A unified algorithm for finding $$k$$ k -IESFs in linguistic truth-valued lattice-valued propositional logic

Abstract

As a symbolic approach for computing with words, linguistic truth-valued lattice-valued propositional logic $$\fancyscript{L}_{V(n\times 2)}P(X)$$ L V ( n × 2 ) P ( X ) can represent and handle both imprecise and incomparable linguistic value-based information. Indecomposable extremely simple form (IESF) is a basic concept of $$\alpha $$ ? -resolution automated reasoning in lattice-valued logic based in lattice implication algebra (LIA). In this paper we establish a unified method for finding the structure of $$k$$ k -IESF in $$\fancyscript{L}_{V(n\times 2)}P(X)$$ L V ( n × 2 ) P ( X ) . Firstly, some operational properties of logical formulae in $$L_6P(X)$$ L 6 P ( X ) are studied, and some rules are obtained for judging whether a given logical formula is a $$k$$ k -IESF, which are used to contrive an algorithm for finding $$k$$ k -IESF in $$L_6P(X)$$ L 6 P ( X ) . Then, all the results are extended into $$\fancyscript{L}_{V(n\times 2)}P(X)$$ L V ( n × 2 ) P ( X ) . Finally, a unified algorithm for finding all $$k$$ k -IESFs in $$\fancyscript{L}_{V(n\times 2)}P(X)$$ L V ( n × 2 ) P ( X ) is proposed. This work provides theoretical foundations and algorithms for $$\alpha $$ ? -resolution automated reasoning in linguistic truth-valued lattice-valued logic based in linguistic truth-valued LIAs and formal tools for symbolic natural language processing.