Abstract
We provide motivation for composition-nominative approach and its main underlying principles. We give a brief introduction to the hierarchy of composition-nominative logics (CNL) and discuss possible applications of these logics in formal approaches for software development. CNL are algebra-based logics of partial predicates and functions. They are constructed in a semantic-syntactic style on the methodological basis, which is common with programming. Main attention in the paper is paid to the first-order CNL. The satisfiability problem for the first-order CNL is addressed. We show the reduction of the problem in hand to the satisfiability problem for classical first-order logic with function symbols. The reduction proposed requires extension of logic language and logic models with an infinite number of unessential variables. The method presented in the paper enables one to use existent satisfiability checking algorithms and tools for solving instances of the CNL satisfiability problem. Thus, many standard techniques developed for classical logics can be applied in CNL-based approaches for program reasoning.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
George, C., Haxthausen, A.E., Hughes, S., et al.: The RAISE Development Method. Prentice Hall, London (1995)
Nikitchenko, N.S.: A Composition Nominative Approach to Program Semantics. Technical Report IT–TR 1998-020, Technical University of Denmark (1998)
Basarab, I.A., Gubsky, B.V., Nikitchenko, N.S., Red’ko, V.N.: Composition Models of Databases. In: Eder, J., Kalinichenko, L.A. (eds.) East-West Database Workshop (Workshops in Computing Series), pp. 221–231. Springer, London (1995)
Nikitchenko, M.S., Shkilnyak, S.S.: Mathematical logic and theory of algorithms. Publishing house of Taras Shevchenko National University of Kyiv (2008) (in Ukrainian)
Nikitchenko, M.S.: Composition-nominative aspects of address programming. Kibernetika I Sistemnyi Analiz 6, 24–35 (2009) (in Russian)
Mendelson, E.: Introduction to Mathematical Logic, 4th edn. Chapman & Hall, London (1997)
Nielson, H.R., Nielson, F.: Semantics with Applications: A Formal Introduction. John Wiley & Sons Inc. (1992)
Winskel, G.: The Formal Semantics of Programming Languages. MIT Press, Cambridge (1993)
Kleene, S.C.: Introduction to Metamathematics. Van Nostrand, New York (1952)
Nikitchenko, M.S., Tymofieiev, V.G.: Satisfiability Problem in Composition-Nominative Logics of Quantifier-Equational Level. In: Proc. 8th Int. Conf. ICTERI 2012, Kherson, Ukraine, June 6-10 (2012), CEUR-WS.org/Vol-848, http://ceur-ws.org/Vol-848/ICTERI-2012-CEUR-WS-paper-38-p-56-70.pdf
Barrett, C., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability Modulo Theories. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability. IOS Press (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nikitchenko, M.S., Tymofieiev, V.G. (2013). Composition-Nominative Logics in Rigorous Development of Software Systems. In: Mayr, H.C., Kop, C., Liddle, S., Ginige, A. (eds) Information Systems: Methods, Models, and Applications. UNISCON 2012. Lecture Notes in Business Information Processing, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38370-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-38370-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38369-4
Online ISBN: 978-3-642-38370-0
eBook Packages: Computer ScienceComputer Science (R0)