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Formal Nonmonotonic Theories and Properties of Human Defeasible Reasoning

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Abstract

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the psychology of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model (i) possible explicit defeaters, as in the Suppression Task, and (ii) more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects (i) regarding the inference system, (ii) the knowledge base, and (iii) possible assumed exceptions for the rule.

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Notes

  1. The expression weak completion is used to denote the difference to completion processes that consider a mapping of undefined atoms to \(\bot \) (cp. Dietz et al. 2015).

  2. For instance, it is without problem to introduce variables F and M to a logical system and, without stating any conditions that these may be mutually exclusive, have states of worlds or individuals for which, one, both, or neither of these variables are true, despite the fact that the user of the formal system intended to encode individuals to female or male with these variables.

  3. That is, “in general one cannot be...”. One might have a key, have been (by accident or deliberately) locked in, have broken in, etc. But in the plausible situations, this rule and thus this connection between the variables holds.

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Acknowledgements

This work is supported by DFG-Grants KI1413/5-1 to G. Kern-Isberner and by RA1934 2/1, RA 1934 4/1 and Heisenberg DFG fellowship RA1934 3/1 to M. Ragni. T. Bock and C. Eichhorn are supported by Grant KI1413/5-1 and A. P. P. Tse by RA1934 2/1. The authors would like to thank Richard Niland and Daniel Lux for discussions.

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  1. Research Group on the Foundations of Artificial Intelligence, Institut für Informatik, Technische Fakultät, Albert-Ludwigs-Universität Freiburg, Georges-Köhler-Allee, Geb. 052, 79110, Freiburg, Germany

    Marco Ragni & Alice Ping Ping Tse

  2. Technische Universität Dortmund, Department of Computer Science, Chair I - Information Engineering, 44221, Dortmund, Germany

    Christian Eichhorn, Tanja Bock & Gabriele Kern-Isberner

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  1. Marco Ragni
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  2. Christian Eichhorn
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Correspondence to Marco Ragni.

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Ragni, M., Eichhorn, C., Bock, T. et al. Formal Nonmonotonic Theories and Properties of Human Defeasible Reasoning. Minds & Machines 27, 79–117 (2017). https://doi.org/10.1007/s11023-016-9414-1

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