Logics with disjunction and proof by cases |
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Authors: | San-min Wang Petr Cintula |
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Institution: | (1) Department of Computer Science and Engineering, Nanchang University, 330031 Nanchang, People’s Republic of China;(2) Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic |
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Abstract: | This paper is a contribution to the general study of consequence relations which contain (definable) connective of “disjunction”.
Our work is centered around the “proof by cases property”, we present several of its equivalent definitions, and show some
interesting applications, namely in constructing axiomatic systems for intersections of logics and recognizing weakly implicative
fuzzy logics among the weakly implicative ones.
The work of the first author was supported by the National Foundation of Natural Sciences of China (Grant no. 60663002) and
by the Grant Project of science and technology of The Education Department of Jiangxi Province under Grant no. 200618. The
work of the second author was supported by grant A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic
and by Institutional Research Plan AVOZ10300504. |
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Keywords: | Logics with disjunction Consequence relation Proof by cases property Intersections of logics Weakly implicative logics Weakly implicative fuzzy logics |
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