A new deduction system for deciding validity in modal logic K

Logic Journal of the IGPL 19 (2): 425-434 (2011)

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Abstract
A new deduction system for deciding validity for the minimal decidable normal modal logic K is presented in this article. Modal logics could be very helpful in modelling dynamic and reactive systems such as bio-inspired systems and process algebras. In fact, recently the Connectionist Modal Logics has been presented, 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 article. The main advantages of this approach are: first, the system is deterministic, i.e. it generates one proof tree for a given formula; second, the system is a validity-checker, hence it generates a proof of a formula ; and third, the language of deduction and the language of a logic coincide. Some of these advantages are compared with other classical approaches
Keywords modal logic  relational logic  dual tableaux
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DOI 10.1093/jigpal/jzq033
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