupposes an algorithm which can be seen as specifying the behaviour of a system in ideal conditions. Such behaviour is closely related to the notion of `competence' in reasoning, and this in turn is often described in terms of logic. Insofar as a logic is taken to specify the competence of reasoners in some domain, it forms a set of conditions on the 'input-output' behaviour of the system, to be accounted for by the algorithm. Cognitive models, however, must also be subjected to empirical test, and indeed are commonly built in a highly empirical manner. A strain can therefore develop between the empirical and the logical pressures on a theory of reasoning. Cognitive theories thus become entangled in a web of recently much-discussed issues concerning the rationality of human reasoners and the justification of a logic as a normative system. There has been an increased interest in the view that logic is subject to revision and development, in which there is a recognised place for the influence of psychological investigation. It is held, in this thesis, that logic and psychology are revealed by these considerations to be interdetermining in interesting ways, under the general a priori requirement that people are in an important and particular sense rational. Johnson-Laird's theory is a paradigm case of the sort of cognitive theory dealt with here. It is especially significant in view of the strong claims he makes about its relation to logic, and the role the latter plays in its justification and in its interpretation. The theory is claimed to be revealing about fundamental issues in semantics, and the nature of rationality. These claims are examined in detail, and several crucial ones refuted. Johnson- Laird's models are found to be wanting in the level of empirical support provided, and in their ability to found the considerable structure of explanation they are required to bear. They fail, most importantly, to be distinguishable from certain other kinds of models, at a level of theory where the putative differences are critical. The conclusion to be drawn is that the difficulties in this field are not yet properly appreciated. Psychological explantion requires a complexity which is hard to reconcile with the clarity and simplicity required for logical insights

Information enforcement in learning with graphics : improving syllogistic reasoning skills

This thesis is an investigation into the factors that contribute to good choices among graphical systems used in teaching, and the feasibility of implementing teaching software that uses this knowledge.The thesis describes a mathematical metric derived from a cognitive theory of human diagram processing. The theory characterises differences among representations by their ability to express information. The theory provides the factors and relationships needed to build the metric. It says that good representations are easily processed because they are more vivid, more tractable and less expressive, than poor representations.The metric is applied to abstract systems for teaching and learning syllogistic reasoning, TARSKI'S WORLD, EULER CIRCLES, VENN DIAGRAMS and CARROLL'S GAME OF LOGIC. A rank ordering reflects the value of each system predicted by the theory and the metric. The theory, the metric and the systems are then tested in empirical studies. Five studies involving sixty-eight learners, examined the benefit of software based on these abstract systems.Studies showed the theory correctly predicted learners' success with the circle systems and poorer performance with TARSKI'S WORLD. The metric showed small but clear differences in expressivity between the circle systems. Differences between results of the learners using the circle systems contradicted the predictions of the metric.Learners with mathematical training were better equipped and more successful at learning syllogistic reasoning with the systems. Performance of learners without mathematical training declined after using the software systems. Diagrams drawn by learners together with video footage collected during problem solving, led to a catalogue of errors, misconceptions and some helpful strategies for learning from graphical systems.A cognitive style test investigated the poor performance of non-mathematically trained learners. Learners with mathematics training showed serialist and versatile learning styles while learners without this training showed a holist learning style. This is consistent with the hypothesis that non-mathematically trained learners emphasise the use of semantic cues during learning and problem solving.A card-sorting task investigated learners' preferences for parts of the graphical lexicon used in the diagram systems. Preferences for the EULER lexicon increased difficulty in explaining the system's poor results in earlier studies. Video footage of learners using the systems in the final study illustrated useful learning strategies and improved performance with EULER while individual instruction was available.Further work describes a preliminary design for an adaptive syllogism tutor and other related work

Essence and Necessity, and the Aristotelian Modal Syllogistic: A Historical and Analytical Study

The following is a critical and historical account of Aristotelian Essentialism informed by recent work on Aristotle’s modal syllogistic. The semantics of the modal syllogistic are interpreted in a way that is motivated by Aristotle, and also make his validity claims in the Prior Analytics consistent to a higher degree than previously developed interpretative models. In Chapter One, ancient and contemporary objections to the Aristotelian modal syllogistic are discussed. A resolution to apparent inconsistencies in Aristotle’s modal syllogistic is proposed and developed out of recent work by Patterson, Rini, and Malink. In particular, I argue that the semantics of negation is distinct in modal context from those of assertoric negative claims. Given my interpretive model of Aristotle’s semantics, in Chapter Two, I provide proofs for each of the mixed apodictic syllogisms, and propose a method of using Venn Diagrams to visualize the validity claims Aristotle makes in the Prior Analytics. Chapter Three explores how Aristotle’s syllogistic fits within Aristotle’s philosophy of science and demonstration, particularly within the context of the Posterior Analytics. Consideration is given to the Aristotelian understanding of the relationship among necessity, explanation, definition, and essence. Chapter Four applies Aristotelian modal logic in contemporary contexts. I contrast Aristotelian modality and essentialism with contemporary modalism based upon the semantics of possible worlds, e.g. Kripke and Putnam. I also develop an account of how Aristotelian modal logic can ground a sortal dependent theory of identity, as discussed by Wiggins

Logic and implementation in human reasoning: the psychology of syllogisms

This thesis presents a novel account of syllogistic reasoning, based on data from a non-standard reasoning task called the Individuals Task. An abstract logical treatment of the system, based on a modalised Euler Circles system (Stenning & Oberlander 1994, 1995) is presented, and it is shown that this can be implemented in a diverse range of notationally distinct ways. The Individual Identification Algorithm, as this method is called, makes use of a logical distinction between the premisses of the syllogism; one has an existential, assertive role, and is called the source premiss, whereas the function of the other is to license inference, and so it is called the conditional premiss. This distinction is central to the way the IIA employs modal information to make the use of Euler Circles tractable.The empirical parts of the thesis are concerned with relating the distinction between source and conditional premisses to the Figural Effect (Johnson-Laird & Steedman 1978). It is argued that the Figural Effect is reducible to a tendency for the terms from the source premiss to occur before the terms from the conditional premiss in Individual Conclusions. Since these are comprised of all three terms in the syllogism, it is possible to test new hypotheses concerning the role of the middle term in inference, and the results are shown to be incompatible with all existing theories of the Figural Effect.Since the Individuals Task is non-standard, it is necessary to compare perfor¬ mance profiles on this task with those on the Standard Task; one result of this comparison is that a primary cause of error in the Standard Task is selection of an appropriate quantifier for the conclusion, a result which concurs with the con¬ clusions of Ford (1994) and Wetherick & Gilhooly (1990), but contradicts those of Mental Models theory (Johnson-Laird 1983).Certain anomalies in the prediction of term order by the source/conditional distinction lead to the postulation of a second process for conclusion generation, called Minimal Linking. This logically unsound strategy has effects similar to the illicit conversion of A premisses (Chapman &; Chapman 1959, Revlis 1975)