Kripke Semantics for Intuitionistic Łukasiewicz Logic

Autor: Paulo Oliva, Edmund Robinson, A. Lewis-Smith
Rok vydání: 2020
Předmět:
Zdroj: Studia Logica. 109:313-339
ISSN: 1572-8730
0039-3215
DOI: 10.1007/s11225-020-09908-z
Popis: This paper proposes a generalization of the Kripke semantics of intuitionistic logicIL appropriate forintuitionistic Łukasiewicz logicIŁL —a logic in the intersection betweenIL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on theposet sumconstruction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009). to show the decidability (and PSPACE completeness) of the quasiequational theory of commutative, integral and bounded GBL algebras. The main idea is that$$w \Vdash \psi $$w⊩ψ—which forILis a relation between worldswand formulas$$\psi $$ψ, and can be seen as a function taking values in the booleans$$(w \Vdash \psi ) \in {{\mathbb {B}}}$$(w⊩ψ)∈B—becomes a function taking values in the unit interval$$(w \Vdash \psi ) \in [0,1]$$(w⊩ψ)∈[0,1]. An appropriate monotonicity restriction (which we callsloping functions) needs to be put on such functions in order to ensure soundness and completeness of the semantics.
Databáze: OpenAIRE
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