We present the experience gained from implementing a new decision procedure for both graded and probabilistic modal logic. While our approach uses standard tableaux for propositional connectives, modal rules are given by linear constraints on the arguments of operators. The implementation uses binary decision diagrams for propositional connectives and a linear programming library for the modal ...

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E . In contrast to the wellknown interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE , but rather by a suitable complete Heyting algebra H . The canonical map relating H and ΩE both serves to interpret equality and provides a modal...

3 Equivalences, Modal and Temporal Logics 5 3.1 Interactive games and bisimulations . . . . . . . . . . . . . . . 7 3.2 Modal logic and bisimulations . . . . . . . . . . . . . . . . . . . 9 3.3 Temporal properties and modal mu-calculus . . . . . . . . . . 10 3.4 Second-order propositional modal logic . . . . . . . . . . . . . . 15 3.5 Fixed point and second-order games . . . . . . . . . . . . ....

This paper proposes two methods for realising automated reasoning about agent-based systems. The framework for modelling intelligent agent behaviour that we focus on is a core of KARO logic, an expressive combination of various modal logics including propositional dynamic logic, a modal logic of knowledge, a modal logic of wishes, and additional non-standard operators. The first method we prese...

This paper introduces a novel monotonic modal logic, allowing us to capture the nonmonotonic variant of the modal logic S4F: we add a second new modal operator into the original language of S4F, and show that the resulting formalism is strong enough to characterise the logical consequence of (nonmonotonic) S4F, as well as its minimal model semantics. The latter underlies major forms of nonmonot...

In this paper we deal with the semantics for quantified modal logic, QML in short, and their philosophical relevance. In the first part we introduce Kripke semantics for the first-order modal language L= with identity, then we consider some unsatisfactory features of this account from an actualist point of view. In addition, we show that the calculus QE .K + BF on free logic, with the Barcan fo...

Algebraic logic compacts many small steps of general logical derivation into large steps of equational reasoning. We illustrate this by representing epistemic logic and game logic in modal semirings and modal Kleene algebras.

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...