Pokaż uproszczony rekord

The (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)

dc.contributor.authorSzmuc, Damian E.
dc.date.accessioned2022-03-10T17:28:33Z
dc.date.available2022-03-10T17:28:33Z
dc.date.issued2021-05-27
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/41065
dc.description.abstractWe examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined in terms of a \(p\)-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints.en
dc.language.isoen
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl
dc.relation.ispartofseriesBulletin of the Section of Logic;4en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0
dc.subjectRelevant logicsen
dc.subjectnon-transitive logicsen
dc.subjectp-matrixen
dc.subjectweak Kleene algebraen
dc.subjectinfectious logicsen
dc.titleThe (Greatest) Fragment of Classical Logic that Respects the Variable-Sharing Principle (in the FMLA-FMLA Framework)en
dc.typeOther
dc.page.number421-453
dc.contributor.authorAffiliationIIF, CONICET-SADAF, C1176ABL, Bulnes 642, Buenos Aires, Argentina; University of Buenos Aires, Department of Philosophyen
dc.identifier.eissn2449-836X
dc.referencesA. Anderson, N. Belnap, Entailment: The Logic of Relevance and Neccessity, vol. 1, Princeton University Press, Princeton (1975).en
dc.referencesG. Badia, Variable sharing in substructural logics: an algebraic characterization, Bulletin of the Section of Logic, vol. 47(2) (2018), pp. 107–115, DOI: https://doi.org/10.18778/0138-0680.47.2.03en
dc.referencesE. Barrio, F. Pailos, D. Szmuc, A Hierarchy of Classical and Paraconsistent Logics, Journal of Philosophical Logic, vol. 1(49) (2020), pp. 93–120, DOI: https://doi.org/10.1007/s10992-019-09513-zen
dc.referencesN. Belnap, How a Computer Should Think, [in:] G. Ryle (ed.), Contemporary Aspects of Philosophy, Oriel Press, Stocksfield (1977), pp. 30–55.en
dc.referencesF. Berto, Simple hyperintensional belief revision, Erkenntnis, vol. 84(3) (2019), pp. 559–575, DOI: https://doi.org/10.1007/s10670-018-9971-1en
dc.referencesD. Bochvar, On a Three-Valued Calculus and its Application in the Analysis of the Paradoxes of the Extended Functional Calculus, Matematicheskii Sbornik, vol. 4 (1938), pp. 287–308.en
dc.referencesW. Carnielli, Methods of proof for relatedness logic and dependence logics, Reports on Mathematical Logic, vol. 21 (1987), pp. 35–46.en
dc.referencesP. Cobreros, P. Égré, D. Ripley, R. van Rooij, Tolerance and mixed consequence in the s’valuationist setting, Studia Logica, vol. 100(4) (2012), pp. 855–877, DOI: https://doi.org/10.1007/s11225-012-9422-yen
dc.referencesP. Cobreros, P. Égré, D. Ripley, R. van Rooij, Tolerant, classical, strict, Journal of Philosophical Logic, vol. 41(2) (2012), pp. 347–385.en
dc.referencesP. Cobreros, P. Égré, D. Ripley, R. van Rooij, Priest’s motorbike and tolerant identity, [in:] R. Ciuni, H. Wansing, C. Wilkommen (eds.), Recent Trends in Philosophical Logic, Springer, Cham (2014), pp. 75–85, DOI: https://doi.org/10.1007/978-3-319-06080-4_6en
dc.referencesP. Cobreros, P. Égré, D. Ripley, R. van Rooij, Reaching transparent truth, Mind, vol. 122(488) (2014), p. 841–866.en
dc.referencesM. Coniglio, M. I. Corbalán, Sequent Calculi for the classical fragment of Bochvar and Halldén’s Nonsense Logics, [in:] Proceedings of the 7th Workshop on Logical and Semantic Frameworks with Applications (LSFA) (2012), pp. 125–136, DOI: https://doi.org/10.4204/EPTCS.113.12en
dc.referencesF. Correia, Weak necessity on weak Kleene matrices, [in:] F. Wolter, H. Wansing, M. de Rijke, M. Zakharyashev (eds.), Advances in Modal Logic, World Scientific, River Edge, NJ (2002), pp. 73–90, DOI: https://doi.org/10.1142/9789812776471_0005en
dc.referencesB. Dicher, F. Paoli, ST, LP, and tolerant metainferences, [in:] C. Başkent, T. M. Ferguson (eds.), Graham Priest on Dialetheism and Paraconsistency, Springer, Dordrecht (2020), pp. 383–407, DOI: https://doi.org/10.1007/978-3-030-25365-3_18en
dc.referencesM. Dunn, Intuitive semantics for first-degree entailments and ‘coupled trees’, Philosophical Studies, vol. 29(3) (1976), pp. 149–168, DOI: https://doi.org/10.1007/BF00373152en
dc.referencesR. Epstein, The Semantic Foundations of Logic, vol. I: Propositional Logics, Springer (1990), DOI: https://doi.org/10.1007/978-94-009-0525-2en
dc.referencesL. Fariñas del Cerro, V. Lugardon, Sequents for dependence logics, Logique et Analyse, vol. 133–134 (1991), pp. 57–71.en
dc.referencesM. Fitting, The Strict/Tolerant Idea and Bilattices, [in:] O. Arieli, A. Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, Springer (2021).en
dc.referencesJ. M. Font, Abstract Algebraic Logic, College Publications, London (2016).en
dc.referencesS. Frankowski, Formalization of a Plausible Inference, Bulletin of the Section of Logic, vol. 33(1) (2004), pp. 41–52.en
dc.referencesR. French, A Simple Sequent Calculus for Angell’s Logic of Analytic Containment, Studia Logica, vol. 105(5) (2017), pp. 971–994, DOI: https://doi.org/10.1007/s11225-017-9719-yen
dc.referencesN. Galatos, P. Jipsen, T. Kowalski, H. Ono, Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Elsevier, San Diego, CA, USA (2007).en
dc.referencesJ.-Y. Girard, Proof theory and logical complexity, Bibliopolis, Napoli (1987).en
dc.referencesS. Halldén, The Logic of Nonsense, Uppsala Universitets Arsskrift, Uppsala (1949).en
dc.referencesL. Humberstone, The Connectives, MIT Press, Cambridge, MA (2011).en
dc.referencesS. C. Kleene, Introduction to metamathematics, North-Holland, Amsterdam (1952).en
dc.referencesS. Kripke, Outline of a theory of truth, Journal of Philosophy, vol. 72(19) (1975), pp. 690–716, DOI: https://doi.org/10.2307/2024634en
dc.referencesE. Mares, Relevance Logic, [in:] E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, spring 2014 ed., Metaphysics Research Lab, Stanford University (2014), URL: https://plato.stanford.edu/archives/spr2014/entries/logic-relevance/en
dc.referencesE. J. Nelson, Intensional relations, Mind, vol. 39(156) (1930), pp. 440–453.en
dc.referencesF. Paoli, Semantics for first-degree relatedness logic, Reports on Mathematical Logic, vol. 27 (1993), pp. 81–94.en
dc.referencesF. Paoli, Tautological entailments and their rivals, [in:] J. Béziau, W. Carnielli, D. Gabbay (eds.), Handbook of Paraconsistency, College Publications, London (2007), pp. 153–175.en
dc.referencesF. Paoli, M. P. Baldi, Proof Theory of Paraconsistent Weak Kleene Logic, Studia Logica, vol. 108(4) (2020), pp. 779–802, DOI: https://doi.org/10.1007/s11225-019-09876-zen
dc.referencesW. T. Parry, Ein Axiomensystem für eine neue Art von Implikation (analytische Implikation), Ergebnisse eines mathematischen Kolloquiums, vol. 4 (1933), pp. 5–6.en
dc.referencesD. Ripley, Conservatively extending classical logic with transparent truth, Review of Symbolic Logic, vol. 5(2) (2012), pp. 354–378, DOI: https://doi.org/10.1017/S1755020312000056en
dc.referencesD. Ripley, Paradoxes and failures of cut, Australasian Journal of Philosophy, vol. 91(1) (2013), pp. 139–164, DOI: https://doi.org/10.1080/00048402.2011.630010en
dc.referencesG. Robles, J. M. Méndez, A Class of Simpler Logical Matrices for the Variable-Sharing Property, Logic and Logical Philosophy, vol. 20(3) (2011), pp. 241–249, DOI: https://doi.org/10.12775/LLP.2011.014en
dc.referencesG. Robles, J. M. Méndez, A general characterization of the variable-sharing property by means of logical matrices, Notre Dame Journal of Formal Logic, vol. 53(2) (2012), pp. 223–244, DOI: https://doi.org/10.1215/00294527-1715707en
dc.referencesG. Robles, J. M. Méndez, F. Salto, A Modal Restriction of R-Mingle with the Variable-Sharing Property, Logic and Logical Philosophy, vol. 19(4) (2010), pp. 341–351, DOI: https://doi.org/10.12775/LLP.2010.013en
dc.referencesC. Scambler, Classical logic and the strict tolerant hierarchy, Journal of Philosophical Logic, vol. 2(49) (2020), p. 351–370, DOI: https://doi.org/10.1007/s10992-019-09520-0en
dc.referencesK. Schütte, Proof Theory, Springer, Berlin (1977).en
dc.referencesD. Szmuc, A simple matrix semantics and sequent calculus for Parry’s logic of Analytic Implication, Studia Logica, (2021), DOI: https://doi.org/10.1007/s11225-020-09926-xen
dc.referencesD. Szmuc, T. M. Ferguson, Meaningless Divisions, forthcoming in Notre Dame Journal of Formal Logic.en
dc.referencesG. Takeuti, Proof Theory, 2nd ed., Elsevier, Amsterdam (1987).en
dc.referencesR. Wójcicki, Some Remarks on the Consequence Operation in Sentential Logics, Fundamenta Mathematicae, vol. 68(1) (1970), pp. 269–279.en
dc.contributor.authorEmailszmucdamian@gmail.com
dc.identifier.doi10.18778/0138-0680.2021.08
dc.relation.volume50


Pliki tej pozycji

Thumbnail
Nazwa:
421-453_Szmuc.pdf
Rozmiar:
574.6KB
Format:
PDF
Oglądaj/Otwórz

Pozycja umieszczona jest w następujących kolekcjach

Pokaż uproszczony rekord

https://creativecommons.org/licenses/by-nc-nd/4.0
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako https://creativecommons.org/licenses/by-nc-nd/4.0