期刊
JOURNAL OF LOGIC AND COMPUTATION
卷 27, 期 1, 页码 155-199出版社
OXFORD UNIV PRESS
DOI: 10.1093/logcom/exv038
关键词
Many-valued modal logic; Belnap logic; bilattices; paraconsistent Nelson logic
资金
- Marie Curie programme of the European Union [PIEF-GA-2010-272737-BMDF]
- VIDI grant of the Netherlands Organization for Scientific Research (NWO) [016.138.314]
- government of Catalonia [2009SGR1433]
- government of Spain [MTM2011-25747]
- European Union
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 and some of its axiomatic extensions. We study the algebraic models of these systems, relating them to the algebraic semantics of classical multi-modal logic. This link allows us to prove that both local and global consequence of the least four-valued modal logic enjoy the finite model property and are therefore decidable.
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