A new deduction system for deciding validity in modal logic K

Abstract

A new deduction system for deciding validity for the minimal decidable normal modal logic K is presented in this paper. Modal logics could be very helpful in modeling dynamic and reactive systems such as bio-inspired systems and process algebras. In fact, recently it has been presented the Connectionist Modal Logics which combines the strengths of modal logics and neural networks. Thus, modal logic K is the basis for these approaches. Soundness, completeness, and the fact that the system itself is a decision procedure are proved in this paper. The main advantages of this approach are: first, the system is deterministic, that is, it generates one proof tree for a given formula; second, the system is a validity-checker, hence it generates a proof of a formula (if such exists); third, the language of deduction and the language of a logic coincide. Some of these advantages are compared to other classical approaches.