Abstract properties for the choice provability relation in nonmonotonic logics

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Abstract

We analyze the relationship between choice provability (derivability in at least one extension) of nonmonotonic logics, and the abstract properties of nonmonotonic inference relations proposed in the literature. We show that choice provability in default, autoepistemic and even cumulative default logic does not satisfy most of these properties. This is not accidental, but lies at the heart of choice provability, as far as formula-manipulating logics are concerned: Any such logic respecting some natural conditions has a noncumulative choice provability relation. In contrast to this result, we show that choice provability in the logic L1 recently introduced by Brewka is cumulative. This is possible because L1 manipulates defaults and not formulas.

Original languageEnglish
Title of host publicationAdvances in Artificial Intelligence - 3rd Congress of the Italian Association for Artificial Intelligence, AI*IA 1993, Proceedings
EditorsPietro Torasso
PublisherSpringer Verlag
Pages35-40
Number of pages6
ISBN (Print)9783540572923
Publication statusPublished - 1 Jan 1993
Externally publishedYes
Event3rd Congress of the Italian Association for Artificial Intelligence - Torino, Italy
Duration: 26 Oct 199328 Oct 1993
Conference number: 3
https://www.springer.com/gp/book/9783540572923

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume728 LNAI
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference3rd Congress of the Italian Association for Artificial Intelligence
Abbreviated titleAI*IA 1993
CountryItaly
CityTorino
Period26/10/9328/10/93
Internet address

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Cite this

Antoniou, G. (1993). Abstract properties for the choice provability relation in nonmonotonic logics. In P. Torasso (Ed.), Advances in Artificial Intelligence - 3rd Congress of the Italian Association for Artificial Intelligence, AI*IA 1993, Proceedings (pp. 35-40). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 728 LNAI). Springer Verlag.