Many-Valued Coalgebraic Modal Logic: One-step Completeness and Finite Model Property

Finite Model Property of Pretransitive Modal Logic

The finite model property of the quasi-transitive modal logic K32 = K ⊕ ✷✷p → ✷✷✷p is proved. This modal logic is conservatively extended to the tense logic Kt32. We present a Gentzen sequent calculus Gt32 for Kt 3 2 which admits cut elimination. The sequent calculus Gt 3 2 is shown to have the finite model property by a construction of finite syntactic model. It follows that Kt32 has the finit...

Coalgebraic modal logic: soundness, completeness and decidability of local consequence

This paper studies finitary modal logics, interpreted over coalgebras for an endofunctor, and establishes soundness, completeness and decidability results. The logics are studied within the abstract framework of coalgebraic modal logic, which can be instantiated with arbitrary endofunctors on the category of sets. This is achieved through the use of predicate liftings, which generalise atomic p...

Coalgebraic modal logic of finite rank

A Finite Model Construction for Coalgebraic Modal Logic

In recent years, a tight connection has emerged between modal logic on the one hand and coalgebras, understood as generic transition systems, on the other hand. Here, we prove that (finitary) coalgebraic modal logic has the finite model property. This fact not only reproves known completeness results for coalgebraic modal logic, which we push further by establishing that every coalgebraic modal...

Tableaus for many-valued modal logic

We continue a series of papers on a family of many-valued modal logics, a family whose Kripke semantics involves many-valued accessibility relations. Earlier papers in the series presented a motivation in terms of a multiple-expert semantics. They also proved completeness of sequent calculus formulations for the logics, formulations using a cut rule in an essential way. In this paper a novel cu...