Kowalski and Sergot's Event Calculus (EC) is a simple temporal formalism that, given a set of event occurrences, derives the maximal validity intervals (MVIs) over which properties initiated or terminated by these events hold. It does so in polynomial time with respect to the number of events. Extensions of its query language with Boolean connectives and operators from modal logic have been sho...

Focused proofs are sequent calculus proofs that group inference rules into alternating negative and positive phases. These phases can then be used to define macro-level inference rules from Gentzen’s original and tiny introduction and structural rules. We show here that the inference rules of labeled proof systems for modal logics can similarly be described as pairs of such negative and positiv...

In this paper we deene two logics, KL n and BL n , and present tableau-based decision procedures for both. KL n is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BL n is somewhat similar; it is a temporal logic that contains con...

We provide a detailed analysis of very weak fragments of modal logic. Our fragments lack connectives that introduce non-determinism and they feature restrictions on the modal operators, which may lead to substantial reductions in complexity. Our main result is a general game-based characterization of the expressive power of our fragments over the class of finite structures.

We provide a detailed analysis of very weak fragments of modal logic. Our fragments lack connectives that introduce nondeterminism and they feature restrictions on the modal operators, which may lead to substantial reductions in complexity. Our main result is a general game-based characterization of the expressive power of our fragments over the class of finite structures.

We consider the problem of obtaining Hennessy-Milner soundness and completeness-the coincidence of logical equivalence and bisimilarity-in the setting of transition systems with synchronous concurrent composition. Starting from a richly expressive modal logic, motivated by resource semantics and distributed systems modelling, including both additive and multiplicative propositional connectives ...

We discuss the logic of preferences, introducing modal connectives that reflect reasons to prefer that one formula rather than another be true. An axiomatic analysis of two such logics is presented.

Sahlqvist correspondence theory [3], [4] is one of the most important and useful results of classical modal logic. It gives a syntactic identification of a class of modal formulas whose associated normal modal logics are strongly complete with respect to elementary (i.e. first-order definable) classes of frames. Every Sahlqvist formula is both canonical and corresponds to some elementary frame ...

This paper presents a temporal belief logic called LTB. In addition to the usual connectives of linear discrete temporal logic, LTB contains an indexed set of modal belief connectives,via which it is possible to represent the belief systems of resource-bounded reasoning agents. The applications of LTB in general, and its use for representing the dynamic properties of multi-agent AI systems in p...

After an overview of EQPL (exogenous quantum propositional logic), the proof of its weak completeness is outlined, using a non trivial extension of the Fagin-Halpern-Megiddo technique. A new logic (EQPL – exogenous quantum propositional logic), embodying all that is stated in the postulates of quantum physics, was proposed in [2, 3, 4] for modeling and reasoning about quantum systems. The logic...