Authors
Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca
Abstract
Łukasiewicz presented two different analyses of modal notions by means of many-valued logics: the linearly ordered systems Ł3,..., Open image in new window,..., \; the 4-valued logic Ł he defined in the last years of his career. Unfortunately, all these systems contain “Łukasiewicz type paradoxes”. On the other hand, Brady’s 4-valued logic BN4 is the basic 4-valued bilattice logic. The aim of this paper is to show that BN4 can be strengthened with modal operators following Łukasiewicz’s strategy for defining truth-functional modal logics. The systems we define lack “Łukasiewicz type paradoxes”. Following Brady, we endow them with Belnap–Dunn type bivalent semantics.
Keywords Many-valued logics  Modal many-valued logics  Łukasiewicz many-valued logics  Bilattice logics  Belnap–Dunn type bivalent semantics
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DOI 10.1007/s10849-016-9237-8
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References found in this work BETA

Reasoning with Logical Bilattices.Ofer Arieli & Arnon Avron - 1996 - Journal of Logic, Language and Information 5 (1):25--63.
Partiality and its Dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.

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