Reasoning About Exceptions (Extended Abstract) (bibtex)

by Leendert W. N. van der Torre, Yao-Hua Tan

Abstract:

In this paper we analyze the conditional logic approach to default logic, the logic that formalizes reasoning about default assumptions. Conditional logic is a popular framework to formalize defeasible reasoning. The conditional sentence ldquoif beta (the antecedent or condition) then by default agr (the consequent or conclusion)rdquo is represented in this framework by the formula beta > agr, where lsquo>rsquo is some kind of implication of conditional logic. In this paper different usages of preference orderings for defeasible conditional logics are discussed. The different usages, so-called minimizing and ordering, are represented by different modal operators. Each operator validates different inference rules. Hence, the combination of different modal operators imposes restrictions on the proof theory of the logic. The restriction discussed in this paper is that a proof rule can be blocked in a derivation due to the fact that another proof rule has already been used earlier in the derivation. We call this the two-phase approach in the proof theory.

Reference:

Reasoning About Exceptions (Extended Abstract) (Leendert W. N. van der Torre, Yao-Hua Tan), In KI, 1997.

Bibtex Entry:

@InProceedings{Torre1997, Title = {Reasoning About Exceptions (Extended Abstract)}, Author = {Leendert W. N. van der Torre and Yao-Hua Tan}, Booktitle = {KI}, Year = {1997}, Pages = {405-408}, Abstract = {In this paper we analyze the conditional logic approach to default logic, the logic that formalizes reasoning about default assumptions. Conditional logic is a popular framework to formalize defeasible reasoning. The conditional sentence ldquoif beta (the antecedent or condition) then by default agr (the consequent or conclusion)rdquo is represented in this framework by the formula beta > agr, where lsquo>rsquo is some kind of implication of conditional logic. In this paper different usages of preference orderings for defeasible conditional logics are discussed. The different usages, so-called minimizing and ordering, are represented by different modal operators. Each operator validates different inference rules. Hence, the combination of different modal operators imposes restrictions on the proof theory of the logic. The restriction discussed in this paper is that a proof rule can be blocked in a derivation due to the fact that another proof rule has already been used earlier in the derivation. We call this the two-phase approach in the proof theory.}, Bdsk-url-1 = {http://icr.uni.lu/leonvandertorre/papers/ki97full.ps.Z}, Bibsource = {DBLP, http://dblp.uni-trier.de}, Crossref = {DBLP:conf/ki/1997}, Date-modified = {2011-12-20 17:12:57 +0100}, Ee = {http://dx.doi.org/10.1007/3540634932_38}, Timestamp = {2013.07.26}, Url = {http://icr.uni.lu/leonvandertorre/papers/ki97full.ps.Z} }

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