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- Title
General form of α-resolution principle for linguistic truth-valued lattice-valued logic.
- Authors
Zhong, Xiaomei; Xu, Yang; Liu, Jun; Chen, Shuwei
- Abstract
This paper is focused on resolution-based automated reasoning theory in linguistic truth-valued lattice-valued logic based on linguistic truth-valued lattice implication algebra. Concretely, the general form of α-resolution principle based on the above lattice-valued logic is equivalently transformed into another simpler lattice-valued logic system. Firstly, the general form of α-resolution principle for lattice-valued propositional logic $$ ({\fancyscript{L}}_{n} \times {\fancyscript{L}}_{2}){\text{P(X)}} $$ is equivalently transformed into that for lattice-valued propositional logic $$ \fancyscript{L}_{n} $$P(X). A similar conclusion is obtained between the general form of α-resolution principle for linguistic truth-valued lattice-valued propositional logic $${\fancyscript{L}}_{V(n \times 2)}$$P(X) and that for lattice-valued propositional logic $${\fancyscript{L}}_{Vn} $$P(X). Secondly, the general form of α-resolution principle for lattice-valued first-order logic $$ ({\fancyscript{L}}_{n} \times {\fancyscript{L}}_{2}) $$F(X) is equivalently transformed into that for $${\fancyscript{L}}_{n} $$P(X). Similarly, this conclusion also holds for linguistic truth-valued lattice-valued first-order $${\fancyscript{L}}_{V(n \times 2)} $$F(X) and $${\fancyscript{L}}_{Vn} $$P(X). The presented work provides a key theoretical support for automated reasoning approaches and algorithms in linguistic truth-valued logic, which can further support linguistic information processing for decision making, i.e., reasoning with words.
- Subjects
TRUTH functions (Mathematical logic); LATTICE field theory; PROGRAMMING languages; FREE resolutions (Algebra); ALGEBRA; EQUIVALENCE relations (Set theory)
- Publication
Soft Computing - A Fusion of Foundations, Methodologies & Applications, 2012, Vol 16, Issue 10, p1767
- ISSN
1432-7643
- Publication type
Article
- DOI
10.1007/s00500-012-0860-2