Abstract
The paper is a survey of studies devoted to polymodal logics based on a class of frames with discrete linear time with current time point clusters. We consider some classes of frames connected to this class. The paper suggests several axiomatic calculi in various polymodal languages. We show that these axiomatic calculi are complete with respect to corresponding classes of frames. Offered calculi, as we show, posses many interesting properties, e.g. the finite model property and decidability.
The author expresses a sincere gratitude to L.L. Maksimova for her comprehensive help.
This is a preview of subscription content, log in via an institution to check access.
References
Calardo, E. (2006). Admissible inference rules in the linear logic of knowledge and time LTK. Logic Journal of the IGPL, 14(1), 15–34.
Calardo, E., & Rybakov, V. V. (2005). Combining time and knowlege, semantic approach. Bulletin of the Section of Logic, 34(1), 13–21.
Calardo, E., & Rybakov, V. V. (2007). An axiomatization for the multi-modal logic of knowledge and time LTK. Logic Journal of the IGPL, 15(3), 239–254.
Chagrov, A., & Zakharyaschev, M. (1997). Modal logics. Oxford logic guides 35 Oxford: Clarendon Press.
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. Cambridge: MIT Press.
Gabbay, D. M., Hodkinson, I. M., & Reynolds, M. A. (1994). Temporal logic: Mathematical foundations and computational aspects (Vol. 1). Oxford: Clarendon Press.
Halpern, J. Y., Van der Meyden, R., & Vardi, M. Y. (2004). Complete axiomatizations for reasoning about knowledge and time. SIAM Journal on Computing, 33(2), 674–703.
Lukyanchuk, A. (2013). Decidability of multi-modal logic \(LTK\) of linear time and knowledge. Journal of Siberian Federal University, 6(2), 220–226.
Luk’yanchuk, A. N., & Rimatskii, V. V. (2013). An axiomatization for the linear logic of knowledge and time \(LTK_r\) with intransitive time relation. Siberian Mathematical Journal, 54(6), 1037–1045.
Rybakov, V. (2008). Discrete linear temporal logic with current time point clasters, deciding algorithms. Logic and Logic Philosophy, 17(1–2), 143–161.
Vakarelov, D. (1988). Modal logics for Knowledge Representation Systems. Preprint No 7, Sofia University.
Vakarelov, D. (1992). Inductive modal logics. Fundamenta Informaticae, 16, 383–405.
Yun, V. F. (2009). Temporal logic of linear time frames with inductions axiom. Siberian Electronic Mathematical Reports, 6, 312–325.
Yun, V. F. (2010). The temporal logic of inductive frames with linear time. Siberian Electronic Mathematical Reports, 7, 445–457.
Yun, V. F. (2015a). On linear logic of knowledge and time with intransitive time relation. Siberian Mathematical Journal, 56(3), 565–568.
Yun, V. F. (2015b). Polymodal logic of the class of inductive linear time frames. Siberian Electronic Mathematical Reports, 12, 421–431.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Yun, V.F. (2018). On Linear Logic of Knowledge and Time. In: Odintsov, S. (eds) Larisa Maksimova on Implication, Interpolation, and Definability. Outstanding Contributions to Logic, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-319-69917-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-69917-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69916-5
Online ISBN: 978-3-319-69917-2
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)