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2020 | 49 | 1 |

Tytuł artykułu

Nilpotent Minimum Logic NM and Pretabularity

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Abstrakty

EN
This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM-. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness.  

Rocznik

Tom

49

Numer

1

Opis fizyczny

Daty

wydano
2020-03-30

Twórcy

autor
  • Jeonbuk National University, Department of Philosophy & Institute of Critical Thinking and Writing

Bibliografia

  • [1] L. Běhounek and P. Cintula, Fuzzy logics as the logics of chains, Fuzzy Sets and Systems, Vol. 157 (2006), pp. 604–610.
  • [2] P. Cintula, Weakly Implicative (Fuzzy) Logics I: Basic properties, Archive for Mathematical Logic, Vol. 45 (2006), pp. 673–704.
  • [3] J. M. Dunn, Algebraic completeness for R-mingle and its extensions, The Journal of Symbolic Logic, Vol. 35 (1970), pp. 1–13.
  • [4] J. M. Dunn and G. Hardegree, Algebraic Methods in Philosophical Logic, Oxford University Press, Oxford, 2001.
  • [5] J. M. Dunn and R. K. Meyer, Algebraic completeness results for Dummett's LC and its extensions, Mathematical Logic Quarterly, Vol. 17 (1971), pp. 225–230.
  • [6] F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems, Vol. 124 (2001), pp. 271–288.
  • [7] D. Gabbay and V. B. Shetman, Undecidability of modal and intermediate first-order logics with two individual variables, The Journal of Symbolic Logic, Vol. 58 (1993), pp. 800–823.
  • [8] L. Galminas and J. G. Mersch, A pretabular classical relevance logic, Studia Logica, Vol. 100 (2012), pp. 1211–1221.
  • [9] J. Gispert, Axiomatic extensions of the nilpotent minimum logic, Reports on Mathematical Logic, Vol. 37 (2003), pp. 113–123.
  • [10] C. Noguera, F. Esteva, and J. Gispert, On triangular norm based axiomatic extensions of the weak nilpotent minimum logic, Mathematical Logic Quarterly, Vol. 54 (2008), pp. 387–409.
  • [11] V. Rybakov, V. Kiyatkin, and M. Terziler, Independent bases for rules admissible in pretabular logics, Logic Journal of the Interest Group in Pure and Applied Logics, Vol. 7 (1999), pp. 253–266.
  • [12] T. Sugihara, Strict implication free from implicational paradoxes, Memoirs of the Faculty of Liberal Arts, Fukui University, Series 1, 1955, pp. 55–59.
  • [13] K. Świrydowicz, There exists an uncountable set of pretabular extensions of the relevant logic R and each logic of this set is generated by a variety of nite height, The Journal of Symbolic Logic, Vol. 73 (2008), pp. 1249–1270.

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Bibliografia

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bwmeta1.element.ojs-doi-10_18778_0138-0680_2020_01
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