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Keith Stenning

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A first degree in Philosophy and Psychology started a career in understanding what logic could contribute to the psychology of reasoning---a colleague redescribed this as banging one's head on a brick wall. Nevertheless a new generation brings hope.

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Matthew J. Brown

Southern Illinois University

University of Nottingham

EHESS-Ecole des hautes études en sciences sociales

University of Vienna

Paul Hoyningen-Huene

Leibniz Universität Hannover

University of Regensburg

Theodore Arabatzis

National & Kapodistrian University of Athens

Massachusetts Institute of Technology (MIT)

Universidade Federal do Rio Grande do Sul

Roberto Horácio Sá Pereira

Universidade Federal do Rio de Janeiro (UFRJ)

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Papers by Keith Stenning

Swallowing squiggles—the internalization of formalisms

Oxford University Press eBooks, Aug 22, 2002

How did we get here?

Multiple logics within argument: how defeasible and classical reasoning work together

Computational Models of Argument, 2012

Exploring quantifier reasoning and autistic-like traits

Logic, Language, and Computation

Lecture Notes in Computer Science, 2011

SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the tra... more SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing so demonstrates the underlying unity and applicability of logic.

Heterogeneous reasoning in learning to model

Proceedings of the Annual Meeting of the Cognitive Science Society, 2000

Conceptual learning in maths and science involves learning to coordinate multiple representation ... more Conceptual learning in maths and science involves learning to coordinate multiple representation systems into smoothly functioning heterogeneous reasoning systems composed of sub-languages, graphics, mathematical representations, etc.. In these heterogeneous systems information can be transformed from one representation to another by inference rules, and learning coordination is learning how and when to apply these rules. Heterogeneous reasoning has a particularly important role to play in teaching students how to apply formalisms to real world problems, rather than merely teaching formalisminternal calculation. This paper analyses three learning incidents which happened in groups of students engaged in learning the mathematics and biology involved in modelling biological populations, from the perspective of the heterogeneous reasoning involved. Greeno, Sommerfeld & Weibe (2000) and Hall (2000) analyse incidents from the same curriculum intervention from other points of view, in this volume. We observe both learning successes and failures that cannot be understood without understanding the seams joining the representation systems involved, and the inference rules and operations required to get from one to another. One conclusion is that even apparently homogeneous natural language has to be seen as heterogeneous in its fully contextualised application.

Strategies and Knowledge Representation

Cambridge University Press eBooks, Nov 3, 2003

Logic, Language and Computation

Proceedings of the 18th Annual Conference of the Cognitive Science Society

We have been studying how students respond to multimodal logic teaching with Hyperproof. Performa... more We have been studying how students respond to multimodal logic teaching with Hyperproof. Performance measures have already indicated that students' pre-existing cognitive styles have a significant impact on teaching outcome. Furthermore, a substantial corpus of proofs has been gathered via automatic logging of proof development. We report results from analyses of final proof structure, exploiting (i) 'proofograms', a novel method of proof visualisation, and (ii) corpus-linguistic bigram analysis of rule use. Results suggest that students' cognitive styles do indeed influence the structure of their logical discourse, and that the effect may be attributable to the relative skill with which students manipulate graphical abstractions.

Spatial Inclusion and Analogy for Set Membership: A Case Study of Analogy at Work

The analogy between spatial inclusion and set membership o ers the opportunity t o go beyond the ... more The analogy between spatial inclusion and set membership o ers the opportunity t o go beyond the study of how w e establish analogical mappings to the investigation of the impact of those mappings on mental process. This analogy is the basis of longstanding didactic techniques for teaching elementary logic (Euler's Circles and Venn Diagrams) and therefore bears on psychological theories of human deductive reasoning (e.g. Erickson 1974). An adequate cognitive theory of analogy must explain how m e n tal processing is aided by analogical mappings. In the case of spatial inclusion as an analogy for set membership this comes down to requiring a theory of how graphical representations aid processing. Here we s k etch a general theory in terms of the speci city of graphics which w e h a ve developed further elsewhere (see Stenning & Oberlander 1991a, 1991b). This general approach to graphical representations rests on the observation that graphical representation systems limit abstraction and thereby p u r c hase computational tractability. In applying this general theory to the case of graphical methods of syllogism solution we s k etch a method of using Euler's Circles and show h o w i n terpretative c o n ventions for graphical objects allow the necessary abstractions. In particular we s h o w that even choosing the least expressive system of diagrams limited to circles, still gives the requisite expressive p o wer. The Euler's Circle method sketched is then used as a guide to connectionist implementation of corresponding internal representations. Graphical representations share some general computationalproperties with connectionist systems. In the domain of the syllogism, the central issue is the implementation of the binding of attributes into type-descriptions. Various proposals for connectionist variable binding in the literature are assessed as partial implementations. Some proposals are made for implementation of novel graphical features of the Euler's Circle algorithm. This case study of an analogy suggests the hypothesis that one important r o l e t h a t analogy may p l a y i s p r o viding a representation which is more limited in expressive p o wer and therefore more computationally tractable than the literal representations analogies supplant.

AAAI Spring Symposium on Empirical Methods in Discourse Interpretation and Generation

National Conference on Artificial Intelligence, 1995

Papers from 1992 AAAI Spring Symposium: Reasoning with Diagrammatic Representations

National Conference on Artificial Intelligence, 1992

Implementing Logics in Diagrams

National Conference on Artificial Intelligence, 1992

Autistic traits moderate closed world interpretation in conditional reasoning

Implicit Knowledge of (Parts of) Logic, and How to Make It Explicit

Routledge eBooks, Dec 14, 2022

Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

Thinking & Reasoning, Mar 8, 2016

Abstract This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic ... more Abstract This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.

Proceedings of the 21st Annual Science Society Conference

Psychometric measures of ability are unsuited to computational descriptions of tasks, primarily b... more Psychometric measures of ability are unsuited to computational descriptions of tasks, primarily because they cannot take process into account. Studies of aptitude-treatment interactions have often failed to replicate from task to task precisely because of this difficulty. The current study aligns psychometric measures with process accounts in the domain of multimodal reasoning. Learning from multimodal logic courses transfers to other reasoning tasks, and this transfer has been found to relate to differences in strategic use of graphical representations in proof construction. The current study is a replication and an extension of these findings. Different goal types are distinguished in terms of: their modality; whether they involve proofs of consequence or non-consequence; and whether they can be solved by constructing single or multiple cases. We report on the interaction of a range of psychometric measures, and the ways in which they relate to the development and deployment of strategies. In particular, students who develop coping strategies to overcome difficulties with certain problems find that these strategies arise at the expense of appropriate use of a variety of strategies. Our approach, which characterises goals in terms of their logical as well as phenomenal properties, supports a computational perspective on psychometric measures in reasoning tasks.

Proceedings of the Workshop on Mathematical Assistants and Theorem Provers

Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society

Conference Cognitive Science, 1994

Hyperproof is a computer program created by Barwise and Etchemendy for teaching logic using multi... more Hyperproof is a computer program created by Barwise and Etchemendy for teaching logic using multimodal graphical and sentential methods, inspired by their theories of heterogeneous reasoning (Barwise and Etchemendy 1994). Elsewhere, we have proposed a theory of the cognitive impact of assigning information to different modalities (Stenning and Oberlander 1992). Our view is that where diagrams are advantageous, it is because they enforce the representation of information, leading to weak expressiveness, thereby facilitating inference. The present study tests and develops these claims by comparing the effects of teaching undergraduate logic classes using Hyperproof and a control syntactic teaching method. Results indicate that there is significant transfer from the logic courses to logical and analytical reasoning problems. There are also significant interactions between theoretically motivated pre-course aptitude measures and teaching method; the interactions influence postcourse reasoning performance in transfer domains. Hyperproof boosts students previously weak on items which benefit from diagram use, whereas the syntactic course appears to degrade the same group of students' graphical strategies. As well as being theoretically interesting, these results provide support for the important practical conclusion that individual differences in aptitude should be taken into account in choosing teaching technique.

Isolationism in psychology of language

Journal of Psycholinguistic Research, Mar 1, 1981

An opportunity to review two introductory textbooks in one's own teaching field is an opportunity... more An opportunity to review two introductory textbooks in one's own teaching field is an opportunity to wonder out loud about why people teach it, what students learn from it, and how this is reflected in the textbooks people write to teach it from. There is some added interest in these questions in this case, since the courses taught are relatively recent additions to the undergraduate and graduate student curriculum of English-speaking psychology departments, and the courses are probably more varied than in. fields under longer cultivation. One thing that has achieved a considerable level of standardization is the titles of the texts. Apart from the two reviewed here, I can see on my

Swallowing squiggles—the internalization of formalisms

Oxford University Press eBooks, Aug 22, 2002

How did we get here?

Multiple logics within argument: how defeasible and classical reasoning work together

Computational Models of Argument, 2012

Exploring quantifier reasoning and autistic-like traits

Logic, Language, and Computation

Lecture Notes in Computer Science, 2011

SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the tra... more SCOPE OF THE SERIES Logic is applied in an increasingly wide variety of disciplines, from the traditional subjects of philosophy and mathematics to the more recent disciplines of cognitive science, computer science, artificial intelligence, and linguistics, leading to new vigor in this ancient subject. Kluwer, through its Applied Logic Series, seeks to provide a home for outstanding books and research monographs in applied logic, and in doing so demonstrates the underlying unity and applicability of logic.

Heterogeneous reasoning in learning to model

Proceedings of the Annual Meeting of the Cognitive Science Society, 2000

Conceptual learning in maths and science involves learning to coordinate multiple representation ... more Conceptual learning in maths and science involves learning to coordinate multiple representation systems into smoothly functioning heterogeneous reasoning systems composed of sub-languages, graphics, mathematical representations, etc.. In these heterogeneous systems information can be transformed from one representation to another by inference rules, and learning coordination is learning how and when to apply these rules. Heterogeneous reasoning has a particularly important role to play in teaching students how to apply formalisms to real world problems, rather than merely teaching formalisminternal calculation. This paper analyses three learning incidents which happened in groups of students engaged in learning the mathematics and biology involved in modelling biological populations, from the perspective of the heterogeneous reasoning involved. Greeno, Sommerfeld & Weibe (2000) and Hall (2000) analyse incidents from the same curriculum intervention from other points of view, in this volume. We observe both learning successes and failures that cannot be understood without understanding the seams joining the representation systems involved, and the inference rules and operations required to get from one to another. One conclusion is that even apparently homogeneous natural language has to be seen as heterogeneous in its fully contextualised application.

Strategies and Knowledge Representation

Cambridge University Press eBooks, Nov 3, 2003

Logic, Language and Computation

Proceedings of the 18th Annual Conference of the Cognitive Science Society

We have been studying how students respond to multimodal logic teaching with Hyperproof. Performa... more We have been studying how students respond to multimodal logic teaching with Hyperproof. Performance measures have already indicated that students' pre-existing cognitive styles have a significant impact on teaching outcome. Furthermore, a substantial corpus of proofs has been gathered via automatic logging of proof development. We report results from analyses of final proof structure, exploiting (i) 'proofograms', a novel method of proof visualisation, and (ii) corpus-linguistic bigram analysis of rule use. Results suggest that students' cognitive styles do indeed influence the structure of their logical discourse, and that the effect may be attributable to the relative skill with which students manipulate graphical abstractions.

Spatial Inclusion and Analogy for Set Membership: A Case Study of Analogy at Work

The analogy between spatial inclusion and set membership o ers the opportunity t o go beyond the ... more The analogy between spatial inclusion and set membership o ers the opportunity t o go beyond the study of how w e establish analogical mappings to the investigation of the impact of those mappings on mental process. This analogy is the basis of longstanding didactic techniques for teaching elementary logic (Euler's Circles and Venn Diagrams) and therefore bears on psychological theories of human deductive reasoning (e.g. Erickson 1974). An adequate cognitive theory of analogy must explain how m e n tal processing is aided by analogical mappings. In the case of spatial inclusion as an analogy for set membership this comes down to requiring a theory of how graphical representations aid processing. Here we s k etch a general theory in terms of the speci city of graphics which w e h a ve developed further elsewhere (see Stenning & Oberlander 1991a, 1991b). This general approach to graphical representations rests on the observation that graphical representation systems limit abstraction and thereby p u r c hase computational tractability. In applying this general theory to the case of graphical methods of syllogism solution we s k etch a method of using Euler's Circles and show h o w i n terpretative c o n ventions for graphical objects allow the necessary abstractions. In particular we s h o w that even choosing the least expressive system of diagrams limited to circles, still gives the requisite expressive p o wer. The Euler's Circle method sketched is then used as a guide to connectionist implementation of corresponding internal representations. Graphical representations share some general computationalproperties with connectionist systems. In the domain of the syllogism, the central issue is the implementation of the binding of attributes into type-descriptions. Various proposals for connectionist variable binding in the literature are assessed as partial implementations. Some proposals are made for implementation of novel graphical features of the Euler's Circle algorithm. This case study of an analogy suggests the hypothesis that one important r o l e t h a t analogy may p l a y i s p r o viding a representation which is more limited in expressive p o wer and therefore more computationally tractable than the literal representations analogies supplant.

AAAI Spring Symposium on Empirical Methods in Discourse Interpretation and Generation

National Conference on Artificial Intelligence, 1995

Papers from 1992 AAAI Spring Symposium: Reasoning with Diagrammatic Representations

National Conference on Artificial Intelligence, 1992

Implementing Logics in Diagrams

National Conference on Artificial Intelligence, 1992

Autistic traits moderate closed world interpretation in conditional reasoning

Implicit Knowledge of (Parts of) Logic, and How to Make It Explicit

Routledge eBooks, Dec 14, 2022

Logic programming, probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

Thinking & Reasoning, Mar 8, 2016

Abstract This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic ... more Abstract This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.

Proceedings of the 21st Annual Science Society Conference

Psychometric measures of ability are unsuited to computational descriptions of tasks, primarily b... more Psychometric measures of ability are unsuited to computational descriptions of tasks, primarily because they cannot take process into account. Studies of aptitude-treatment interactions have often failed to replicate from task to task precisely because of this difficulty. The current study aligns psychometric measures with process accounts in the domain of multimodal reasoning. Learning from multimodal logic courses transfers to other reasoning tasks, and this transfer has been found to relate to differences in strategic use of graphical representations in proof construction. The current study is a replication and an extension of these findings. Different goal types are distinguished in terms of: their modality; whether they involve proofs of consequence or non-consequence; and whether they can be solved by constructing single or multiple cases. We report on the interaction of a range of psychometric measures, and the ways in which they relate to the development and deployment of strategies. In particular, students who develop coping strategies to overcome difficulties with certain problems find that these strategies arise at the expense of appropriate use of a variety of strategies. Our approach, which characterises goals in terms of their logical as well as phenomenal properties, supports a computational perspective on psychometric measures in reasoning tasks.

Proceedings of the Workshop on Mathematical Assistants and Theorem Provers

Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society

Conference Cognitive Science, 1994

Hyperproof is a computer program created by Barwise and Etchemendy for teaching logic using multi... more Hyperproof is a computer program created by Barwise and Etchemendy for teaching logic using multimodal graphical and sentential methods, inspired by their theories of heterogeneous reasoning (Barwise and Etchemendy 1994). Elsewhere, we have proposed a theory of the cognitive impact of assigning information to different modalities (Stenning and Oberlander 1992). Our view is that where diagrams are advantageous, it is because they enforce the representation of information, leading to weak expressiveness, thereby facilitating inference. The present study tests and develops these claims by comparing the effects of teaching undergraduate logic classes using Hyperproof and a control syntactic teaching method. Results indicate that there is significant transfer from the logic courses to logical and analytical reasoning problems. There are also significant interactions between theoretically motivated pre-course aptitude measures and teaching method; the interactions influence postcourse reasoning performance in transfer domains. Hyperproof boosts students previously weak on items which benefit from diagram use, whereas the syntactic course appears to degrade the same group of students' graphical strategies. As well as being theoretically interesting, these results provide support for the important practical conclusion that individual differences in aptitude should be taken into account in choosing teaching technique.

Isolationism in psychology of language

Journal of Psycholinguistic Research, Mar 1, 1981

An opportunity to review two introductory textbooks in one's own teaching field is an opportunity... more An opportunity to review two introductory textbooks in one's own teaching field is an opportunity to wonder out loud about why people teach it, what students learn from it, and how this is reflected in the textbooks people write to teach it from. There is some added interest in these questions in this case, since the courses taught are relatively recent additions to the undergraduate and graduate student curriculum of English-speaking psychology departments, and the courses are probably more varied than in. fields under longer cultivation. One thing that has achieved a considerable level of standardization is the titles of the texts. Apart from the two reviewed here, I can see on my

Reasoning and discourse coherence in Autism Spectrum Disorder

by Michiel van Lambalgen and Keith Stenning