Abstract
In [12] it was shown that the factor semantics based on the notion ofT-F-sequences is a correct model of the Łukasiewicz's infinite-valued logics. But we could not consider some important aspects of the structure of this model because of the short size of paper. In this paper we give a more complete study of this problem: A new proof of the completeness of the factor semantic for Łukasiewicz's logic using Wajsberg algebras [3] (and not MV-algebras in [1]) and Symmetrical Heyting monoids [7] is proposed. Some consequences of such an approach are investigated.
Similar content being viewed by others
References
C. C. Chang,An algebraic analysis of many-valued logics,Trans. Amer. Math. Soc., 88 (1958), pp. 263–265.
P. M. Cohn,Universal Algebra, New York, Evanston and London 1965.
J. M. Font, A. J. Rodrigues andA. Torrens,Wajsberg algebras,Stochastica, v.III, 1 (1984), pp. 5–31.
R. S. Grigolia,Lattice of all finitely approximated extensions of Countable-valued Lukasiewicz's logic, in:Investigations on set theory and non-classical logics, (in Russian), Moscow, 1976, pp. 221 – 228.
A. S. Karpenko,Factor Semantics for Infinite-valued Lukasiewicz's logic, in:Non-classical Logics (Proceedings of the Scientific Seminar on Logic of the Institute of Philosophy), (in Russian), Moscow 1985, pp. 20 – 26.
A. S. Karpenko,Logic as Truth-values, in:8th International Congress of Logic, Methodology and Philosophy of Science (Abstracts), vol.1, Moscow 1987, pp. 263 – 265.
A. S. Karpenko andV. L. Vasyukov,Symmetrical Heyting monoid: a model for Infinite-valued logic of Lukasiewicz, in:Non-classical Logics and Propositional Attitudes (Proceedings of the Scientific Seminar on Logic of the Institute of Philosophy), (in Russian), Moscow 1987, pp. 118 – 124.
P. Mangani,On certain algebras related to many-valued logics,Boll. Univ. Math. J., (4), 8 (1973), pp. 68–78.
C. Mortensen,Model structures and set algebras for Sugihara matrices,Notre Dame J.Form.Log., v.23, 1 (1982), pp. 85–90.
R. Routley andR. Meyer,The Semantics of Entailment, in: H. Leblanc (ed.),Truth, Syntax, Modality, North-Holland, Amsterdam 1973, pp. 199–243.
A. Urquhart,An Interpretation of many-valued logic,Zeitschr.Math.Log. und Grundl.Math., 19 (1973), pp. 111–114.
V. L. Vasyukov,The correctness of the discrete model for Infinite-valued logic of Lukasiewicz, in:Many-valued, Relevant and Paraconsistent Logics (Proceedings of the Scientific Seminar on Logic of the Institute of Philosophy), (in Russian), Moscow 1984, pp. 55 – 64.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vasyukov, V.L. The completeness of the factor semantics for Łukasiewicz's infinite-valued logics. Stud Logica 52, 143–167 (1993). https://doi.org/10.1007/BF01053068
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01053068