Refinement modal logic

Refinement Modal Logic

In this paper we present refinement modal logic. A refinement is like a bisimulation, except that from the three relational requirements only ‘atoms’ and ‘back’ need to be satisfied. Our logic contains a new operator ∀ in additional to the standard modalities 2 for each agent. The operator ∀ acts as a quantifier over the set of all refinements of a given model. We call it the refinement operato...

Algebraic semantics of refinement modal logic

We develop algebraic semantics of refinement modal logic using duality theory. Refinement modal logic has quantifiers that are interpreted using a refinement relation. A refinement relation is like a bisimulation, except that from the three relational requirements only ‘atoms’ and ‘back’ have to be satisfied. We study the dual notion of refinement on algebras and present algebraic semantics of ...

Closing a Gap in the Complexity of Refinement Modal Logic

Refinement Modal Logic (RML), which was recently introduced by Bozzelli et al., is an extension of classical modal logic which allows one to reason about a changing model. In this paper we study computational complexity questions related to this logic, settling a number of open problems. Specifically, we study the complexity of satisfiability for the existential fragment of RML, a problem posed...

The Complexity of One-Agent Refinement Modal Logic

We investigate the complexity of satisfiability for one-agent Refinement Modal Logic (RML), a known extension of basic modal logic (ML) obtained by adding refinement quantifiers on structures. It is known that RML has the same expressiveness as ML, but the translation of RML into ML is of non-elementary complexity, and RML is at least doubly exponentially more succinct than ML. In this paper, w...

Modal Logic