We present the dual to Birkhoff’s variety theorem in terms of predicates over the carrier of a cofree coalgebra (i.e., in terms of “coequations”). We then discuss the dual to Birkhoff’s completeness theorem, showing how closure under deductive rules dualizes to yield two modal operators acting on coequations. We discuss the properties of these operators and show, given a familiar condition on t...

We propose a family of dynamic logics of propositional control. They extend classical propositional logic by a variety of modal operators of assignment, and modal operators of transfer of control over a propositional variable. We also present an extension with operators of knowledge. We essentially focus on their formal properties, stating their complexity and their proof theory.

This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction a...

We present a coinductive definition of models for modal logics and show that it provides a homogeneous framework in which it is possible to include different modal languages ranging from classical modalities to operators from hybrid and memory logics. Moreover, results that had to be proved separately for each different language –but whose proofs were known to be mere routine– now can be proved...

We consider the modal-calculus due to Kozen, which is a nitary modal logic with least and greatest xed points of monotone operators. We extend the existing duality between the category of modal algebras with homomorphisms and the category of descriptive modal frames with contractions to the case of having xed point operators. As a corollary, we obtain completeness results for two proof systems ...

Higher dimensional automata (HDA) are a model of concurrency that can express most of the traditional partial order models like Mazurkiewicz traces, pomsets, event structures, or Petri nets. Modal logics, interpreted over Kripke structures, are the logics for reasoning about sequential behavior and interleaved concurrency. Modal logic is a well behaved subset of first-order logic; many variants...

Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from so-called predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence ...

The parameters of the parametrized modal operators [p] and 〈p〉 usually represent agents (in the epistemic interpretation) or actions (in the dynamic logic interpretation) or the like. In this paper the application of the idea of parametrized modal operators is extended in two ways: First of all a modified neighbourhood semantics is defined which permits among others the interpretation of the pa...