α-Lock resolution method for a lattice-valued first-order logic

Authors:
Xingxing He;Yang Xu;Jun Liu;Da Ruan
Affiliations:
Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China;Intelligent Control Development Center, Southwest Jiaotong University, Chengdu 610031, Sichuan, PR China;School of Computing and Mathematics, University of Ulster, Northern Ireland, UK;Belgian Nuclear Research Centre (SCK CEN), Mol, Belgium and Ghent University, Gent, Belgium
Venue:
Engineering Applications of Artificial Intelligence
Year:
2011

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Abstract

This paper focuses on resolution-based automated reasoning approaches in a lattice-valued first-order logic LF(X) with truth-values defined in a logical algebraic structure-lattice implication algebra (LIA), which aims at providing the logic foundation to represent and handle both imprecision and incomparability. In order to improve the efficiency of @a-resolution approach proposed for LF(X), firstly the concepts of @a-lock resolution principle and deduction are introduced for lattice-valued propositional logic LP(X) based on LIA, along with its soundness and weak completeness theorems. Then all the results are extended into LF(X) by using Lifting Lemma. Finally an @a-lock resolution automated reasoning algorithm in LF(X) is proposed for the implementation purpose. This work provides a theoretical foundation for more efficient resolution-based automated reasoning algorithm in lattice-valued logic LF(X).