Proof theory for hybrid(ised) logics

Abstract

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. In a series of papers this process has been detailed and taken as a basis for a specification methodology for reconfigurable systems. The present paper extends this work by showing how a proof calculus (in both a Hilbert and a tableau based format) for the hybridised version of a logic can be systematically generated from a proof calculus for the latter. Such developments provide the basis for a complete proof theory for hybrid(ised) logics, and thus pave the way to the development of (dedicated) proof support.

Asymmetric Combination of Logics is Functorial: A Survey

“…Often such a study has been made on a case-by-case basis e.g. [11,26,27]. This paper, on the other hand, surveys a more general, functorial perspective using three different asymmetric combinations of logics as case-studies.…”

A method for rigorous design of reconfigurable systems

“…In some cases, moreover, it may lead to simpler verification strategies. Actually, references [87,88] show that the hybridisation method can be extended so that not only the logic is hybridised but also its calculus is systematically enriched into a calculus for the hybridised logic. The latter is shown to be sound and complete whenever the calculus associated to the underlying, base logic is.…”

Adding Proof Calculi to Epistemic Logics with Structured Knowledge

“…The structure of knowledge representation, as introduced in the reference [19], was further endowed with an entailment system adequate for the respective satisfaction relation. The parametric principle of the constructions of logic calculus and the respective characterisations are inspired in the approach we followed for parametrised hybrid logics in the reference [22].…”