Nonmonotonic Logics and Semantics

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dc.creatorLehmann, Daniel
dc.date2002-02-15
dc.date2002-04-15
dc.date.accessioned2026-07-07T03:18:07Z
dc.date.available2026-07-07T03:18:07Z
dc.descriptionTarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may be deduced from a set A of formulas iff a holds in all of the "preferred" models in which all the elements of A hold. Shoham proposed that the notion of "preferred" models be defined by a partial ordering on the models of the underlying language. A more general semantics is described in this paper, based on a set of natural properties of choice functions. This semantics is here shown to be equivalent to a semantics based on comparing the relative "importance" of sets of models, by what amounts to a qualitative probability measure. The consequence operations defined by the equivalent semantics are then characterized by a weakening of Tarski's properties in which the monotonicity requirement is replaced by three weaker conditions. Classical propositional connectives are characterized by natural introduction-elimination rules in a nonmonotonic setting. Even in the nonmonotonic setting, one obtains classical propositional logic, thus showing that monotonicity is not required to justify classical propositional connectives.
dc.description28 pages. Misprint corrected 15/04/02
dc.identifierhttps://arxiv.org/abs/cs/0202018
dc.identifierhttp://arxiv.org/abs/cs/0202018
dc.identifierJournal of Logic and Computation, Vol. 11 No.2, pp.229-256 2001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/30990
dc.subjectArtificial Intelligence
dc.subjectLogic in Computer Science
dc.subjectLogic
dc.subjectI.2.3
dc.titleNonmonotonic Logics and Semantics
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