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Syntax theory of finite lattice-valued propositional logic

PAN XiaoDong  MENG Dan  XU Yang  
【摘要】:In this paper,we establish the graded syntax theory of lattice-valued propositional logic based on finite lattice implication algebras,define the notions of syntactic consequence operation and formal proof,and develop a kind of graded finite lattice-valued propositional calculus.By generalizing classic provable equivalence relation,we present a kind of generalized provable equivalence relation,and establish the corresponding quotient algebra.Finally,we establish the generalized deduction theorem by syntactic consequence operation,and establish the completeness in Pavelka's sense based on finite chains.

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