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Cognitive Argumentation for Human Syllogistic Reasoning

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Abstract

This paper brings together work from the psychology of reasoning and computational argumentation in AI to propose a cognitive computational model for human reasoning and in particular for human syllogistic reasoning. The model is grounded in the formal framework of argumentation in AI with its dialectic semantics for the quality of arguments. Arguments for logical conclusions are constructed via a set of proposed argument schemes, chosen for their cognitive validity, as supported by studies in cognitive psychology. The proposed model with its cognitive principles of argumentation can encompass together in a uniform way both formal and informal logical reasoning, capturing well the empirical data of human syllogistic reasoning in the recent Syllogism Challenge 2017 on cognitive modeling. The paper also argues that the proposed approach could be applied more generally to other forms of high-level human reasoning.

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Notes

  1. http://homepage.ruhr-uni-bochum.de/defeasible-reasoning/ArgRea-2018.html

  2. http://aic2018.pa.icar.cnr.it/

  3. http://ratiolog.uni-koblenz.de/bridging2018

  4. The underlined letters denote the abbreviations in the sequel.

  5. See for example the special issue of Argument and Computation, 5(1), 2014 on tutorials of structured argumentation and the recent Handbook on Formal Argumentation [17].

  6. Here and in the sequel, we omit \(\sigma \) in the indices and only specify the relevant predicates in parantheses after the scheme.

  7. The notion of complement is part of the given language \({{\mathcal {L}}}\). For example, when our language contains a negation operator then A is in conflict with \(\lnot A\) and vice versa for any atom A. Accordingly, the complement, \({\overline{L}} = \lnot A\) when \(L = A\) and \({\overline{L}} = A\) when \(L = \lnot A\).

  8. See http://gorgiasb.tuc.gr/Apps.html

  9. http://www.cs.ucy.ac.cy/~nkd/gorgias/,

    http://gorgiasb.tuc.gr/

  10. This also corresponds to its Aristotelian interpretation [29].

  11. This applies in II1, II2, II3, II4, OO3, OO4, IO1, IO4, OI2 and OI4.

    \(p,q,p',q',r\) and s are substituted according to \(\varSigma = \{ (a,b,b,c,a,c),\)

    (b, a, c, b, a, c), (a, b, c, b, a, c), (b, a, b, c, a, c), (a, b, b, c, c, a),  \((b,a,c,b,c,a), (a,b,c,b,c,a), (b,a,b,c,c,a)\}\).

  12. In Figs. 1, 2 and 3 , \({\uparrow , \updownarrow }\) show attacks and \({\Uparrow }, \Updownarrow \) show defenses.

  13. www.cc.uni-freiburg.de/modelingchallenge/challenge-2017

  14. www.fernuni-hagen.de/wbs/dkbkik2017

  15. The interested reader who would like to study the representation in Gorgias can request this from the authors.

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Authors and Affiliations

  1. International Center for Computational Logic, TU Dresden, Dresden, Germany

    Emmanuelle-Anna Dietz Saldanha

  2. Department of Computer Science, University of Cyprus, Nicosia, Cyprus

    Antonis Kakas

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  1. Emmanuelle-Anna Dietz Saldanha
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  2. Antonis Kakas
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Correspondence to Emmanuelle-Anna Dietz Saldanha.

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Saldanha, EA.D., Kakas, A. Cognitive Argumentation for Human Syllogistic Reasoning. Künstl Intell 33, 229–242 (2019). https://doi.org/10.1007/s13218-019-00608-y

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