Continuous propositional modal logic. Issue 4 (2nd October 2018)

• Record Type: Journal Article
• Authors: Baratella, Stefano
• Is Part Of: Journal of applied non-classical logics. Volume 28:Issue 4(2018)
• Page Start: 297
• Page End: 312
• Publication Date: 2018-10-02
• Subjects: Continuous logic -- propositional modal logic -- approximated completeness -- Pavelka-style completeness; Nonclassical mathematical logic -- Periodicals; Wiskundige logica; Logic; Periodicals; 511.3105
• DOI: 10.1080/11663081.2018.1468677
• Languages: English
• ISSNs: 1166-3081

Abstract

Abstract: We introduce a propositional many-valued modal logic which is an extension of the Continuous Propositional Logic to a modal system. Otherwise said, we extend the minimal modal logic to a Continuous Logic system. After introducing semantics, axioms and deduction rules, we establish some preliminary results. Then we prove the equivalence between consistency and satisfiability. As straightforward consequences, we get compactness, an approximated completeness theorem, in the vein of Continuous Logic, and a Pavelka-style completeness theorem.