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Logic Journal of IGPL 2005 13(5):599-609; doi:10.1093/jigpal/jzi044
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© The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Cut and Weakening in Fuzzy Horn Logic

Vilém Vychodil

Dept. Computer Science, Palacky University, Tomkova 40, CZ-779 00, Olomouc, Czech Republic. Email: vilem.vychodil{at}upol.cz

We study generalized deduction rules of cut and weakening in the context of equational fragment of Pavelka-style fuzzy logic using complete residuated lattices as the structures of truth degrees. The deduction rules in question are parameterized by a truth stresser, an additional unary operation on the structure of truth degrees. It is shown that the deductive system of fuzzy Horn logic can be replaced by several equivalent systems which use cut and weakening instead of the monotony rule.

Key Words: cut, fuzzy equality, fuzzy logic, Horn logic, weakening


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