We present matrix proof systems for both constantand varying-domain versions of the first-order modal logics K, K4, D, D4, T, 84 and 86 based on modal versions of Herbrand's Theorem specifically formulated to support efficient automated proof search. The systems treat the mil modal language (no normal-forming) and admit straightforward structure sharing implementations. A key fsature of our app...

Characterization results for modal logics below first order identifies them as a fragment of first order logic. These results are very important to analyze the expressive power of a given logic. The first work in this direction was done by van Benthem [12] who used bisimulations to characterize the basic modal logic as the bisimulation invariant fragment of first order logic. There exists a hug...

We take the well-known intuitionistic modal logic of Fischer Servi with semantics in bi-relational Kripke frames, and give the natural extension to topological Kripke frames. Fischer Servi’s two interaction conditions relating the intuitionistic pre-order (or partial-order) with the modal accessibility relation generalise to the requirement that the relation and its inverse be lower semi-contin...

Most of the work on quantum logic (since the seminal paper [4]) has continued to adopt the lattice of closed subspaces of a Hilbert space as the basis for its semantics [11, 8]. Here we take a quite different approach, what we call the exogenous approach. The key idea is to keep the models of the classical logic (say propositional logic) as they are, to produce models for the envisaged quantum ...

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. T...

A framework is developed that extends calculi for propositional, modal and predicate logics to calculi for team-based logics. This method is applied to classical and quantified propositional logic, first-order logic and the modal logic K. Complete axiomatizations for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL and the dependence-atom-free fragmen...

This article considers the link between theory and practice in agentoriented programming. We begin by rigorously defining a new formal specification language for autonomous agents. This language is the expressive branching time logic CTL , enriched by the addition of two further modal connectives, for representing knowledge and seeing to it that (stit). These connectives are grounded: given a c...

Linear logic presents a unified framework for describing and reasoning about stateful systems. Because of its view of hypotheses as resources, it supports such phenomena as concurrency, external and internal choice, and state transitions that are common in such domains as protocol verification, concurrent computation, process calculi and games. It accomplishes this unifying view by providing lo...

A modal analogue of Lindstrr om's characterization of rst-order logic is proved. Basic modal logics are characterized as the only modal logics that have a notion of nite rank, or, equivalently, as the strongest modal logic whose formulas are preserved under ultra-products over !. Also, basic modal logic is the strongest classical logic whose formulas are preserved under bisimulations and ultra-...

This paper presents the extension of results on reasoning with totally ordered belief bases to the partially ordered case. The idea is to reason from logical bases equipped with a partial order expressing relative certainty and to construct a partially ordered deductive closure. The difficult point lies in the fact that equivalent definitions in the totally ordered case are no longer equivalent...