Abstract
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.
Original language | English |
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Pages (from-to) | 155-199 |
Number of pages | 45 |
Journal | Journal of Logic and Computation |
Volume | 27 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2017 |
Keywords
- Belnap logic
- Bilattices
- Many-valued modal logic
- Paraconsistent Nelson logic