Semantic Analysis of Rough Logic

Semantic Analysis of Rough Logic

Qing Liu
DOI: 10.4018/978-1-60566-324-1.ch011
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In this Chapter, we analyse the semantics of the rough logic. Related operations and related properties of semantics based on the rough logic are also discussed. Related reasoning of the semantis are also studied. Significant of studying semantics of the rough logic will hopefully offer a new idea for the applications to classical logic and other nonstandard logic, also hopefully offer a new theory and methodology for problem resolving in artificial intelligence.
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1. Introduction

Rough logic in this chapter is viewed as a nonstandard logic defined on a given information system 978-1-60566-324-1.ch011.m01. Atomic formulae of the logic are defined as 978-1-60566-324-1.ch011.m02 or 978-1-60566-324-1.ch011.m03. It is interpreted as 978-1-60566-324-1.ch011.m04, where 978-1-60566-324-1.ch011.m05 is an attribute in 978-1-60566-324-1.ch011.m06, 978-1-60566-324-1.ch011.m07 is a individual variable on 978-1-60566-324-1.ch011.m08, and 978-1-60566-324-1.ch011.m09 is an attribute value. The compound formulae are consisted of the atomic formulae and usual logical connectives. The rough logic is abbreviated as 978-1-60566-324-1.ch011.m10. Its truth value is the multi-valued.

Senmantic analysis of logic is a means of studying logic. Kripks tried to study modal logic through Semantic Analysis of Modal Logic978-1-60566-324-1.ch011.m11, Luis try also to define semantics of Modal Logic as a subset of state space, to study the resolution of Modal Logic by semantics of modal logic978-1-60566-324-1.ch011.m12. Zadeh tried to change his research from Fuzzy Logic to its semantic, he defined the meaning of fuzzy propositional logical formula as a set of elements of satisfying this fuzzy propositional logical formula in 1979978-1-60566-324-1.ch011.m13. In this Chapter, we analyse related properties and approximate reasoning of the rough logical semantics. Pawlak proposed Rough Sets based on the semantics of indiscernibility relation, to define the upper and the lower approximations of a undefinable set978-1-60566-324-1.ch011.m14, so Pawlak’s rough set approach solved the problem of computing elements on boundary by Frege in 1914978-1-60566-324-1.ch011.m15. From the view of problem solving in artificial intelligence, Hobbs tried to define indiscernibility relation based on the semantics of predicates in logical formulae978-1-60566-324-1.ch011.m16, he offer a new theoretical tool and methodology for problem solving in artificial intelligence.

In the Chapter, rough logic is described in Section 2. Truth values of the rough logical formulae are defined in Section 3. Sematic model of the rough logic is described in Section 4. Satisfiability of meaning based on rough logical formulae is also described in Section 5. The Related operations of semantics based the rough logic are presented in Section 6. Related properties of semantics based on the rough logic are given in Section 7. The normal forms of meaning of rough logical formulae are discussed in Section 8. Reasoning based on semantics of rough logical formula is discussed in Section 9. Applications of the semantics based on rough logic are presented in Section 10. Final Section is the perspective of studying the semantics of rough logic.

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