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On structure of Tichy - inspired logical spacetime

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Języki publikacji
EN
Abstrakty
EN
This paper presents the construction and structural analysis of the logical spacetime- the single unique and real underlying structure of the extensional model of Transparent Intensional Logic. The proposed solution aims to help bridge the gap between the theoretical nature of this logical system and its practical applications while addressing two key challenges. Tichy’s objections to the very existence of such a model as well as the ambiguity in Kripke’s influential approach, which, rather than defining a single model, specifies various categories of models based on the relational properties of their underlying structures.
Rocznik
Strony
51--74
Opis fizyczny
Bibliogr. 35 poz., rys.
Twórcy
  • Faculty of Electrical Engineering and Informatics, Technical University of Kosice Kosice, Slovakia
  • Faculty of Electrical Engineering and Informatics, Technical University of Kosice Kosice, Slovakia
  • Faculty of Electrical Engineering and Informatics, Technical University of Kosice Kosice, Slovakia
Bibliografia
  • [1] Fitting, M., & Mendelsohn, R.L. (2023). Modal Logic, an Introduction. In First-Order Modal Logic (pp. 51-76). Springer International Publishing.
  • [2] Demri, S., Goranko, V., &Lange, M.(2016). Temporal Logics in Computer Science: Finite-State Systems (Vol. 58). Cambridge University Press.
  • [3] Prior, A.N. (1955). Time and Modality. Greenwood Press.
  • [4] Kripke, S.A. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica, 16, 83-94.
  • [5] Minkowski, H. (1909). Raum und Zeit. Jahresbericht der Deutschen Mathematiker-Vereinigung, 18, 75-88.
  • [6] Goldblatt, R. (1980). Diodorean modality in Minkowski spacetime. Studia Logica, 39, 219-236.
  • [7] Hirsch, R., & McLean, B. (2022). Temporal Logic of Minkowski Spacetime. In: Düntsch, I., Mares, E. (eds.) Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Outstanding Contributions to Logic, 22. Cham: Springer.
  • [8] Perissutti, A.M. (2021). About truth and possible worlds. Slovo a smysl, 18, 38, 111-124.
  • [9] Andreansky, E. (2010). Mozne svety z pohladu logickej semantiky a analytickej filozofie (Pos sible Worlds from the Perspective of Logical Semantics and Analytical Philosophy). Faculty of Philosophy, Pavol Jozef Safarik University in Kosice.
  • [10] Carnap, R. (1947). Meaning and Necessity: A Study in Semantics and Modal Logic. The Univer sity of Chicago Press.
  • [11] Peregrin, J. (1993). Possible worlds: A critical analysis. The Prague Bulletin of Mathematical Linguistics, 59, 9-21.
  • [12] Peregrin, J. (2005). Mozne svety v logice. (Possible worlds in logic.) ALUZE: Revue pro literaturu, filozofii a jine, 1, 135-141.
  • [13] Stalnaker, R. (1986). Possible worlds and situations. Journal of Philosophical Logic, 15(1), 109-123.
  • [14] Frege, G. (1892). Uber Sinn und Bedeutung. Zeitschrift f¨ur Philosophie und philosophische Kritik, 100, 25-50.
  • [15] Tichy, P. (1988). The Foundations of Frege’s Logic. De Gruyter.
  • [16] Copeland, B.J. (2022). Arthur Prior. In: Edward N. Zalta and Uri Nodelman (eds.), The Stan ford Encyclopedia of Philosophy (Winter 2022 Edition). Metaphysics Research Lab, Stanford University. Retrieved from https://plato.stanford.edu/archives/fall2022/entries/prior/.
  • [17] Prior, A.N. (1958). The syntax of time-distinctions. Franciscan Studies, 18(2), 105-120.
  • [18] Ploug, T., & Øhrstrøm, P. (2012). Branching time, indeterminism and tense logic: unveiling the Prior-Kripke connection. Logic and Logical Philosophy, 21(4), 341-353.
  • [19] Emerson, E.A., & Halpern, J.Y. (1985). Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Sciences, 30(1), 1-24. Retrieved from https://www.sciencedirect.com/science/article/pii/0022000085900017.
  • [20] Rescher, N., & Urquhart, A. (1975). Temporal logic. Philosophy of Science, 42(1), 100-103.
  • [21] Belnap, N. (2001). Facing the Future: Agents and Choices in Our Indeterminist World. Oxford University Press.
  • [22] Raclavsky, J., Kuchynka, P., & Pezlar, I. (2015). Transparent Intensional Logic as Characteris tica Universalis and Calculus Ratiocinator. Brno: Masaryk University (Munipress).
  • [23] Duzı, M., & Horak, A. (2015). TIL as hyperintensional logic for natural language analysis. In RASLAN 2015: Recent Advances in Slavonic Natural Language Processing (p. 113).
  • [24] Bilanova, Z., & Uchnar, M. (2017). Comparison of the approaches of Montague andTich´y within a logical analysis of an English sentence. POSTER 2017. Czech Technical University, 1-6.
  • [25] Tichy, P., Svoboda, V., Jespersen, B., & Cheyne, C. (2004). Pavel Tichy’s Collected Papers in Logic and Philosophy. Filosofia.
  • [26] Pezlar, I. (2022). Going Nowhere and Back: Is Trivialization the Same as Zero Execution? In: Materna, P., & Jespersen, B. (eds.). Logically Speaking. A Festschrift for Marie Duzı (pp. 187-202).
  • [27] Novotny S., Duzı M., Steingatner W., & Perhac J. (2025). Towards Resolving Type Incoher ence in Transparent Intensional Logic. In Information Modelling and Knowledge Bases XXXV (accepted).
  • [28] Rybarıkova, Z. (2023). Specification of time in Tichy’s transparent intensional logic and Prior’s temporal logic. Synthese, 201, 5, 164.
  • [29] Duzı, M., & Fait, M. (2019). Type checking algorithm for the TIL-Script language. Frontiers in Artificial Intelligence and Applications, 312, 219-236.
  • [30] Novotny S., Duzı M., & Steingatner W. (2025). Implementation of Transparent Intensional Logic Framework in Haskell. In Information Modelling and Knowledge Bases XXXV (accepted).
  • [31] Bilanova, Z., Perhac, J., Chovancova, E., & Chovanec, M. (2020). Logic analysis of natural language based on predicate linear logic. Acta Polytechnica Hungarica, 17(6), 239-252.
  • [32] Duzı, M. (2025). Dual TIL as a logical experiment in a procedural λ-calculus. In Synthese (accepted).
  • [33] Novotny, S., Michalko, M., Perhac, J., Novitzka, V., & Jakab, F. (2022). Formalization and modeling of communication within multi-agent systems based on transparent intensional logic. Symmetry, 14, 3, 588.
  • [34] Novotny, S., Steingartner, W., & Perhac, J. (2024). Another Empirical Proof of Transparent Intensional Logic’s Expressive Power in the Field of Temporal Logical Systems. In 2024 IEEE 17th International Scientific Conference on Informatics (Informatics) (pp. 259-263). DOI: 10.1109/Informatics62280.2024.10900822.
  • [35] Hintikka, J. (1962) The modes of modality. Proceedings of a Colloquium on Modal and Many - valued Logics Acta.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-a2236eec-0654-4ab4-a4dc-ac64ab0c173b
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