Linguistic Information Processing Based on Lattice Structrure

Abstract

In 1993, Xu (1993) proposed a kind of lattice structure by combining lattice and implication algebra, named lattice implication algebra, which is a new logical algebraic system. The aims of lattice implication algebras are to process fuzziness and incomparability associated with human’s intelligent activities in the real world. From the symbolism point of view, intelligent information processing depends on the logical foundation and the corresponding uncertainty reasoning theory. Inspired by these academic ideas, Xu et al. (2000a,b,c, 2001a,b, 2003, 2007a,b) investigated lattice valued logic based on lattice implication algebras, and the corresponding theories and methods of uncertainty reasoning and automated reasoning. According to these research works, in last few years, Xu’s research group and some other researchers have done many works on linguistic truth-valued lattice implication algebra [Ma et al. (2006); Meng et al. (2006); Pei and Xu (2004); Pei (2007); Xu et al. (2006b)], linguistic truth-valued propositional logic [Ma et al. (2004); Zou et al. (2005b, 2006)], linguistic truth-valued uncertainty reasoning [Chen et al. (2005); Li et al. (2007); Pei et al. (2007a); Zou et al. (2008)] and automated reasoning theory and approaches [Li et al. (2006); Liu et al. (2003);Ma et al. (2006, 2007);Meng et al. (2003, 2005); Xu et al. (2007b); Zou et al. (2005a)]. These research works provided new approaches for linguistic information processing.