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

As a symbolic approach for computing with words, linguistic truth-valued lattice-valued propositional logic $$\fancyscript{L}_{V(n\times 2)}P(X)$$ 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 $$k$$ -IESF in $$\fancyscript{L}_{V(n\times 2)}P(X)$$ . Firstly, some operational properties of logical formulae in $$L_6P(X)$$ are studied, and some rules are obtained for judging whether a given logical formula is a $$k$$ -IESF, which are used to contrive an algorithm for finding $$k$$ -IESF in $$L_6P(X)$$ . Then, all the results are extended into $$\fancyscript{L}_{V(n\times 2)}P(X)$$ . Finally, a unified algorithm for finding all $$k$$ -IESFs in $$\fancyscript{L}_{V(n\times 2)}P(X)$$ 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. [ABSTRACT FROM AUTHOR]