Simulating Human Inferences in the Light of New Information: A Formal Analysis

Human answer patterns in psychological reasoning experiments systematically deviate from predictions of classical logic. When interactions between any artificial reasoning system and humans are necessary this difference can be useful in some cases and lead to problems in other cases. Hence, other approaches than classical logic might be better suited to capture human inference processes. Evaluations are rare of how good such other approaches, e.g., non-monotonic logics, can explain psychological findings. In this article we consider the so-called Suppression Task, a core example in cognitive science about human reasoning that demonstrates that some additional information can lead to the suppression of simple inferences like the modus ponens. The psychological findings for this task have often been replicated and demonstrate a key-effect of human inferences. We analyze inferences of selected formal approaches and compare them by their capacity to cover human inference observed in the Suppression Task. A discussion on formal properties of successful theories conclude the paper.

[1]  Moisés Goldszmidt,et al.  On the Consistency of Defeasible Databases , 1991, Artif. Intell..

[2]  Didier Dubois,et al.  Inconsistency Management and Prioritized Syntax-Based Entailment , 1993, IJCAI.

[3]  Judea Pearl,et al.  System Z: a Natural Ordering of Defaults with Tractable Applications to Nonmonotonic Reasoning^ , 1990 .

[4]  N. Chater,et al.  Précis of Bayesian Rationality: The Probabilistic Approach to Human Reasoning , 2009, Behavioral and Brain Sciences.

[5]  Judea Pearl,et al.  Qualitative Probabilities for Default Reasoning, Belief Revision, and Causal Modeling , 1996, Artif. Intell..

[6]  Keith Stenning,et al.  Human Reasoning and Cognitive Science , 2008 .

[7]  Marco Ragni,et al.  Can Formal Non-monotonic Systems Properly Describe Human Reasoning? , 2014, CogSci.

[8]  Wolfgang Spohn,et al.  The Laws of Belief - Ranking Theory and Its Philosophical Applications , 2012 .

[9]  Gabriele Kern-Isberner,et al.  Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering Conditionals as Agents , 2001 .

[10]  Chitta Baral,et al.  Knowledge Representation, Reasoning and Declarative Problem Solving , 2003 .

[11]  David Makinson,et al.  General patterns in nonmonotonic reasoning , 1994 .

[12]  Ken Manktelow,et al.  Reasoning and Thinking , 1999 .

[13]  R. Byrne Précis of The Rational Imagination: How People Create Alternatives to Reality , 2007, Behavioral and Brain Sciences.

[14]  Steffen Hölldobler,et al.  Logic Programs under Three-Valued Lukasiewicz Semantics , 2009, ICLP.

[15]  Peter Szolovits,et al.  What Is a Knowledge Representation? , 1993, AI Mag..

[16]  Jean-François Bonnefon,et al.  An Empirical Test of Patterns for Nonmonotonic Inference , 2002, Annals of Mathematics and Artificial Intelligence.

[17]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[18]  S. C. Kleene,et al.  Introduction to Metamathematics , 1952 .

[19]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[20]  Niki Pfeifer,et al.  Coherence and Nonmonotonicity in Human Reasoning , 2005, Synthese.

[21]  L. M. M.-T. Theory of Probability , 1929, Nature.

[22]  Gabriele Kern-Isberner,et al.  A Thorough Axiomatization of a Principle of Conditional Preservation in Belief Revision , 2004, Annals of Mathematics and Artificial Intelligence.

[23]  R. Byrne Suppressing valid inferences with conditionals , 1989, Cognition.

[24]  P C Wason,et al.  Reasoning about a Rule , 1968, The Quarterly journal of experimental psychology.

[25]  Gabriele Kern-Isberner,et al.  Conditionals in Nonmonotonic Reasoning and Belief Revision , 2001, Lecture Notes in Computer Science.

[26]  Melvin Fitting,et al.  A Kripke-Kleene Semantics for Logic Programs , 1985, J. Log. Program..

[27]  Grigoris Antoniou,et al.  Nonmonotonic reasoning , 1997 .

[28]  Verzekeren Naar Sparen,et al.  Cambridge , 1969, Humphrey Burton: In My Own Time.