Framing human inference by coherence based probability logic

We take coherence based probability logic as the basic reference theory to model human deductive reasoning. The conditional and probabilistic argument forms are explored. We give a brief overview of recent developments of combining logic and probability in psychology. A study on conditional inferences illustrates our approach. First steps towards a process model of conditional inferences conclude the paper.

[1]  Niki Pfeifer,et al.  Human reasoning with imprecise probabilities: Modus ponens and denying the antecedent , 2007 .

[2]  N Chater,et al.  Probabilities and polarity biases in conditional inference. , 2000, Journal of experimental psychology. Learning, memory, and cognition.

[3]  S. Katti.  Operational Subjective Statistical Methods , 1998 .

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

[5]  David E Over,et al.  Conditionals and conditional probability. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[6]  In-mao Liu,et al.  A Probabilistic Interpretation of “If-Then” , 1996 .

[7]  Laurence R. Horn.  A Natural History of Negation , 1989 .

[8]  Georg J. W. Dorn.  Popper’s Laws of the Excess of the Probability of the Conditional over the Conditional Probability , 1992 .

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

[10]  Philip N. Johnson-Laird,et al.  THE PROBABILITY OF CONDITIONALS , 2004 .

[11]  O. Wilhelm,et al.  The meaning(s) of conditionals: conditional probabilities, mental models, and personal utilities. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[12]  Angelo Gilio,et al.  Totally coherent set-valued probability assessments , 1998, Kybernetika.

[13]  Niki Pfeifer,et al.  Inference in conditional probability logic , 2006, Kybernetika.

[14]  P. Walley.  Statistical Reasoning with Imprecise Probabilities , 1990 .

[15]  Romano Scozzafava,et al.  Conditional probability, fuzzy sets, and possibility: a unifying view , 2004, Fuzzy Sets Syst..

[16]  B. M. Hill,et al.  Theory of Probability , 1990 .

[17]  Charles Leake,et al.  Conditional Inference and Logic for Intelligent Systems , 1993 .

[18]  G. Kleiter,et al.  Nonmonotonicity and Human Probabilistic Reasoning , 2003 .

[19]  S. Sloman,et al.  The probability of causal conditionals , 2007, Cognitive Psychology.

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

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

[22]  Karl R. Popper,et al.  A SET OF INDEPENDENT AXIOMS FOR PROBABILITY , 1938 .

[23]  Giulianella Coletti,et al.  Conditioning in a coherent setting: Theory and applications , 2005, Fuzzy Sets Syst..

[24]  Angelo Gilio,et al.  Probabilistic Reasoning Under Coherence in System P , 2002, Annals of Mathematics and Artificial Intelligence.

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

[26]  N. Chater,et al.  The probabilistic approach to human reasoning , 2001, Trends in Cognitive Sciences.

[27]  Ernest W. Adams,et al.  A primer of probability logic , 1996 .

[28]  F. Lad.  Operational Subjective Statistical Methods: A Mathematical, Philosophical, and Historical Introduction , 1996 .

[29]  F. Ramsey.  General Propositions and Causality , 1931 .

[30]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[31]  Hung T. Nguyen,et al.  Conditional inference and logic for intelligent systems - a theory of measure-free conditioning , 1991 .

[32]  A. Rényi.  On a new axiomatic theory of probability , 1955 .

[33]  Philip N. Johnson-Laird,et al.  Naive Probability: A Mental Model Theory of Extensional Reasoning , 1999 .

[34]  J. Kacprzyk,et al.  Technologies for constructing intelligent systems: Tasks , 2002 .

[35]  Niki Pfeifer,et al.  Is Human Reasoning about Nonmonotonic Conditionals Probabilistically Coherent , 2006 .

[36]  In-mao Liu,et al.  Conditional reasoning and conditionalization. , 2003, Journal of experimental psychology. Learning, memory, and cognition.

[37]  E. W. Adams,et al.  The logic of conditionals , 1975 .

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

[39]  Joseph K. Blitzstein,et al.  Conditional probability , 2018, Fat Chance.

[40]  R. Scozzafava,et al.  Probabilistic Logic in a Coherent Setting , 2002 .

[41]  Bernadette Bouchon-Meunier,et al.  Conditional possibility and necessity , 2002 .