Continuous propositional modal logic
Journal of Applied Non-Classical Logics, ISSN: 1958-5780, Vol: 28, Issue: 4, Page: 297-312
2018
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Article Description
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 K 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.
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