Geodesic
Satisfiability in a temporal multi-valueted logic based on $\mathbb{Z}$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 56-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we continue the series of papers by V. V. Rybakov devoted to properties of multi-valueted logics and where he propose a new approach for modelling knowledge and reasoning of agents in a multi-agent system. We prove that the satisfiability problem is decidable in a temporal multi-valueted logic based on $\mathbb{Z}$.
Keywords: temporal logic, multi-agent logic, epistemic modal logic, multi-valueted logic, satisfiability, decidability in logic, knowledge representation and reasoning, multi-agent systems. 
@article{JSFU_2022_15_1_a6,
     author = {Vladimir R. Kiyatkin and Anna V. Kosheleva},
     title = {Satisfiability in a temporal multi-valueted logic based on $\mathbb{Z}$},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {56--74},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a6/}
}
TY  - JOUR
AU  - Vladimir R. Kiyatkin
AU  - Anna V. Kosheleva
TI  - Satisfiability in a temporal multi-valueted logic based on $\mathbb{Z}$
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2022
SP  - 56
EP  - 74
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a6/
LA  - en
ID  - JSFU_2022_15_1_a6
ER  - 
%0 Journal Article
%A Vladimir R. Kiyatkin
%A Anna V. Kosheleva
%T Satisfiability in a temporal multi-valueted logic based on $\mathbb{Z}$
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2022
%P 56-74
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a6/
%G en
%F JSFU_2022_15_1_a6
Vladimir R. Kiyatkin; Anna V. Kosheleva. Satisfiability in a temporal multi-valueted logic based on $\mathbb{Z}$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 1, pp. 56-74. http://geodesic.mathdoc.fr/item/JSFU_2022_15_1_a6/

[1] R. Aumann, A. Brandenburger, “Epistemic Conditions for Nash Equilibrium”, Econometrica, 63:5 (1995), 161–180 | DOI | MR

[2] F. Baader, “Ontology-Based Monitoring of Dynamic Systems”, Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning, KR'14, AAAI Press, Vienna, Austria, 2014, 678–681

[3] S.V. Babenyshev, V.V. Rybakov, “Logic of plausibility for discovery in multi-agent environment deciding algorithms”, Knowledge-based intelligent information and engineering systems, Lect. Notes Comput. Sci., 5179, Springer, Berlin-Heidelberg, 2008, 210–217 | DOI | MR

[4] M. Bacharach, P. Mongin, “Epistemic logic and the foundations of game theory”, Theory and Decision, 37:1 (1994), 1–6 | DOI | MR

[5] S.I. Bashmakov, A.V. Kosheleva, V.V. Rybakov, “Non-unifiability in linear temporal logic of knowledge with multi-agent relations”, Sib. Elektron. Mat. Izv., 13 (2016), 656–663 | MR | Zbl

[6] S.I. Bashmakov, A.V. Kosheleva, V.V. Rybakov, “Projective formulas and unification in linear discrete temporal multi-agent logics”, Sib. Elektron. Mat. Izv., 13 (2016), 923–929 | MR | Zbl

[7] J. van Benthem, Logic in games, MIT Press, Cambridge MA, 2012 | MR

[8] H. van Ditmarsch, J. Halpern, W. van der Hoek, B. Kooi, Handbook of Epistemic Logic, College Publications, London, 2015 | MR | Zbl

[9] R. Fagin, J. Halpern, Y. Moses, M. Vardi, Reasoning about knowledge, MIT Press, Cambridge, 1995 | MR | Zbl

[10] R. Fagin, J. Halpern, Y. Moses, M Vardi, “A nonstandard approach to the logical omniscience problem”, Artificial Intelligence, 79 (1995), 203–240 | DOI | MR | Zbl

[11] J. Hintikka, Knowledge and belief: an introduction to the logic of the two notions, Cornell University Press, 1962

[12] W. van der Hoek, M. Wooldridge, “Logics for Multi-Agent Systems”, Multi-Agent Systems, second edition, ed. G. Weiss, MIT Press, 2013, 671–810

[13] E. Pacuit, O. Roy, “Epistemic Foundations of Game Theory”, The Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/epistemic-game/ | MR

[14] A. Perea, Epistemic Game Theory: Reasoning and Choice, Cambridge University Press, Cambridge, 2012 | MR

[15] A. Perea, “From Classical to Epistemic Game Theory”, International Game Theory Review, 16:1 (1440), 1440001 | DOI | MR

[16] N. Rescher, Epistemic Logic: A Survey Of the Logic Of Knowledge, University of Pittsburgh Press, 2005 | MR

[17] V.V. Rybakov, “Multiagent temporal logics with multivaluations”, Siberian Mathematical Journal, 59:4 (2018), 710–720 | DOI | MR | Zbl

[18] V.V. Rybakov, “Temporal multi-valued logic with lost worlds in the past”, Siberian Electronic Mathematical Reports, 15 (2018), 436–449 | DOI | MR | Zbl

[19] V.V. Rybakov, M.A. Moor, “Many-valuated multi-modal logics, satisfiability problem”, Siberian Electronic Mathematical Reports, 15 (2018), 829–838 | DOI | MR | Zbl

[20] V.V. Rybakov, “Multi-Agent Logics with Multi-Valuations and Intensional Logical Operations”, Lobachevskii Journal of Mathematics, 41 (2020), 243–251 | DOI | MR | Zbl

[21] Y. Shoham, K. Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge University Press, New York, 2009 | Zbl

[22] M. Vardi, “An automata-theoretic approach to linear temporal logic”, Y. Banff Higher Order Workshop, 1995, 238–266

[23] M. Vardi, “Reasoning about the past with two-way automata”, International Colloquium on Automata, Languages, and Programming (ICALP), Lect. Notes Comput. Sci., 1443, Springer-Verl., Berlin, 1998, 628–641 | DOI | MR | Zbl