Allegories are enriched categories generalizing a category of sets and binary relations. In this paper, we extend a new, recently-introduced conceptual data model based on allegories by adding support for modal operators and developing a modal interpretation of the model in any allegory satisfying certain additional (but natural) axioms. The possibility of using different allegories allows us t...

We study dynamic modal operators that can change the model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to swap, delete or add pairs of related elements of the domain, while traversing an edge of the accessibility relation. We study these languages together with the sabotage modal logic, which can arbitrarily delete edges of...

We briefly examine the modal formulae that can be derived in Multiplicative Additive Linear Logic (MALL) and some extensions by using Tarksi’s extensional modal operators. We also breifly compare this with a substructural form of the modal logic K.

The aim of this paper is to introduce a new formalism for multi-agent systems that captures (true) concurrency and independence. We begin describing a complete and decidable propositional multi-modal logic. The language, similar to Propositional Dynamic Logic in many aspects, di ers from usual modal logic: modal operators are non-atomic (they are built out of basic actions) and capture concurre...

Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspondence proof of Löb’s formula from modal logic. It gives calculational proofs of two fundamental st...

(a) the modal auxiliaries ‘might’ and ‘must’, (b) the (sentential) adverbs ‘possibly’ and ‘probably’, (c) the various sentential operators that can be constructed from the modal adjectives ‘possible’ and ‘probable’, such as ‘it’s (very) possible that’, ‘it’s (very) probable that’, ‘there is a strong possibility that’, ‘is at least as probable as’, ‘is more probable than’, etc., and (d) those op...

A distributed system, possibly asynchronous, is said to have perfect recall if at all times each processor's state includes a record of all its previous states. The completeness of a propositional modal logic of knowledge and time with respect to such systems is established. The logic includes modal operators for knowledge, and the temporal operators \next" and \until."

Description Logics (DLs) are a family of logic-based formalisms for the representation of and reasoning about knowledge. Classical DLs are fragments of first-order logic and therefore aim at capturing static knowledge. Alas, the lack of means of DLs to capture dynamic aspects of knowledge has been often criticized because many important DL applications depend on this kind of knowledge. As a rea...

We introduce a formal language for multi-agent systems based on new modal operators. The modal operators express concurrency at the syntactic level. Operators containing quantifiers describe the evolution of a system where each agent has knowledge of other agents’ attitude toward a goal but not of their actions. This result is obtained without introducing standard epistemic operators. The seman...

This paper investigates refinement techniques for semantic tableau calculi. The focus is on techniques to reduce branching in inference rules and thus allow more effective ways of carrying out deductions. We introduce an easy to apply, general principle of atomic rule refinement, which depends on a purely syntactic condition that can be easily verified. The refinement has a wide scope, for exam...