Semi-normal forms and functional representation of product fuzzy logic

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Authors:
Petr Cintula
Brunella Gerla
Title: Semi-normal forms and functional representation of product fuzzy logic
Journal: Fuzzy Sets and Systems
Volume 143
Number 1
Pages: 89-110
Year: 2004




Abstract

By McNaughton famous theorem, the class of functions representable by formulas of Lukasiewicz logic is the class of piecewise linear functions with integer coefficients.

The first goal of this work to find an analogy of the McNaughton result for product logic. The second goal is to define a conjunctive and disjunctive semi-normal form (CsNF, DsNF) of the formulas of product logic (these forms are a syntactical counterpart of the piecewise monomial functions).

These results show us how the functions expressible by the formulas of product logic look like. Furthermore, this is the first step in creating an automated theorem prover for product logic.