A History of Positional Logic
DOI:
https://doi.org/10.12775/szhf.2025.000Słowa kluczowe
positional logic, topological logic, temporal logic, epistemic logicAbstrakt
This paper offers a comprehensive historical study of positional logic, a branch of logic that is closely intertwined with temporal and epistemic logic. Given its significance in the realm of philosophical logic, there is a notable absence of a thorough historical analysis of this subject. To address this gap, our work aims to provide a detailed examination of the most important systems of positional logic, highlighting key results in the field, and offering a comprehensive list of publications that have contributed to the development of positional logic.
Bibliografia
Emery Nina, Ned Markosian, Meghan Sullivan. 2023. “Time in The Stanford Encyclopedia of Philosophy”. URL: https://plato.stanford.edu/archives/win2020/entries/time/
Garson James. 1969. The Logics of Space and Time. Pittsburgh: University of Pittsburgh.
Garson James. 1972 . “Two New Interpretations of Modality”. Nouvelle Serie 15, 59–60: 443–459.
Garson James. 1973a . “The Completeness of an Intensional Logic: Definite Topological Logic”. Notre Dame Journal of Formal Logic 14, 2: 175–184.
Garson James. 1973b . “Indefinite Topological Logic”. Journal of Philosophical Logic 2: 102–118.
Garson James. 1974 . “The Substitution Interpretation in Topological Logic”. Journal of Symbolic Logic 3, 1–2: 109–132.
Hiż Henryk. 1951 . “Review of: J. Ło ˙ s, Podstawy Analizy Metodologicznej Kanonów ´Milla”. Journal of Symbolic Logic 16, 1: 58–59.
Jarmużek Tomasz. 2006 . “Rekonstrukcje Rozumowania Diodora Kronosa w Ontologii ˙Czasu Punktowego [Reconstruction of Diodorus Cronus’ Argument in Frame of Ontology of Time Consisted of Points]”. Analiza i Egzystencja 3: 197–215.
Jarmużek Tomasz. 2007. “Minimal Logical Systems with R-operator: Their Metalogical ˙Properties and Ways of Extensions”. In: Perspectives on Universal Logic, ed. Béziau Jean-Yves, Alexandre Costa-Leite. Milan: Polimetrica Publisher. pp. 319–333.
Jarmużek Tomasz. 2013. ˙ Jutrzejsza Bitwa Morska. Rozumowanie Diodora Kronosa. Toruń:´ Wydawnictwo Naukowe UMK.
Jarmużek Tomasz. 2018. ˙ On the Sea Battle Tomorrow That May Not Happen. A Logical and Philosophical Analysis of the Master Argument. Bern: Peter Lang GmbH.
Jarmużek Tomasz, Aleksander Parol. 2020 . “On Some Language Extension of Logic MR: ˙A Semantic and Tableau Approach”. Roczniki Filozoficzne 68, 4: 345–366.
Jarmużek Tomasz, Andrzej Pietruszczak. 2004 . “Completeness of Minimal Positional Calculus”. Logic and Logical Philosophy 13: 147–162.
Jarmużek Tomasz, Marcin Tkaczyk. 2015. ˙ Normalne Logiki Pozycyjne. Lublin: Wydawnictwo KUL.
Jarmużek Tomasz, Marcin Tkaczyk. 2019 ˙ a . “Expressive Power of the Positional Operator R: A Case Study in Modal Logic and Modal Philosophy”. Ruch Filozoficzny 75, 2: 91–107.
Jarmużek Tomasz, Marcin Tkaczyk. 2019 ˙ b . “Jerzy Łoś Positional Calculus and the Origin ´of Temporal Logic”. Logic and Logical Philosophy 28: 259–276.
Jarmużek Tomasz, Tomasz Kupś. 2020 . “The Heritage of Jerzy Łoś’s Philosophical Logic ´and the Polish Question. An Introduction to the Volume”. Studia z Historii Filozofii 11, 3: 7–19.
Karczewska Anna. 2017 . “Maximality of the Minimal R-Logic”. Logic and Logical Philosophy 27, 2: 193–203.
Karczewska Anna. 2021a . “On the Modal Interpretation of the Connective of Realization”. Journal of Applied Non-Classical Logics 31, 3-4: 221–233.
Karczewska Anna. 2021b . “Set-Theoretic Semantics for Many-Valued Positional Calculi”. Roczniki Filozoficzne 68, 4: 367–384.
Klonowski Mateusz, Krzysztof Krawczyk. 2019 . “Problem Wszechwiedzy Logicznej. Krytyka Nienormalnych Światów i Propozycja Nowego Rozwiązania [The Problem of Logical Omniscience. The Critique of Non-normal Worlds and the Proposition of New Solution]”. Filozofia Nauki 27, 1: 27–48.
Klonowski Mateusz, Krzysztof Krawczyk, Bozena Pi˛eta. 2021 . “Tableau Systems for Epistemic Positional Logics”. Bulletin of the Section of Logic 50, 2: 177–204.
Klonowski Mateusz, Rafał Palczewski. 2020 . “Epistemic Contextualism and Positional Logic”. Studia z Historii Filozofii 11, 3: 67–104.
Krawczyk Krzysztof, Bożena Pięta. 2020 . “The Forgotten Jerzy Łoś’s Contribution to Philosophical Logic. Logics with Realization Operator R”. Ruch Filozoficzny 75, 2: 179–187.
Lechniak Marek. 1988 . “Logika Epistemiczna Jerzego Łosia a Teoria Racjonalnego Zachowania [Epistemic Logic of Jerzy Łos and the Theory of Rational Behavior]”. ´ Roczniki Filozoficzne 36: 77–89.
Lechniak Marek. 2020 . “Jerzy Łos’s Epistemic Logic and the Origins of Epistemic Logics”. ´
Studia z Historii Filozofii 11, 3: 21–49.
Łoś Jerzy. 1947 . “Podstawy Analizy Metodologicznej Kanonów Milla”. ´ Annales Universitatis Mariae Curie-Skłodowska 2, 5: 269–301.
Łoś Jerzy. 1948 . “Logiki Wielowartościowe a Formalizacja Funkcji”. ´ Kwartalnik Filozoficzny 17, 1–2: 59–78.
Malinowski Jacek, Krzysztof Pietrowicz, Joanna Szalacha-Jarmuzek. 2020 . “Logic of Social ˙Ontology and Łoś Operator”. ´ Logic and Logical Philosophy 29: 239–258.
Mares Edwin. 2023. “Propositional Function in The Stanford Encyclopedia of Philosophy”. URL: https://plato.stanford.edu/archives/win2019/entries/propositional-function/
McGrath Matthew, Frank Devin. 2023. “Propositions in The Stanford Encyclopedia of Philosophy”. URL: https://plato.stanford.edu/archives/win2020/entries/propositions
Nishimura Hirokazu. 1979a . “Is the Semantics of Branching Structures Adequate for Chronological Modal Logics?”. Journal of Philosophical Logic 8: 469–475.
Nishimura Hirokazu. 1979b . “On the Completeness of Chronological Logics with Modal Operators”. Mathematical Logic Quarterly 25, 31: 487–496.
Øhrstrøm Peter, Per Hasle. 2019. “The Significance of the Contributions of A. N. Prior and Jerzy Łoś in the Early History of Modern Temporal Logic”. In: ´ Logic and Philosophy of Time: Further Themes from Prior. Vol. 2, ed. Blackburn Patrick, Per Hasle, Peter Øhrstrøm. Aalborg: Aalborg University Press. pp. 31–40.
Parol Aleksander. 2020 . “The Influence of Jerzy Łos on Early Developments in Temporal ´Logic”. Studia z Historii Filozofii 11, 3: 105–126.
Parol Aleksander, Krzysztof Pietrowicz, Joanna Szalacha-Jarmużek. 2021 . “Extended MR ˙with Nesting of Predicate Expressions as a Basic Logic for Social Phenomena”. Bulletin of the Section of Logic 50, 2: 205–227.
Prior N. Arthur. 1955. Formal Logic. Oxford: Clarendon Press.
Prior N. Arthur. 1956 . “Modality and Quantification in S5”. The Journal of Symbolic Logic 21, 1: 60–62.
Prior N. Arthur. 1957. Time and Modality. Oxford: Oxford University Press.
Prior N. Arthur. 1967. Past, Present and Future. Oxford: Clarendon Press.
Rescher Nicholas. 1966 . “On the Logic of Chronological Propositions”. Mind 77: 75–96.
Rescher Nicholas. 2005. Epistemic Logic: A Survey of the Logic of Knowledge. Pittsburgh: University of Pittsburgh Press.
Rescher Nicholas, Alasdair Urquhart. 1971. Temporal Logic. New York: Springer Verlag.
Rescher Nicholas, James Garson. 1967 . “A Note on Chronological Logic”. Teoria 33: 39–44.
Rescher Nicholas, James Garson. 1968a. “Assertion Logic”. In: Topics in Philosophical Logic, ed. Rescher Nicholas. Dordrecht, the Netherlands: Springer. pp. 250–286.
Rescher Nicholas, James Garson. 1968b. “Topological Logic”. In: Topics in Philosophical Logic, ed. Rescher Nicholas. Dordrecht, the Netherlands: Springer. pp. 229–249.
Russell Bertrand, Arthur N. Whitehead. 1910. Principia Mathematica. Cambridge: Cambridge University Press.
Suszko Roman. 1949 . “Review: Jerzy Łos, Many-Valued Logics and Formalization of Intensional Functions”. Journal of Symbolic Logic 14, 1: 64–65.
Szalacha-Jarmużek Joanna, Krzysztof Pietrowicz. 2020 . “Going Beyond the Dichotomy. ˙Problems of Contemporary Sociology in the Context of the Proposals by Jerzy Łoś”. ´Studia z Historii Filozofii 9, 3: 51–56.
Tkaczyk Marcin. 2009. Logika Czasu Empirycznego. Funktor Realizacji Czasowej w J˛ęzykach Teorii Fizykalnych. Lublin: Wydawnictwo KUL.
Pobrania
Opublikowane
Jak cytować
Numer
Dział
Licencja
Utwór dostępny jest na licencji Creative Commons Uznanie autorstwa – Bez utworów zależnych 4.0 Międzynarodowe.
Statystyki
Liczba wyświetleń i pobrań: 17
Liczba cytowań: 0