Abstract
We propose \(\varepsilon^\downarrow(\mathcal{\vec{D}})\)-logic as a formal foundation for the specification and development of event-based systems with data states. The framework is presented as an institution in the sense of Goguen and Burstall and the logic itself is parametrised by an underlying institution \(\mathcal{\vec{D}}\) whose structures are used to model data states. \(\varepsilon^\downarrow(\mathcal{\vec{D}})\)-logic is intended to cover a broad range of abstraction levels from abstract requirements specifications up to constructive specifications. It uses modal diamond and box operators over complex actions adopted from dynamic logic. Atomic actions are pairs where e is an event and \(\psi\) a state transition predicate capturing the allowed reactions to the event. To write concrete specifications of recursive process structures we integrate (control) state variables and binders of hybrid logic. The semantic interpretation relies on event/data transition systems. For the presentation of constructive specifications we propose operational event/data specifications allowing for familiar, diagrammatic representations by state transition graphs. We show that \(\varepsilon^\downarrow(\mathcal{\vec{D}})\)-logic is powerful enough to characterise the semantics of an operational specification by a single \(\varepsilon^\downarrow(\mathcal{\vec{D}})\)-sentence. Thus the whole (formal) development process for event/data-based systems relies on \(\varepsilon^\downarrow(\mathcal{\vec{D}})\)-logic and its semantics as a common basis. It is supported by a variety of implementation constructors which can express, among others, event refinement and parallel composition. Due to the genericity of the approach, it is also possible to change a data state institution during system development when needed. All steps of our formal treatment are illustrated by a running example.
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References
Abrial J-R (2013) Modeling in event-B: system and software engineering. Cambridge University Press
Bauer SS, Hennicker R, Wirsing M (2011) Interface theories concurrency and data. Theor Comput Sci 412(28):3101-3121
Bohrer B, Platzer A (2018) A hybrid, dynamic logic for hybrid-dynamic information flow. In: Dawar A,Grädel E (eds)Proc 33rd ann ACM/IEEE symp logic in computerscience, pp 115-124. ACM
Bräuner T (2010) Hybrid logic and its proof-theory. Appl Log Ser. Springer
deAlfaro L, Henzinger TA (2001) Interface automata. In: Min Tjoa A, Gruhn V (eds) Proc8th Europ software engineering conf 9th ACM SIGSOFT intl. symp. foundations of software engineering, pp 109-120. ACM
Diaconescu R (2008) Institution-independent model theory. Studies inuniversal logic. Birkhäuser
Diaconescu R, Madeira A (2016) Encoding hybridized institutions into first-order logic. Math Struct Comput Sci 26(5):745-788
Diaconescu R, Stefaneas PS (2007) Ultraproducts and possible worlds semantics in institutions.Theor Comput Sci 379(1-2):210-230
Fajardo R, Finger M (2002) Non-normal modalisation. In: Balbiani P,Suzuki N-Y, Wolter F, Zakharyaschev M (eds) Advances in modal logic 4, papers from the fourth conference on ``advances in modal logic,'' held in Toulouse, France, 30 September-2 October 2002, pp83-96. King's College Publications
Finger M, Gabbay DM (1992) Adding a temporal dimension to a logic system. J Log Lang Inform 1(3):203-233
Farrell M, Monahan R, Power JF (2017) An institution for event-B.In: James P, Roggenbach M (eds) Rev sel papers 23rd IFIP WG 1.3 intl ws recent trends in algebraic development techniques, vol 10644 of lect notes comp sci, pp 104-119. Springer
Goguen JA, Burstall RM (1992) Institutions: abstract model theory for specification and programming. J ACM 39:95-146
Groote JF, Mousavi MR (2014) Modeling and analysis of communicatingsystems. MIT Press
Goranko V (1994) Temporal logic with reference pointers. In: Proc1st intl conf temporal logic, vol 827 of lect notes comp sci, pp133-148. Springer
Gorrieri R, Rensink A (2000) Action refinement. In: Bergstra JA,Ponse A, Smolka SA (eds) Handbook of process algebra, pp 1047-1147. Elsevier
Goguen JA, Rosu G (2002) Institution morphisms. Formal Asp Comput 13(3-5):274-307
Harel D, Kozen D, Tiuryn J (2000) Dynamic logic. MIT Press
Hennicker R, Madeira A, Knapp A (2019) A hybrid dynamic logic forevent/data-based systems. In: Hähnle R, van der Aalst WMP (eds) Proc 22nd intl conf fundamental approaches to software engineering, vol 11424 of lect notes comp sci, pp 79-97. Springer
Knapp A, Mossakowski T, Roggenbach M, Glauer M (2015) An institution for simple UML state machines. In: Egyed A, Schaefer I (eds) Proc 18th intl conf fundamental approaches to software engineering,vol 9033 of lect notes comp. sci, pp 3-18. Springer
Lamport L (2003) Specifying systems: the TLA+ language and tools for hardware and software engineers. Addison-Wesley
Lynch NA (2003) Input/output automata: basic, timed, hybrid, probabilistic, dynamic, \(\ldots\). In: Amadio RM, Lugiez D (eds) Proc 14th intl conf concurrency theory, vol 2761 of lect notes comp sci, pp 187-188. Springer
Mac Lane S (1998) Categories for the working mathematician, 2nd edn. Springer
Madeira A, Barbosa LS, Hennicker R, Martins MA (2018) A logic for the stepwise development of reactive systems. Theor Comput Sci 744:78-96
Mouelhi S, Chouali S, Mountassir H (2009) Refinement of interface automata strengthened by action semantics. Electron Notes Theor Comput Sci 253(1):111-126
Mossakowski T, Diaconescu R, Tarlecki A (2009) What is a logic translation? Logica Universalis 3(1):95-124
Martins MA, Madeira A, Diaconescu R, Barbosa LS (2011) Hybridization of institutions. In: Corradini A, Klin B, Cîrstea C (eds) Proc 4th intl conf algebra and coalgebra in computer science, vol 6859 of lect notes comp sci, pp 283-297. Springer
Mossakowski T, Maeder C, Lüttich K (2007) The heterogeneous tool set (Hets). In: Beckert B (ed) Proc 4th intl verification ws, vol 259 of CEUR ws proc CEUR-WS.org
OMG (Object Management Group) (2014) Object constraint language.Standard formal/14-02-03. OMG
OMG (Object Management Group) (2017) Unified modeling language. Standard formal/17-12-05. OMG
Poizat P, Royer J-C (2006) A formal architectural description language based on symbolic transition systems and modal logic. J Univ Comput Sci 12(12):1741-1782
Sannella D, Tarlecki A (1988) Toward formal development of programs from algebraic specifications: implementations revisited. Acta Inf 25(3):233-281
Sannella D, Tarlecki A (2012) Foundations of algebraic specification and formal software development. EATCS Monographs in Theoretical Computer Science. Springer
ter Beek MH, Fantechi A, Gnesi S, Mazzanti F ( 2008) An action/state-based model-checking approach for the analysis of communication protocols for service-oriented applications. In: Leue S, Merino P (eds) Sel papers 12th intl ws formal methods for industrial critical systems, vol 4916 of lect notes comp sci, pp 133-148. Springer
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James Woodcock
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A. Madeira is supported by the European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 and by National Funds through the Portuguese funding agency FCT - within the Projects POCI-01-0145-FEDER-029946 and UID/MAT/04106/2019.
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Hennicker, R., Knapp, A. & Madeira, A. Hybrid dynamic logic institutions for event/data-based systems. Form Asp Comp 33, 1209–1248 (2021). https://doi.org/10.1007/s00165-021-00550-7
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DOI: https://doi.org/10.1007/s00165-021-00550-7