Abstract
Memory logics is a family of modal logics whose semantics is specified in terms of relational models enriched with additional data structure to represent a memory. The logical language includes a collection of operations to access and modify the data structure. In this paper we study basic model properties of memory logics, and prove results concerning characterization, definability and interpolation. While the first two properties hold for all memory logics introduced in this article, interpolation fails in most cases.
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References
Areces, C., Figueira, D., Figueira, S., Mera, S.: The expressive power of memory logics. Review of Symbolic Logic 4(1) (2010)
Areces, C., Figueira, D., Gorín, D., Mera, S.: Tableaux and model checking for memory logics. In: Giese, M., Waaler, A. (eds.) TABLEAUX 2009. LNCS, vol. 5607, pp. 47–61. Springer, Heidelberg (2009)
Areces, C., Figueira, S., Mera, S.: Completeness results for memory logics. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 16–30. Springer, Heidelberg (2008)
Areces, C., Figueira, D., Figueira, S., Mera, S.: Expressive power and decidability for memory logics. In: Hodges, W., de Queiroz, R. (eds.) WoLLIC 2008. LNCS (LNAI), vol. 5110, pp. 56–68. Springer, Heidelberg (2008)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Blackburn, P., Wolter, F., van Benthem, J. (eds.): Handbook of Modal Logics. Elsevier, Amsterdam (2006)
Carreiro, F.: Characterization and definability in modal first-order fragments. Master’s thesis, Universidad de Buenos Aires, arXiv:1011.4718 (2010)
Chang, C., Keisler, H.: Model Theory, Studies in Logic and the Foundations of Mathematics, 3rd edn., vol. 73. North-Holland Publishing Co., Amsterdam (1990)
Doets, K.: Basic model theory. University of Chicago Press, Chicago (1996)
Hoogland, E.: Definability and interpolation: Model-theoretic investigations. Ph.D. thesis, ILLC. Universiteit van Amsterdam (2001)
Keisler, H.J.: The ultraproduct construction. In: Proceedings of the Ultramath Conference, Pisa, Italy (2008)
Marx, M., Venema, Y.: Multi-dimensional modal logic. Kluwer, Dordrecht (1997)
Mera, S.: Modal Memory Logics. Ph.D. thesis, Universidad de Buenos Aires & Université Henri Poincare, Buenos Aires, Argentina (2009)
ten Cate, B.: Model theory for extended modal languages. Ph.D. thesis, University of Amsterdam, ILLC Publications, Ph. D. Dissertation series, Amsterdam (2005)
Venema, Y.: Ultrafilter unions: an exercise in modal definability. In: First Workshop on Logic and Language, pp. 303–310. Universidad de Sevilla (2000)
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Areces, C., Carreiro, F., Figueira, S., Mera, S. (2011). Basic Model Theory for Memory Logics. In: Beklemishev, L.D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2011. Lecture Notes in Computer Science(), vol 6642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20920-8_8
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DOI: https://doi.org/10.1007/978-3-642-20920-8_8
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