An Implicative Expansion of Belnap’s Four-Valued Matrix: A Modal Four-Valued Logic Without Strong Modal Lukasiewicz-Type Paradoxes
نویسندگان
چکیده
منابع مشابه
On Lukasiewicz's Four-Valued Modal Logic
à Lukasiewicz’s four-valued modal logic is surveyed and analyzed, together with à Lukasiewicz’s motivations to develop it. A faithful interpretation of it into classical (non-modal) two-valued logic is presented, and some consequences are drawn concerning its classification and its algebraic behaviour. Some counter-intuitive aspects of this logic are discussed under the light of the presented r...
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In this paper we propose to enrich the four-valued modal logic associated to Monteiro’s Tetravalent modal algebras (TMAs) with a deductive implication, that is, such that the Deduction Meta–theorem holds in the resulting logic. All this lead us to establish some new connections between TMAs, symmetric (or involutive) Boolean algebras, and modal algebras for extensions of S5, as well as their lo...
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In this paper several systems of modal logic based on four-valued matrices are presented. We start with pure modal logics, i.e. modal logics with modal operators as the only operators, using the Polish framework of structural consequence relation. We show that with a four-valued matrix we can define modal operators which have the same behavior as in pure S5 (S5 with only modal operators). We th...
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We introduce a family of modal expansions of Belnap-Dunn four-valued logic and related systems, and interpret them in many-valued Kripke structures. Using algebraic logic techniques and topological duality for modal algebras, and generalizing the so-called twist-structure representation, we axiomatize by means of Hilbert-style calculi the least modal logic over the four-element Belnap lattice a...
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It is well-known that satisfiability (and hence validity) in the minimal classical modal logic is a PSPACE-complete problem. In this paper we consider the satisfiability and validity problems (here they are not dual, although mutually reducible) for the minimal modal logic over a finite Lukasiewicz chain, and show that they also are PSPACE-complete. This result is also true when adding either t...
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ژورنال
عنوان ژورنال: The Bulletin of Symbolic Logic
سال: 2020
ISSN: 1079-8986,1943-5894
DOI: 10.1017/bsl.2020.27