The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as ‘preface’ and ‘lottery’ rules.

[1]  Henry E. Kyburg,et al.  Probability and the logic of rational belief , 1970 .

[2]  Alexander Bochman,et al.  A Logical Theory of Nonmonotonic Inference and Belief Change , 2001, Artificial Intelligence.

[3]  John L. Pollock,et al.  The Paradox of the Preface , 1986, Philosophy of Science.

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

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

[6]  James Hawthorne,et al.  On the logic of nonmonotonic conditionals and conditional probabilities , 1996, J. Philos. Log..

[7]  Johan van Benthem,et al.  Foundations of conditional logic , 1984, J. Philos. Log..

[8]  Ernest W. Adams,et al.  Four probability-preserving properties of inferences , 1996, J. Philos. Log..

[9]  David Makinson,et al.  Bridges from classical to nonmonotonic logic , 2005, Texts in computing.

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

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

[12]  John P. Burgess,et al.  Quick completeness proofs for some logics of conditionals , 1981, Notre Dame J. Formal Log..

[13]  Ramón Pino Pérez,et al.  Beyond Rational Monotony: Some Strong Non-Horn Rules for Nonmonotonic Inference Relations , 1997, J. Log. Comput..

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

[15]  Henry E. Kyburg,et al.  Conditionals and consequences , 2007, J. Appl. Log..

[16]  James Hawthorne,et al.  Nonmonotonic conditionals that behave like conditional probabilities above a threshold , 2007, J. Appl. Log..

[17]  Robert Stalnaker.  A Theory of Conditionals , 2019, Knowledge and Conditionals.

[18]  Didier Dubois,et al.  Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification , 2001, Annals of Mathematics and Artificial Intelligence.

[19]  Michael Freund,et al.  Injective Models and Disjunctive Relations , 1993, J. Log. Comput..