Transition systems can be viewed either as process diagrams or as Kripke structures. The rst perspective is that of process theory, the second that of modal logic. This paper shows how various formalisms of modal logic can be brought to bear on processes. Notions of bisimulation can not only be motivated by operations on transition systems, but they can also be suggested by investigations of mo...

ABSTRACT: Deontic logic can be used to formalise legal rules. The automation of reasoning in deontic logic can therefore be used as the basis of a legal expert system. In this paper we investigate the automation of deontic logic using tableau calculi for modal logics. The correspondance between the deontic and modal logics is outlined and the tableau for the modal logics used in the prover are ...

This paper investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We rst develop matrix as well as Kripke style semantics for those logics. Then, by extending the Godel-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting...

We discuss Saul Kripke’s seminal 1963 paper ’Semantical Considerations on Modal Logic’, and sketch subsequent developments in modal logic with a view to their general logical thrust.

We present a syntactic abstraction method to reason about first-order modal logics by using theorem provers for standard first-order logic and for propositional modal logic.

We develop a translation-based view dual of modal logic as the study of intensional languages that are at the same time interesting expressive and decidable parts of standard logical systems. This tandem approach improves our understanding of modal logic – while at the same time, it extends the range of modal notions and techniques into broader areas of standard logic. 1 Translation as a Way of...

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw(φ → ψ) → (Kwφ → Kwψ). Knowing whether logic cannot define many common frame properties, and its expressive po...

While propositional modal logic is a standard tool, first-order modal logic is not. Indeed, it is not generally understood that conventional first-order syntax is insufficiently expressible. In this paper we sketch a natural syntax and semantics for first-order modal logic, and show how it easily copes with well-known problems. And we provide formal tableau proof rules to go with the semantics,...

Propositional modal logic is a standard tool in many disciplines, but first-order modal logic is not. There are several reasons for this, including multiplicity of versions and inadequate syntax. In this paper we sketch a syntax and semantics for a natural, well-behaved version of first-order modal logic, and show it copes easily with several familiar difficulties. And we provide tableau proof ...

We present ongoing work into the systematic study of the use of dual adjunctions in coalgebraic modal logic. We introduce a category of internal models for a modal logic. These are constructed from syntax, and yield a generalised notion of canonical model. Further, expressivity of a modal logic is shown to be characterised by factorisation of its models via internal models and the existence of ...