Modal Logic over Finite Structures

Modal Logic over Finite Structures

Elementary Modal Logics over Transitive Structures

We show that modal logic over universally first-order definable classes of transitive frames is decidable. More precisely, let K be an arbitrary class of transitive Kripke frames definable by a universal first-order sentence. We show that the global and finite global satisfiability problems of modal logic over K are decidable in NP, regardless of choice of K. We also show that the local satisfi...

Satisfiability vs. Finite Satisfiability in Elementary Modal Logics

We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our attention to finite structures. Many decidability and undecidability results for the elementary modal logics were proved separately for general satisfiability and fo...

Four-valued modal logic: Kripke semantics and duality

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...

Decomposing Modal Logic

We provide a detailed analysis of very weak fragments of modal logic. Our fragments lack connectives that introduce non-determinism and they feature restrictions on the modal operators, which may lead to substantial reductions in complexity. Our main result is a general game-based characterization of the expressive power of our fragments over the class of finite structures.