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Algebraic analysis of \(\text{LPC} +\text{Ch}\) calculus. (English) Zbl 0857.03042

Summary: The paper deals with Mattila’s LPC+Ch Calculus [J. K. Mattila, “On modifier logic”, in: L. A. Zadeh et al. (eds.), Fuzzy logic for the management of uncertainty, 191-209 (1992)]. This fuzzy inference system is an attempt to introduce linguistic objects into mathematical logic without defining these objects mathematically. The LPC+Ch Calculus is analyzed from an algebraic point of view and it is demonstrated that a suitable factorization of the set of well-formed formulae (in fact, the Lindenbaum algebra) leads to a structure called ET-algebra, which is introduced at the beginning of the paper. On its basis, all the theorems presented by Mattila [loc. cit.] and many others can be proved in a simple way, which is demonstrated in Lemmas 1 and 2 and Propositions 1-3. The conclusion critically discusses some other issues of the LPC+Ch Calculus in particular that no formal semantics is given.

MSC:

03G25 Other algebras related to logic
68T27 Logic in artificial intelligence

Citations:

Zbl 0729.03017
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References:

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[2] J. K. Mattila: On modifier logic. Fuzzy Logic for the Management of Uncertainty (L.A. Zadeh and J. Kacprzyk,), J. Wiley and Sons, New York, 1092, pp. 191-209.
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