α-Generalized lock resolution method in linguistic truth-valued lattice-valued logic

Abstract

This paper focuses on efficient non-clausal resolution-based automated reasoning methods and algorithms for a lattice-ordered linguistic truth-valued logic, which corresponds to extensions of α-lock resolution. Firstly, α-generalized lock resolution is proposed for lattice-valued propositional logic and first order logic, respectively, along with their concepts, soundness and completeness. Then, α-generalized lock resolution for first order linguistic truth-valued lattice-valued logic L V(n×2) F(X) is equivalently transformed into that for propositional logic L n P(X), which can greatly reduce the complexity of the resolution procedure. Finally, α-generalized linear semi-lock resolution is discussed, and its general algorithm is also contrived. This work provides more efficient and natural resolution automated reasoning scheme in linguistic truth-valued logic based on lattice implication algebra with the aim at establishing formal tools for symbolic natural language processing.

$$\alpha $$-Paramodulation method for a lattice-valued logic $$L_nF(X)$$ with equality

“…Concretely, for the automated reasoning aspect, the α-resolution principle is developed in lattice-valued propositional logic LP(X) [15,30] and lattice-valued first-order logic LF(X) [29] as well as their soundness and weak completeness. Its approximate reasoning scheme was also investigated and reported in [9,[12][13][14][31][32][33][34].…”

A Decision Making Approach with Linguistic Weight and Unavoidable Incomparable Ranking

“…Lattice implication algebra (LIA) structure can imitate the uncertain and both comparable and incomparable characteristic [7]. Many researchers have studied in varied direction of LIA [23,24]. Jun Liu et al have proposed an axiomatizable lattice ordered qualitative linguistic truth-valued logic system, which is a foundation for establishing formal linguistic truth-valued logic [25].…”