Towards a mental probability logic

We propose probability logic as an appropriate standard of reference for evaluating human inferences. Probability logical accounts of nonmonotonic reasoning with SYSTEM P, and conditional syllogisms (MODUS PONENS, etc.) are explored. Furthermore, we present categorical syllogisms with intermediate quantifiers, like the "MOST …" quantifier. While most of the paper is theoretical and intended to stimulate psychological studies, we also summarize our empirical studies on human nonmonotonic reasoning.

[1]  D. Steinberg,et al.  Deductive Reasoning , 2021, Encyclopedic Dictionary of Archaeology.

[2]  M. E. R..  “If” , 1921, Definitions.

[3]  Marilyn Ford.  Human Nonmonotonic Reasoning: the Importance of Seeing the Logical Strength of Arguments , 2005, Synthese.

[4]  Salem Benferhat,et al.  An Overview of Possibilistic Handling of Default Reasoning, with Experimental Studies , 2005, Synthese.

[5]  Gerhard Schurz,et al.  Non-Monotonic Reasoning from an Evolution-Theoretic Perspective: Ontic, Logical and Cognitive Foundations , 2005, Synthese.

[6]  M. Ford.  On using human nonmonotonic reasoning to inform artificial systems , 2005 .

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

[8]  Imre Hronszky,et al.  Rationality in an Uncertain World , 2005 .

[9]  Guy Politzer.  Some precursors of current theories of syllogistic reasoning , 2005 .

[10]  Carl G. Wagner.  Modus Tollens Probabilized , 2004, The British Journal for the Philosophy of Science.

[11]  Jonathan St. B. T. Evans,et al.  Belief Bias and Figural Bias in Syllogistic Reasoning , 2004, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[12]  Marilyn Ford,et al.  System LS: A Three‐Tiered Nonmonotonic Reasoning System , 2004, Comput. Intell..

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

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

[15]  Nick Chater,et al.  Rationality, rational analysis and human reasoning , 2004 .

[16]  S. Newstead,et al.  Can natural language semantics explain syllogistic reasoning? , 2003, Cognition.

[17]  David E. Over,et al.  The probability of conditionals: The psychological evidence , 2003 .

[18]  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.

[19]  Stephen E. Newstead,et al.  Individual differences in strategies for syllogistic reasoning , 2003 .

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

[21]  Bart Geurts,et al.  Reasoning with quantifiers , 2003, Cognition.

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

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

[24]  Gregory L. Brake,et al.  The psychophysics metaphor in calibration research , 2002 .

[25]  Guy Politzer,et al.  Deductive reasoning from uncertain conditionals. , 2002, British journal of psychology.

[26]  H. Pashler.  STEVENS' HANDBOOK OF EXPERIMENTAL PSYCHOLOGY , 2002 .

[27]  M. Oaksford.  Contrast classes and matching bias as explanations of the effects of negation on conditional reasoning , 2002 .

[28]  Jonathan Evans.  Matching bias and set sizes: A discussion of Yama (2001) , 2002 .

[29]  Jean-François Bonnefon,et al.  The suppression of Modus Ponens as a case of pragmatic preconditional reasoning , 2002 .

[30]  Thomas Lukasiewicz,et al.  Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P , 2002, J. Appl. Non Class. Logics.

[31]  Rosemary J. Stevenson,et al.  Reasoning from uncertain premises: Effects of expertise and conversational context , 2001 .

[32]  H. Yama.  Matching versus optimal data selection in the Wason selection task , 2001 .

[33]  Donald Nute,et al.  Defeasible Logic , 1994, INAP.

[34]  Marilyn Ford,et al.  Strategies in Human Nonmonotonic Reasoning , 2000, Comput. Intell..

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

[36]  Angelo Gilio,et al.  A generalization of the fundamental theorem of de Finetti for imprecise conditional probability assessments , 2000, Int. J. Approx. Reason..

[37]  K. Stanovich,et al.  Heuristics and Biases: Individual Differences in Reasoning: Implications for the Rationality Debate? , 2002 .

[38]  N. Chater,et al.  The Probability Heuristics Model of Syllogistic Reasoning , 1999, Cognitive Psychology.

[39]  P N Johnson-Laird,et al.  Deductive reasoning. , 1999, Annual review of psychology.

[40]  Gerhard Schurz,et al.  Probabilistic Semantics for Delgrande's Conditional Logic and a Counterexample to His Default Logic , 1998, Artif. Intell..

[41]  Gernot D. Kleiter,et al.  Do subjects understand base rates , 1997 .

[42]  Rudolf Kruse,et al.  Qualitative and Quantitative Practical Reasoning , 1997, Lecture Notes in Computer Science.

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

[44]  T. Hailperin,et al.  Sentential Probability Logic: Origins, Development, Current Status, and Technical Applications , 1996 .

[45]  Joseph Y. Halpern,et al.  From Statistical Knowledge Bases to Degrees of Belief , 1996, Artif. Intell..

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

[47]  Alessandro Saffiotti,et al.  Belief functions and default reasoning , 1995, Artif. Intell..

[48]  Nick Chater,et al.  A rational analysis of the selection task as optimal data selection. , 1994 .

[49]  John L. Pollock,et al.  Justification and Defeat , 1994, Artif. Intell..

[50]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

[51]  Kurt Konolige,et al.  Autoepistemic logic , 1994 .

[52]  H. Prade,et al.  Possibilistic logic , 1994 .

[53]  L. Rips.  The Psychology of Proof: Deductive Reasoning in Human Thinking , 1994 .

[54]  Dov M. Gabbay,et al.  Nonmonotonic reasoning and uncertain reasoning , 1994 .

[55]  Dov M. Gabbay,et al.  Handbook of logic in artificial intelligence and logic programming (vol. 1) , 1993 .

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

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

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

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

[60]  Arie Tzvieli.  Possibility theory: An approach to computerized processing of uncertainty , 1990, J. Am. Soc. Inf. Sci..

[61]  Daniel Lehmann,et al.  What does a Conditional Knowledge Base Entail? , 1989, Artif. Intell..

[62]  H. Markovits.  Conditional Reasoning, Representation, and Empirical Evidence on a Concrete Task , 1988 .

[63]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

[64]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[65]  James P. Delgrande,et al.  An Approach to Default Reasoning Based on a First-Order Conditional Logic: Revised Report , 1987, Artif. Intell..

[66]  David S. Touretzky,et al.  The Mathematics of Inheritance Systems , 1984 .

[67]  Robert C. Moore.  Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[68]  Martin D. S. Braine,et al.  Conversational comprehension processes are responsible for reasoning fallacies in children as well as adults: If is not the biconditional. , 1983 .

[69]  H. Mirels,et al.  Scientists' Understanding of Propositional Logic: An Experimental Investigation , 1983 .

[70]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

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

[72]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[73]  J. S. Evans,et al.  Linguistic Factors in Reasoning , 1977 .

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

[75]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[76]  John E. Taplin,et al.  Reasoning with conditional sentences , 1971 .

[77]  Patrick Suppes,et al.  Logic, Methodology and Philosophy of Science , 1963 .

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

[79]  Helly.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1936 .

[80]  K. Popper,et al.  Logik der Forschung , 1935 .

[81]  A. Kolmogoroff.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

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

[83]  S. Amano,et al.  Psychology of Reasoning , 1923 .