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Abstrakty
The aim of this article is developing a formal system suitable for reasoning about the distance between propositional formulas. We introduce and study a formal language which is the extension of the classical propositional language obtained by adding new binary operators D≤s and D≥s , s ∈ Range, where Range is a fixed finite set. In our language it is allowed to make formulas of the form D≤s (α ; β ) with the intended meaning ’distance between formulas α and β is less than or equal to s ’. The semantics of the proposed language consists of possible worlds with a distance function defined between sets of worlds.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
185--199
Opis fizyczny
Bibliogr. 27 poz., tab.
Twórcy
autor
- Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia
autor
- Faculty of Mathematics, University of Belgrade, 11000 Belgrade, Serbia
autor
- Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia
Bibliografia
- [1] Alur R, Henzinger TA. Logics and models of real time: A survey. In: J.W. de Bakker, C. Huizing, W.P. de Roever, G. Rozenberg (Eds.), Real-Time: Theory in Practice: REX Workshop Mook, The Netherlands, June 3-7, 1991 Proceedings, Springer Berlin Heidelberg, 1992 pp. 74-106. doi:10.1007/BFb0031988.
- [2] Du H, Alechina N. Qualitative Spatial Logics for Buffered Geometries, Journal of Artificial Intelligence Research, 2016 (56):693-745. doi:10.1613/jair.5140.
- [3] Du H, Alechina N, Stock K, Jackson M. The Logic of NEAR and FAR, Spatial Information Theory - 11th International Conference, COSIT 2013, Scarborough, UK, 2013 pp. 475-494. doi:10.1007/978-3-319-01790-7_26.
- [4] Fujita O. Metrics based on average distance between sets, Japan Journal of Industrial and Applied Mathematics, 2013 30(1):1-19. doi:10.1007/s13160-012-0089-6.
- [5] Ikodinović N, Ognjanović Z. A logic with coherent conditional probabilities, Lecture Notes in Computer Science vol. 3571, (Subseries: Lecture Notes in Artificial Intelligence), 2005 pp. 726-736. doi:10.1007/11518655_61.
- [6] Jansana R. Some Logics Related to von Wright’s Logic of Place, Notre Dame J. Formal Logic, 1994 35(1):88-98.
- [7] Kamp H. Tense Logic and the Theory of Linear Order, Ph.D. Thesis, University of California, Los Angeles, 1968.
- [8] Keisler HJ. Probability quantifiers. In Model-Theoretic Logics, Chapiter XIV, J. Barwise, S. Feferman, eds. Springer-Verlag 1985 pp. 507-556.
- [9] Kutz O. Notes on Logics of Metric Spaces, Studia Logica, 2007 85(1):75-104. doi:10.1007/s11225-007-9023-3.
- [10] Kutz O, Sturm H, Suzuki N-Y, Wolter F, Zakharyaschev M. Axiomatizing distance logics, Journal of Applied Non-Classical Logic, 2002 12(3-4):425-440. doi:10.3166/jancl.12.425-439.
- [11] Kutz O, Sturm H, Suzuki N-Y, Wolter F, Zakharyaschev M. Logics of metric spaces, ACM Transactions on Computational Logic, 2003 4(2):260-294. doi:10.1145/635499.635504.
- [12] Lee S. Reasoning about Uncertainty in Metric Spaces, Proceedings of the 22nd Conference on Uncertainty in Artificial Intelligence, UAI, 2006 pp. 289-297.
- [13] Lemon O, Pratt I. On the incompleteness of modal logics of space: Advancing complete modal logics of place, In Advances in Modal Logic, M. Kracht, M. de Rijke, H. Wansing, M. Zakharyaschev, eds. CSLI, 1998 pp. 115-132.
- [14] Montanari A. Metric and layered temporal logic for time granularity, Ph.D. Thesis, Interfacultary Research Institutes, Institute for Logic, Language and Computation (ILLC), Amsterdam, 1996. ISBN:9074795579, 9789074795579.
- [15] Ognjanović Z, Ikodinović N. A logic with higher order conditional probabilities, Publications De l’Institut Mathematique, 2007 82(96):141-154. doi:102298/PIM0796141O.
- [16] Ognjanović Z, Rašković M. Some probability logics with new types of probability operators, Journal of logic and Computation, 1999 9(2):181-195. doi:10.1093/logcom/9.2.181.
- [17] Ognjanović Z, Rašković M, Marković Z. Probability logics, in Zbornik radova, subseries Logic in computer science, Mathematical institute, 2009 12(20):35-111.
- [18] Ognjanović Z, Rašković M, Marković Z. Probability Logics, Probability-Based Formalization of Uncertain Reasoning, Springer International Publishing, 2016. ISBN:978-3-319-47011-5, 978-3-319-83637-9.
- [19] Rasković M. Classical logic with some probability operators, Publications De l’Institut Mathematique, 1993 53(67):1-3. ISSN:0350-1302.
- [20] Rasković M, Djordjević R. Probability Quantifiers and Operators, VESTA, Beograd, 1996.
- [21] Rescher N, Garson J. Topological logic, Journal of Symbolic Logic, 1969 33(4):537-548. doi:10.2307/2271360.
- [22] Rucklidge W. Efficient Visual Recognition Using the Hausdorff Distance, Lecture Notes in Artificial Intelligence, Springer-Verlag Berlin Heidelberg, 1996. ISBN:978-3-540-61993-2, 0302-9743.
- [23] Segerberg K. A note on the logic of elsewhere, Theoria, 1980 46(2-3):183-187. doi:10.1111/j.1755-2567.1980.tb00696.x.
- [24] Stojanović N, Ikodinović N, Djordjević R. A propositional logic with binary metric operators, Journal of Applied Logics - IFCoLog Journal of Logics and their Applications, 2018 5(8):1605-1622. ID: 198489905.
- [25] Vikent’ev A, Avilov M. New Model Distances and Uncertainty Measures for Multivalued Logic. In: C. Dichev, G. Agre (eds) Artificial Intelligence: Methodology, Systems, and Applications, AIMSA 2016, vol. 9883 Lecture Notes in Computer Science, Springer, 2016 pp. 89-98. doi:10.1007/978-3-319-44748-3_9.
- [26] Vikent’ev A. Distances and degrees of uncertainty in many-valued propositions of experts and application of these concepts in problems of pattern recognition and clustering, Pattern Recognition and Image Analysis, 2014 24(4):489-501. doi:10.1134/S1054661814020163.
- [27] Von Wright GH. A modal logic of place, In The Philosophy of Nicholas Rescher, E. Sosa, Ed. D. Reidel, Dordrecht, 1979 pp. 65-73. doi:10.1007/978-94-009-9407-2_9.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
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