Abstract
We provide decomposition and quotienting results for multi-modal logic with respect to a composition operator, traditionally used for epistemic models, due to van Eijck et al. (Journal of Applied Non-Classical Logics 21(3–4):397–425, 2011), that involves sets of atomic propositions and valuation functions from Kripke models. While the composition operator was originally defined only for epistemic S5n models, our results apply to the composition of any pair of Kripke models. In particular, our quotienting result extends a specific result in the above mentioned paper by van Eijck et al. for the composition of epistemic models with disjoint sets of atomic propositions to compositions of any two Kripke models regardless of their sets of atomic propositions. We also explore the complexity of the formulas we construct in our decomposition result.
Luca Aceto and Anna Ingólfsdóttir were partially supported by the project ‘Processes and Modal Logics’ (project nr. 100048021) of the Icelandic Research Fund. Joshua Sack was partially supported by the VIDI research programme number 639.072.904, which is financed by the Netherlands Organisation for Scientific Research.
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Aceto, L., Ingolfsdottir, A., Prisacariu, C., Sack, J.: Compositional reasoning for multi-modal logics. Technical Report 419, Department of Informatics, University of Oslo, Oslo, Norway (September 2012)
Andersen, H.R.: Partial model checking (extended abstract). In: 10th IEEE Symposium on Logic in Computer Science (LICS 1995), pp. 398–407. IEEE Computer Society (1995)
Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press (1998)
Baeten, J.C.M., Basten, T., Reniers, M.A.: Process Algebra: Equational Theories of Communicating Processes. Cambridge Tracts in Theoretical Computer Science 50. Cambridge University Press (2009)
Baltag, A., Moss, L.S.: Logics for epistemic programs. Synthese 139(2), 165–224 (2004)
Bloom, B., Fokkink, W., van Glabbeek, R.J.: Precongruence formats for decorated trace semantics. ACM Transactions on Computational Logic 5(1), 26–78 (2004)
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers 35(8), 677–691 (1986)
Castellani, I., Mukund, M., Thiagarajan, P.S.: Synthesizing Distributed Transition Systems from Global Specifications. In: Pandu Rangan, C., Raman, V., Ramanujam, R. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 219–231. Springer, Heidelberg (1999)
Fokkink, W., van Glabbeek, R.J., de Wind, P.: Compositionality of Hennessy-Milner logic by structural operational semantics. Theoretical Computer Science 354(3), 421–440 (2006)
Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of ACM 32(1), 137–161 (1985)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall (1985)
Kozen, D.: Complexity of finitely presented algebras. In: Proceedings of the Ninth Annual ACM Symposium on Theory of Computing, pp. 164–177. ACM (1977)
Kozen, D.: Results on the propositional mu-calculus. Theoretical Computer Science 27, 333–354 (1983)
Laroussinie, F., Larsen, K.G.: Compositional Model Checking of Real Time Systems. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 27–41. Springer, Heidelberg (1995)
Larsen, K.G., Xinxin, L.: Compositionality through an operational semantics of contexts. Journal of Logic and Computation 1(6), 761–795 (1991)
Lomuscio, A., Raimondi, F.: The complexity of model checking concurrent programs against CTLK specifications. In: Nakashima, H., Wellman, M.P., Weiss, G., Stone, P. (eds.) 5th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2006), pp. 548–550. ACM (2006)
McNulty, G.F.: Fragments of first order logic, I: Universal Horn logic. The Journal of Symbolic Logic 42(2), 221–237 (1977)
Milner, R.: Calculi for synchrony and asynchrony. Theorethical Computer Science 25, 267–310 (1983)
Milner, R.: Communication and Concurrency. Prentice Hall (1989)
Mohalik, S., Ramanujam, R.: A presentation of regular languages in the assumption - commitment framework. In: Proceedings of the 1998 International Conference on Application of Concurrency to System Design, ACSD 1998, pp. 250–260. IEEE Computer Society, Washington, DC (1998)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2007)
van Eijck, J., Sietsma, F., Wang, Y.: Composing models. Journal of Applied Non-Classical Logics 21(3-4), 397–425 (2011)
Winskel, G.: A Complete System for SCCS with Modal Assertions. In: Maheshwari, S.N. (ed.) FSTTCS 1985. LNCS, vol. 206, pp. 392–410. Springer, Heidelberg (1985)
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Aceto, L., Ingólfsdóttir, A., Prisacariu, C., Sack, J. (2013). Compositional Reasoning for Multi-modal Logics. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35722-0_1
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