Abstract

The concept of the truth degree of a formula is the crucial tool and the building block in quantitative logic. So how to compute the truth degree of a formula efficiently is a principal question in this subject. This paper aims at bringing an optimal method for doing this job. Firstly, characterizations of the concept of truth degree are made with concepts from soft constraint theory. Particularly, two soft constraint systems are proposed such that formulas can be taken as soft constraints over them. Then by exploiting the algebraic properties of both constraint systems and n-valued propositional systems, it is shown that different soft constraint systems plays different roles in the computation of truth degree of formulas. An optimal method named splitting algorithm for computing truth degrees of formulas is proposed.

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