An augmented modal logic.

On an Intuitionistic Modal Logic

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4—our formulation has several important metatheoretic properties. In addition, we study models of IS4, not in the framework of Kripke semantics, but in the more general framework of category theo...

An S4F-related Monotonic Modal Logic

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...

An Industrial Application of Modal Process Logic

Modal process logic is an extension of CCS that allows for more expressive specifications. We show how modal process logic was successfully applied in the development of a failure recovery protocol for an air-traffic information system now in service at Heathrow airport. Two example systems are used to show that CCS itself was not suitable for this application.

Modal Logic

Acyclic modal logic: an exercise in irreflexivization

Given a unimodal logic Λ extending the modal logic of reflexive frames T = K⊕2p→ p (the symbol ⊕ is used in the same way as in [3]), we can define several irreflexive or non-reflexive counterparts of Λ. Our first approach will be semantical. As usual, given a set W , define ∆W := {〈x, x〉 | x ∈W}. Definition 1.1 The irreflexivization of a frame F = 〈W,R〉 is 〈W,R〉• := 〈W,R − ∆W 〉. For X a class o...