Coalgebraic modal logic of finite rank

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...

Coalgebraic Modal Logic in CoCasl

We extend the algebraic-coalgebraic specification language CoCasl by full coalgebraic modal logic based on predicate liftings for functors. This logic is more general than the modal logic previously used in CoCasl and supports the specification of a variety of modal logics, such as graded modal logic, majority logic, and probabilistic modal logic. CoCasl thus becomes a modern modal language tha...

Coalgebraic Modal Logic Beyond Sets

Polyadic coalgebraic modal logic is studied in the setting of locally presentable categories. It is shown that under certain assumptions, accessible functors admit expressive logics for their coalgebras. Examples include typical functors used to describe systems with name binding, interpreted in nominal sets.

Rank-1 Modal Logics Are Coalgebraic

Coalgebras provide a unifying semantic framework for a wide variety of modal logics. It has previously been shown that the class of coalgebras for an endofunctor can always be axiomatised in rank 1. Here we establish the converse, i.e. every rank 1 modal logic has a sound and strongly complete coalgebraic semantics. As a consequence, recent results on coalgebraic modal logic, in particular gene...