PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2021 | 50 | 1 | 35-53
Tytuł artykułu

A Semi-lattice of Four-valued Literal-paraconsistent-paracomplete Logics

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we consider the class of four-valued literal-paraconsistent-paracomplete logics constructed by combination of isomorphs of classical logic CPC. These logics form a 10-element upper semi-lattice with respect to the functional embeddinig one logic into another. The mechanism of variation of paraconsistency and paracompleteness properties in logics is demonstrated on the example of two four-element lattices included in the upper semi-lattice. Functional properties and sets of tautologies of corresponding literal-paraconsistent-paracomplete matrices are investigated. Among the considered matrices there are the matrix of Puga and da Costa's logic V and the matrix of paranormal logic P1I1, which is the part of a sequence of paranormal matrices proposed by V. Fernández.
Rocznik
Tom
50
Numer
1
Strony
35-53
Opis fizyczny
Daty
wydano
2021-03-30
Twórcy
  • Russian Academy of Sciences, Institute of Philosophy, Goncharnaya 12/1, 109240 Moscow, Russian Federation
Bibliografia
  • [1] O. Arieli, A. Avron, Four-valued paradefinite logics, Studia Logica, vol. 105(6) (2017), pp. 1087–1122, DOI: https://doi.org/10.1007/s11225-017-9721-4
  • [2] D. A. Bochvar, V. K. Finn, On many-valued logics admitting formalization of the analysis of antinomies. 1, [in:] Studies in mathematical linguistics, mathematical logic and information languages, Nauka, Moscow (1972), pp. 238–295.
  • [3] L. Bolc, P. Borowik, Many-valued Logics: 1: Theoretical Foundations , Springer-Verlag Berlin Heidelberg (1992).
  • [4] J. Ciuciura, A weakly-intuitionistic logic I1, Logical Investigations, vol. 21(2) (2015), pp. 53–60.
  • [5] L. Y. Devyatkin, On a continual class of four-valued maximally paranormal logics, Logical Investigations, vol. 24(2) (2018), pp. 85–91, DOI: https://doi.org/10.21146/2074-1472-2018-24-2-85-91 , in Russian.
  • [6] V. L. Fernández, Semântica de Sociedades para Lógicas n-valentes, Master's thesis, Campinas: IFCH-UNICAMP (2001).
  • [7] V. L. Fernández, M. E. Coniglio, Combining valuations with society semantics, Journal of Applied Non-Classical Logics, vol. 13(1) (2003), pp. 21–46, DOI: https://doi.org/10.3166/jancl.13.21-46
  • [8] S. Jaśkowski, A propositional calculus for inconsistent deductive systems, Studia Logica, vol. 24 (1969), pp. 143–157.
  • [9] A. Karpenko, N. Tomova, Bochvar's three-valued logic and literal paralogics: the lattice and functional equivalence, Logic and Logical Philosophy, vol. 26(2) (2017), pp. 207–235, DOI: https://doi.org/10.12775/LLP.2016.029
  • [10] A. S. Karpenko, Jaśkowski's criterion and three-valued paraconsistent logics, Logic and Logical Philosophy, vol. 7 (1999), pp. 81–86, DOI: https://doi.org/10.12775/LLP.1999.006
  • [11] A. S. Karpenko, A maximal paraconsistent logic: The combination of two three-valued isomorphs of classical propositional logic, [in:] D. Batens, C. Mortensen, G. Priest, J.-P. Van Bendegem (eds.), Frontiers of Paraconsistent Logic, Baldock Research Studies Press (2000), pp. 181–187.
  • [12] A. S. Karpenko, N. E. Tomova, Bochvar's three-valued logic and literal paralogics, Institute of Philosophy of Russian Academy of Science, Moscow (2016).
  • [13] R. A. Lewin, I. F. Mikenberg, Literal-paraconsistent and literal-paracomplete matrices, Mathematical Logic Quarterly, vol. 52(5) (2006), pp. 478–493, DOI: https://doi.org/10.1002/malq.200510044
  • [14] E. Mendelson, Introduction to Mathematical Logic, 4th ed., Chapman & Hall (1997).
  • [15] Y. I. Petrukhin, Deduction Normalization Theorem for Sette's Logic and Its Modifications, Moscow University Mathematics Bulletin, vol. 74(1) (2019), pp. 25–31, DOI: https://doi.org/10.3103/S0027132219010054
  • [16] V. M. Popov, On the logics related to A. Arruda's system V1, Logic and Logical Philosophy, vol. 7 (1999), pp. 87–90, DOI: https://doi.org/10.12775/LLP.1999.007
  • [17] G. Priest, K. Tanaka, Z. Weber, Paraconsistent logic (2013), URL: http://plato.stanford.edu/entries/logic-paraconsistent , Stanford Encyclopedia of Philosophy.
  • [18] L. Z. Puga, N. C. A. Da Costa, On the imaginary logic of N. A. Vasiliev, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, vol. 34 (1988), pp. 205–211.
  • [19] A. M. Sette, On propositional calculus P1, Mathematica Japonicae, vol. 18 (1973), pp. 173–180.
  • [20] A. M. Sette, E. H. Alves, On the equivalence between some systems of non-classical logic, Bulletin of the Section of Logic, vol. 25(2) (1973), pp. 68–72.
  • [21] A. M. Sette, W. A. Carnielli, Maximal weakly-intuitionistic logics, Studia Logica, vol. 55(1) (1995), pp. 181–203, DOI: https://doi.org/10.1007/BF01053037
  • [22] N. E. Tomova, On properties of a class of four-valued papranormal logics, Logical Investigations, vol. 24(1) (2018), pp. 75–89, DOI: https://doi.org/10.21146/2074-1472-2018-24-1-75-89
  • [23] N. E. Tomova, A. N. Nepeivoda, Functional properties of four-valued paralogics, Logical-Philosophical Studies, vol. 16(1–2) (2018), pp. 130–132.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ojs-doi-10_18778_0138-0680_2020_24
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.