First-order logic as a constraint satisfaction problem

In this paper, we discourse an analysis of classical first-order predicate logic as a constraint satisfaction problem, CSP. First, will offer our general framework for CSPs, and then apply it to logic. We claim would function new semantics, Then, prove the soundness completeness theorems with respect semantics. The latter theorem, which be proven by proof-search method, implies cut-elimination theorem. Furthermore, using make proof Craig interpolation Also, provide feasible algorithms generate interpolants some decidable fragments logic: propositional monadic fragments. algorithms, reflecting ‘projection’ indexed relation, show how transform given formulas syntactically obtain interpolants.