A refoundation of modal logic.

Modal Logic

Modal Logic As Dialogical Logic

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...

A Simplest Undecidable Modal Logic

Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very “simple” modal logics can be undecidable: We show that there is an undecidable modal logic that can be obtained by restricting the allowed models with a first-order formula in which only universal quantifiers appear.

A Real-Valued Modal Logic

A many-valued modal logic is introduced that combines the usual Kripke frame semantics of the modal logic K with connectives interpreted locally at worlds by lattice and group operations over the real numbers. A labelled tableau system is provided and a coNEXPTIME upper bound obtained for checking validity in the logic. Focussing on the modal-multiplicative fragment, the labelled tableau system...

Circumscription in a Modal Logic

In this paper, we extend circumscription [McCarthy, 80] to a propositional modal logic of knowledge of one agent. Instead of circumscribing a predicate, we circumscribe the knowledge operator "K" in a formula. In order to have a nontrivial circumscription schema, we extend $5 modal logic of knowledge by adding another modality "Val" and a universal quantifier over base sentences (sentences whic...