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.

Continuous propositional modal logic / Baratella, Stefano. - In: JOURNAL OF APPLIED NON-CLASSICAL LOGICS. - ISSN 1958-5780. - STAMPA. - 28:4(2018), pp. 297-312. [10.1080/11663081.2018.1468677]

Continuous propositional modal logic

Stefano Baratella
2018

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 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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Baratella, Stefano
Continuous propositional modal logic / Baratella, Stefano. - In: JOURNAL OF APPLIED NON-CLASSICAL LOGICS. - ISSN 1958-5780. - STAMPA. - 28:4(2018), pp. 297-312. [10.1080/11663081.2018.1468677]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/209002
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