This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and fixes the bad. In essence, modal logic is a simple formalism for working with relational structures (or multigraphs). But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its effectiveness as a representa...

The aim of the present paper is to discuss two different approaches for formulating independence friendly (IF) modal logic. In one of them, the language of basic modal logic is enriched with the slash notation familiar from IF first-order logics, and the resulting logic is interpreted in terms of games and uniform strategies. A different approach is formulated in the present paper: an IF modal ...

Sabotage modal logic was proposed in 2003 as a format for analyzing games that modify the graphs they are played on. We investigate some model-theoretic and proof-theoretic aspects of sabotage modal logic, which has largely come to be viewed as an early dynamic logic of graph change. Our first contribution is a characterization theorem for sabotage modal logic as a fragment of first-order logic...

A framework is developed that extends Hilbert-style proof systems for propositional and modal logics to comprehend their team-based counterparts. The method is applied to classical propositional logic and the modal logic K. Complete axiomatizations for their team-based extensions, propositional team logic PTL and modal team logic MTL, are presented. 1998 ACM Subject Classification F.4.1 Mathema...

In the last 20 years modal logic has been applied to numerous areas of computer science, including artificial intelligence, program verification, hardware verification, database theory, and distributed computing. There are twomain computational problems associated with modal logic. The first problem is checking if a given formula is true in a given state of a given structure. This problem is kn...

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...

In the study of knowledge representation formalisms, there is a current interest in the question of how different formal languages compare in their ability to compactly express semantic properties. Recently, French et al. [9] have shown that modal logics with a modality for public announcement, for everybody knows, and for somebody knows are all exponentially more succinct than basic modal logi...

Frank M. Brown Abstract: The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather dis...

We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and modal logic. In addition, we give novel labeled tableau calculi for PD, MDL, and EMDL. We prove soundness, completeness and termination for each of the labeled ...

The title reflects my conviction that, viewed semantically, modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notab...