Show simple item record

Basic Four-Valued Systems of Cyclic Negations

dc.contributor.authorGrigoriev, Oleg
dc.contributor.authorZaitsev, Dmitry
dc.date.accessioned2023-02-10T07:50:38Z
dc.date.available2023-02-10T07:50:38Z
dc.date.issued2022-10-25
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/45870
dc.description.abstractWe consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the systems of binary consequence relation and proving correctness and completeness theorems for these deductive systems.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.subjectGeneralized truth valuesen
dc.subjectconsequence relationen
dc.subjectfirst degree entailmenten
dc.titleBasic Four-Valued Systems of Cyclic Negationsen
dc.typeOther
dc.page.number507-533
dc.contributor.authorAffiliationGrigoriev, Oleg - Lomonosov Moscow State University, Faculty of Philosophy, Department of Logic, 119234, Lomonosovskiy prospect 24, Building 4, Moscow, Russiaen
dc.contributor.authorAffiliationZaitsev, Dmitry - Lomonosov Moscow State University, Faculty of Philosophy, Department of Logic, 119234, Lomonosovskiy prospect 24, Building 4, Moscow, Russiaen
dc.identifier.eissn2449-836X
dc.referencesN. D. Belnap, A Useful Four-Valued Logic, [in:] J. M. Dunn, G. Epstein (eds.), Modern Uses of Multiple-Valued Logic, Springer Netherlands, Dordrecht (1977), pp. 5–37, DOI: https://doi.org/10.1007/978-94-010-1161-7_2en
dc.referencesN. D. Belnap, How a Computer Should Think, [in:] H. Omori, H. Wansing (eds.), New Essays on Belnap-Dunn Logic, Springer International Publishing, Cham (2019), pp. 35–53, DOI: https://doi.org/10.1007/978-3-030-31136-0_4en
dc.referencesJ. V. Benthem, Logical dynamics meets logical pluralism?, The Australasian Journal of Logic, vol. 6 (2008), pp. 182–209, DOI: https://doi.org/10.26686/ajl.v6i0.1801en
dc.referencesM. L. D. Chiara, R. Giuntini, R. Greechie, Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics, vol. 22 of Trends in Logic, Springer Science & Business Media (2013), DOI: https://doi.org/https://doi.org/10.1007/978-94-017-0526-4en
dc.referencesM. L. D. Chiara, R. Giuntini, R. Leporini, Logics from quantum computation, International Journal of Quantum Information, vol. 03(02) (2005), pp. 293–337, DOI: https://doi.org/10.1142/s0219749905000943en
dc.referencesD. Deutsch, A. Ekert, R. Lupacchini, Machines, logic and quantum physics, Bulletin of Symbolic Logic, vol. 6(3) (2000), pp. 265–283, DOI: https://doi.org/10.2307/421056en
dc.referencesÍ. M. L. D'Ottaviano, H. de Araujo Feitosa, Many-valued logics and translations, Journal of Applied Non-Classical Logics, vol. 9(1) (1999), pp. 121–140, DOI: https://doi.org/10.1080/11663081.1999.10510960en
dc.referencesJ. M. Dunn, Star and perp: Two treatments of negation, Philosophical Perspectives, vol. 7 (1993), pp. 331–357, DOI: https://doi.org/10.2307/2214128en
dc.referencesJ. M. Dunn, Partiality and its dual, Studia Logica, vol. 66 (2000), pp. 5–40, DOI: https://doi.org/10.1023/A:1026740726955en
dc.referencesJ. M. Dunn, G. Hardegree, Algebraic Methods in Philosophical Logic, Oxford University Press (2001).en
dc.referencesH. A. Feitosa, I. M. L. D'Ottaviano, Conservative translations, Annals of Pure and Applied Logic, vol. 108(1–3) (2001), pp. 205–227, DOI: https://doi.org/10.1016/s0168-0072(00)00046-4en
dc.referencesR. French, Translational embeddings in modal logic, Ph.D. thesis, Monash University (2010).en
dc.referencesD. M. Gabbay, H. Wansing (eds.), What is a negation?, vol. 13 of Applied Logic Series, Springer Netherlands (1999), DOI: https://doi.org/10.1007/978-94-015-9309-0en
dc.referencesL. Humberstone, Negation by iteration, Theoria, vol. 61(1) (1995), pp. 1–24, DOI: https://doi.org/10.1111/j.1755-2567.1995.tb00489.xen
dc.referencesN. Kamide, Paraconsistent double negations as classical and intuitionistic negations, Studia Logica, vol. 105(6) (2017), pp. 1167–1191, DOI: https://doi.org/10.1007/s11225-017-9731-2en
dc.referencesS. P. Odintsov, Constructive Negations and Paraconsistency, Springer Netherlands (2008), DOI: https://doi.org/10.1007/978-1-4020-6867-6en
dc.referencesH. Omori, K. Sano, Generalizing functional completeness in Belnap-Dunn logic, Studia Logica, vol. 103(5) (2015), pp. 883–917, DOI: https://doi.org/10.1007/s11225-014-9597-5en
dc.referencesH. Omori, H. Wansing, On contra-classical variants of Nelson logic N4 and its classical extension, The Review of Symbolic Logic, vol. 11 (2018), pp. 805–820, DOI: https://doi.org/10.1017/s1755020318000308en
dc.referencesF. Paoli, Bilattice Logics and Demi-Negation, [in:] H. Omori, H. Wansing (eds.), New Essays on Belnap–Dunn Logic, Springer International Publishing, Cham (2019), pp. 233–253, DOI: https://doi.org/10.1007/978-3-030-31136-0_14en
dc.referencesE. Post, Introduction to a general theory of elementary propositions, American Journal of Mathematics, vol. 43 (1921), pp. 163–185, DOI: https://doi.org/10.2307/2370324en
dc.referencesH. Rasiowa, An Algebraic Approach to Non-Classical Logics, vol. 78 of Studies in Logic and Foundations of Mathematics, North-Holland, Amsterdam (1974).en
dc.referencesP. Ruet, Complete set of connectives and complete sequent calculus for Belnap’s logic, Tech. rep., École Normale Supérieure, Logic Colloquium 96, Document LIENS-96–28 (1996).en
dc.referencesY. Shramko, J. M. Dunn, T. Takenaka, The trilattice of constructive truth values, Journal of Logic and Computation, vol. 11(6) (2001), pp. 761–788, DOI: https://doi.org/10.1093/logcom/11.6.761en
dc.referencesY. Shramko, H. Wansing, Some useful 16-valued logics: How a computer network should think, Journal of Philosophical Logic, vol. 34(2) (2005), pp. 121–153, DOI: https://doi.org/10.1007/s10992-005-0556-5en
dc.referencesJ. van Benthem, Logical Dynamics of Information and Interaction, Cambridge University Press (2011), DOI: https://doi.org/10.1017/cbo9780511974533en
dc.referencesH. Wansing (ed.), Negation: A notion in focus, vol. 7 of Perspectives in Analytical Philosophy, W. De Gruyter (1996), DOI: https://doi.org/10.1515/9783110876802en
dc.referencesD. Zaitsev, A few more useful 8-valued logics for reasoning with tetralattice EIGHT₄, Studia Logica, vol. 92(2) (2009), pp. 265–280, DOI: https://doi.org/10.1007/s11225-009-9198-xen
dc.referencesD. Zaitsev, O. Grigoriev, Two kinds of truth – one logic, Logical Investigations, vol. 17 (2011), pp. 121–139, DOI: https://doi.org/https://doi.org/10.21146/2074-1472-2011-17-0-121-139, (in Russian).en
dc.referencesD. Zaitsev, Y. Shramko, Bi-facial truth: A case for generalized truth values, Studia Logica, vol. 101(6) (2013), pp. 1299–1318, DOI: https://doi.org/10.1007/s11225-013-9534-zen
dc.contributor.authorEmailGrigoriev, Oleg - grig@philos.msu.ru
dc.contributor.authorEmailZaitsev, Dmitry - zaitsev@philos.msu.ru
dc.identifier.doi10.18778/0138-0680.2022.21
dc.relation.volume51


Files in this item

Thumbnail
Name:
507-533_Grigoriev,_Zaitsev.pdf
Size:
1.842Mb
Format:
PDF
View/Open

This item appears in the following Collection(s)

Show simple item record

https://creativecommons.org/licenses/by-nc-nd/4.0
Except where otherwise noted, this item's license is described as https://creativecommons.org/licenses/by-nc-nd/4.0