α-resolution principle based on lattice-valued propositional logic LP(X)

Yang Xu; Da Ruan; Etienne E. Kerre; Jun Liu

doi:10.1016/S0020-0255(00)00069-4

α-resolution principle based on lattice-valued propositional logic LP(X)

Yang Xu, Da Ruan, Etienne E. Kerre, Jun Liu

Research output › peer-review

Abstract

In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the α-resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra - lattice implication algebra, is investigated. Finally, an α-resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level α (i.e., α-false), is established, and the theorems of both soundness and completeness of this α-resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).

Original language	English
Pages (from-to)	195-223
Number of pages	29
Journal	Information Sciences
Volume	130
Issue number	1-4
DOIs	https://doi.org/10.1016/S0020-0255(00)00069-4
State	Published - Dec 2000

Funding

Funders	Funder number
Not added	69674015, 69774016

ASJC Scopus subject areas

Software
Control and Systems Engineering
Theoretical Computer Science
Computer Science Applications
Information Systems and Management
Artificial Intelligence

Access to Document

10.1016/S0020-0255(00)00069-4

Cite this

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title = "α-resolution principle based on lattice-valued propositional logic LP(X)",

abstract = "In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the α-resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra - lattice implication algebra, is investigated. Finally, an α-resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level α (i.e., α-false), is established, and the theorems of both soundness and completeness of this α-resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).",

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AU - Kerre, Etienne E.

AU - Liu, Jun

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Y1 - 2000/12

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AB - In the present paper, resolution-based automated reasoning theory in an L-type fuzzy logic is focused. Concretely, the α-resolution principle, which is based on lattice-valued propositional logic LP(X) with truth-value in a logical algebra - lattice implication algebra, is investigated. Finally, an α-resolution principle that can be used to judge if a lattice-valued logical formula in LP(X) is always false at a truth-valued level α (i.e., α-false), is established, and the theorems of both soundness and completeness of this α-resolution principle are also proved. This will become the theoretical foundation for automated reasoning based on lattice-valued logical LP(X).

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