Semi-normal forms and functional representation of product fuzzy logic

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.