Theories of Rational Reasoning (P. Jirků)

Syllabus of the course
(Charles University, Philosophical Faculty)

Goal of the Course

In this course students will learn most influential approaches to representational issues concerning nonmonotonic reasoning, commonsense reasoning and other nondeductive kinds of reasoning including uncertain reasoning.

Knowledge Representation in Logic

Deductive reasoning, commonsense reasoning, meta reasoning. Deductive databases. Closed world assumption (naive, generalized, careful, and extended CWA). Theory completion. Theories of nonmonotonic inference. Partial logics.

Default Logic

Reiter's default logic: defaults, closed defaults, fixed points, extensions of a closed default theory, minimality of extensions. Restricted defaults: normal defaults. Closed normal default theory, semimonotonicity, orthogonality of extensions. Default proofs. Extension membership problem. Stable model semantics. Closed normal default theories and the revision of beliefs. Other consistency based logics. Modal nonmonotonic logics, maximal consistency logics.

Circumscriptive Logics

Propositional circumscriptions, models, predicate completion, circumscriptive theories. Protected circumscription. Second-order circumscription.

Autoepistemic Logics

Belief sets and fixed points. Stable sets. Possible-worlds semantics.

Revisable Reasoning

Nute's defeasible logic. Inheritance hierarchies. Thruth-maintenance systems. Conditional logic: Stalnaker model theory, systems of spheres.

Reasoning with Uncertain and Incomplete Knowledge

Belief functions. Measures and probabilities. Possibilistic logic (possibility and necessity). Belnap four-valued logic. Belief revisions. Rationality postulates. Reasoning with incomplete knowledge.

References:

Bochman Alexander: A Logical Theory of Nonmonotonic Inference and Belief Change. Springer-Verlag, Berlin, Heidelberg 2001. ISBN 3-540-41766-4
Brewka Gerhard, Dix Jurgen, and Konolige Kurt: Nonmonotonic Reasoning. CSLI Lecture Notes number 73. Stanford, California 1997. 179 p. ISBN 1-881526-83-6
Gabbay Dow M., Hogger C. J., and Robinson J. A. (eds.): Handbook of Logic in Artificial Intelligence and Logic Programming. Vol 3, Nonmonotonic Reasoning and Uncertain Reasoning. Clarendon Press, Oxford 1994, 529 p. ISBN 0-19-853747-6
Jirků Petr: Teorie racionálního usuzování. (Theories of Rational Reasoning) under preparation.
Lukasiewicz Witold: Non-monotonic Reasoning. Formalization of Commonsense Reasoning. Ellis Horwood, New York - London - Toronto - Sydney - Tokyo - Singapore 1990, 328 p. ISBN 0-13-624446-7
Marek V W. and Truszcynski M.: Nonmonotonic Logic. Context-Dependent Reasoning. Springer-Verlag 1993, 420 p. ISBN 3-540-56448-9
Thayse A. (ed.): From Standard Logic to Logic Programming. John Wiley & Sons, Chichester - New York - Brisbane - Totonto - Singapore 1988, 343 p. ISBN 0-471-011838-5
Thayse A. (ed.): From Modal Logic to Deductive Databases. John Wiley & Sons, Chichester - New York - Brisbane - Toronto - Singapore 1989, 380 p. ISBN 0-471-92345-1
Turner Raymond: Truth and Modality for Knowledge Representatiom. Pitman Publ., London 1990.

Last modified: 7 February 2002