Abstract:

The paper deals with Mattila's LPC+Ch Calculus (cf. [2]). This fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically. LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstrated that suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented in [2] and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2 and Propositions 1 - 3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.