By taking finite lattice implication algebra as a truth2value field , a syntactic system of lattice2 valued propositional logic based on finite lattice implication algebra was proposed. The basic definitions of syntactic implies , proof and consistency of the system on level A were given axiomatically. Finally , the soundness theorem , consistency theorem , weak complete theorem and weak deduction theoremof the system were proved.

Cheng, X; Ouyang, D; Zhang, C(SRCE University Computing Centre,, 2003-01)

We propose a many-sorted general framework to incorporate algebraic computation with logical reasoning, which equally encompasses following systems as special cases: lattice-valued fuzzy logic, operator fuzzy logic, operator ...

The linguistic truth values with linguistic hedges is considered. The linguistic hedge operators in the proposition are put forward and the truth values are divided into different grades. Based on lattice implication algebra ...

Summary form only given. The (meta) logic underlying classical theory of computation is Boolean (two-valued) logic. Quantum logic was proposed by Birkhoff and von Neumann as a logic of quantum mechanics. It is currently ...