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Logic and information II (Nonmonotonic logics)
Dpt of Logic, Faculty of Arts, Charles University in Prague
2/0 Zk
Topics
 Classical consequence relation and operation
 Consistency and consequnece
 Basic properties of classical (Tarski) consequence (reflexivity, cumulative transitivity, monotony  Horn rules)
 Supraclassicality
 Paraclassicality
 Compactness and maximality
 Substitution (closed under substitution)
 How to get more?
 Additional background assumptions
 Pivotalassumptions
 Defaultassumptions (cautious monotony, noncompactness)
 Restrictions of the set of models (valuations)
 Pivotalvaluations (noncompactness, definable sets of valuations)
 Defaultvaluations (preferential models, consistency preservation, nonmonotonicity, nontransitivity,
cautious monotony for wellfounded relations on models, not consistency preservation)
 Additional background rules
 Pivotalrules (neither disjunction in the premisses nor contraposition)
 Defaultrules
 Default logic
 Default rules
 Default theories
 Operational semantics (process, extension)
 General properties (consistency preservation, cautious monotony)
 Normal default theories (existence of extensions, monotony in defaults, orthogonalitz of extensions)
 Representation in normal default theories (nonnormality required)
 Seminormal default theories
 Proof theory for default logic
 Joint consistency of justifications
 Modified extensions
 Priorities among defaults
 Nonmonotonic modal logics and Autoepistemic logics
Exercises
 Exercises AD (pdffile)
 Exercises E (pdffile)
Study
The course is also maintained at Moodle UK under the title Logika a informace II.
All topics and terms introduced in lectures are covered
by emphasized literature, by slides and handouts (see below), and by exercises. Some papers are available at Moodle UK.
Moreover, the exercises include all basic terms and theorems. They fully cover the contents of handouts
Introduction to Nonmonotonic Logics.
For the topics AD we recommend the book [Makinson 2005], some parts of chapters 14. Default logic (with operational
semantics, topic E) is presented in [Antoniou 1997], some parts of chapters 37. See also [Meyer and van der Hoek 1995].
References  books
 G Antoniou. Nonmonotonic Reasoning. MIT Press, 1997
 D Batens, C Mortensen, G Priest, JP Van Bendegem (eds.) Frontiers of Paraconsistent Logic. Research Studies Press Ltd., 2000
 A Bochman. A Logical Theory of Nonmonotonic Inference and Belief Change. Springer, 2001
 P Doherty (ed.) Partiality, Modality, and Nonmonotonicity. CSLI, 1996
 R Fagin, JY Halpern, Y Moses, MY Vardi. Reasoning about Knowledge. MIT Press, 1995
 DM Gabbay, CJ Hogger, JA Robinason (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming. Vol 3. Nonmonotonic Reasoning and Uncertain Reasoning. Clarendon Press, Oxford 1994
 JY Halpern. Reasoning about Uncertainty. MIT Press, 2005
 JW Lloyd. Foundations of Logic Programming. Springer, 1987
 D Makinson. Bridges from Classical to Nonmonotonic Logic. King's College Publications, 2005
 JJ Meyer, W van der Hoek. Epistemic logic for AI and Computer Science. Cambridge, 1995
 G Priest. An Introduction to NonClassical Logic. Cambridge, 2001
Slides and handouts
