Abstract
This paper introduces a method to build dynamic logics with a graded semantics. The construction is parametrized by a structure to support both the spaces of truth and of the domain of computations. Possible instantiations of the method range from classical (assertional) dynamic logic to less common graded logics suitable to deal with programs whose transitional semantics exhibits fuzzy or weighted behaviour. This leads to the systematic derivation of program logics tailored to specific program classes.
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References
Beckert, B.: A dynamic logic for the formal verification of java card programs. In: Attali, I., Jensen, T. (eds.) JavaCard 2000. LNCS, vol. 2041, pp. 6–24. Springer, Heidelberg (2001)
Droste, M., Gastin, P.: Weighted automata and weighted logics. Theor. Comput. Sci. 380(1–2), 69–86 (2007)
Furusawa, H.: The categories of kleene algebras, action algebras and action lattices are related by adjunctions. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2003/Kleene-Algebra Ws 2003. LNCS, vol. 3051, pp. 124–136. Springer, Heidelberg (2004)
Goble, S.F.: Grades of modality. Logique et Analyse 13, 323–334 (1970)
Gottwald, S.: A Treatise on Many-Valued Logics. Studies in Logic and Computation, vol. 9. Research Studies Press (2001)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press (2000)
Kozen, D.: On action algebras. manuscript in: Logic and Flow of Information, Amsterdam (1991)
Kozen, D.: A probabilistic PDL. J. Comput. Syst. Sci. 30(2), 162–178 (1985)
Kozen, D.: A completeness theorem for kleene algebras and the algebra of regular events. Inf. Comput. 110(2), 366–390 (1994)
Lopes, B., Benevides, M.R.F., Haeusler, E.H.: Propositional dynamic logic for petri nets. Logic Journal of the IGPL 22(5), 721–736 (2014)
Mürk, O., Larsson, D., Hähnle, R.: KeY-C: a tool for verification of c programs. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 385–390. Springer, Heidelberg (2007)
Nilsson, N.J.: Probabilistic logic. Artif. Intell. 28(1), 71–87 (1986)
Platzer, A.: Logical Analysis of Hybrid Systems: Proving Theorems for Complex Dynamics. Springer (2010)
Platzer, A.: A complete axiomatization of quantified differential dynamic logic for distributed hybrid systems. Logical Methods in Computer Science 8(4) (2012)
Pratt, V.: Action logic and pure induction. In: van Eijck, J. (ed.) Logics in AI. LNCS, vol. 478, pp. 97–120. Springer, Heidelberg (1991)
van der Hoek, W.: On the semantics of graded modalities. Journal of Applied Non-Classical Logics 2(1) (1992)
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Madeira, A., Neves, R., Martins, M.A., Barbosa, L.S. (2015). A Dynamic Logic for Every Season. In: Braga, C., Martí-Oliet, N. (eds) Formal Methods: Foundations and Applications. SBMF 2014. Lecture Notes in Computer Science(), vol 8941. Springer, Cham. https://doi.org/10.1007/978-3-319-15075-8_9
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DOI: https://doi.org/10.1007/978-3-319-15075-8_9
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