Completeness and Decidability Results for Hybrid(ised) Logics

Science of Computer Programming

Martins

et al. 2016

Self Cite

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.

Section: Motivation and Contextsupporting

confidence: 57%

Proof theory for hybrid(ised) logics

Neves

Science of Computer Programming

Martins

et al. 2016

Self Cite

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.

“…Recent work [45] reports preliminary general results in this direction. In particular, it is shown that, whenever the base logic has the usual Boolean connectives, hybridisation preserves decidability, and furthermore, the generated calculus is sound and complete whenever the one for the base logic is.…”

Section: Concludingmentioning

confidence: 98%

Reuse and Integration of Specification Logics: The Hybridisation Perspective

Barbosa

Martins

Theoretical Information Reuse and Integration

et al. 2016

Self Cite

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. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system's configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration.

“…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.…”

Section: Natural Transformationsmentioning

confidence: 99%

Asymmetric Combination of Logics is Functorial: A Survey

Neves

Recent Trends in Algebraic Development Techniques

Barbosa

et al. 2017

Self Cite

Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a given base logic. These examples are surveyed in the paper under a particular perspective -that this sort of combination of logics possesses a functorial nature. Such a view gives rise to several interesting questions. They range from the problem of combining translations (between logics), to that of ensuring property preservation along the process, and the way different asymmetric combinations can be related through appropriate natural transformations.3 (_) op applied to a functor F : C → D induces a functor F op : C op → D op such that for any object or arrow a in C, F op (a) = F (a).