Hybridization of Institutions

Abstract

Abstract. Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to 'universalize' the hybridization idea. Following the lines of [16], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institution-independent level. The method extends arbitrary institutions with Kripke semantics (for multi-modalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL) determines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features.

Paraconsistency in hybrid logic

“…Works on hierarchical hybrid logic [71] and hybridization [76,70,79] have been especially addressed lately.…”

Refinement in hybridised institutions

“…Instead of choosing a particular version of hybrid logic, we play with hybridised logics. The latter are the result of hybridising [MMDB11] whatever logic is found suitable for expressing and reasoning about the requirements at the configuration (static) level. This process, hybridisation, was characterised in [MMDB11,DM14] as well as in [Mad13].…”

“…The latter are the result of hybridising [MMDB11] whatever logic is found suitable for expressing and reasoning about the requirements at the configuration (static) level. This process, hybridisation, was characterised in [MMDB11,DM14] as well as in [Mad13]. To be completely general, it is framed in the context of the theory of institutions of J. Goguen and R. Burstall [GB92,Dia08], each logic (base and hybridised) treated abstractly as an institution.…”

“…This paper extends preliminary work on refinement in hybridised institutions [MMB13] along three main directions: i) the proof of a Hennessy-Milner result for hybridised logics, ii) the characterisation of two dual notions of refinement, forward and backward, and iii) a discussion on refinement of specifications. From a wider perspective, it is part of a broader research line on logics for software reconfigurabilty documented in [MMDB11,DM14] (for the hybridisation process), and [MFMB11, MNMB13, MMDB11, MMB13] (for the associated design methodology).…”

“…The paper is organised as follows: Section 2 recalls institutions as abstract characterisations of logics and provides a brief, and simplified, overview of the hybridisation method proposed in [MMDB11,DM14]. This forms the context for the paper's contribution.…”