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2014 | 23 | 4 | 371–390
Article title

A simple Henkin-style completeness proof for Gödel 3-valued logic G3

Authors
Title variants
Languages of publication
EN
Abstracts
EN
A simple Henkin-style completeness proof for Gödel 3-valued propositional logic G3 is provided. The idea is to endow G3 with an under-determined semantics (u-semantics) of the type defined by Dunn. The key concept in u-semantics is that of “under-determined interpretation” (u-interpretation). It is shown that consistent prime theories built upon G3 can be understood as (canonical) u-interpretations. In order to prove this fact we follow Brady by defining G3 as an extension of Anderson and Belnap’s positive fragment of First Degree Entailment Logic.
Year
Volume
23
Issue
4
Pages
371–390
Physical description
Dates
published
2014-12-01
online
2014-01-07 2014-12-01
Contributors
author
  • Dpto. de Psicología, Sociología y Filosofía, Universidad de León, Campus de Vegazana, s/n, 24071, León, Spain
References
  • Anderson, A.R., and N.D. Belnap, Jr., Entailment. The Logic of Relevance and Necessity, vol. I, Princeton University Press, 1975.
  • Baaz, M., N. Preining, and R. Zach, “First-Order Gödel Logics”, Annals of Pure and Applied Logic, 147 (2007): 23–47. DOI: 10.1016/j.apal.2007.03.001
  • Brady, R., “Completeness Proofs for the Systems RM3 and BN4”, Logique et Analyse, 25 (1982): 9–32.
  • Dunn, J.M., “The algebra of intensional logics” (1966). Doctoral dissertation, University of Pittsburgh (Ann Arbor, University Microfilms).
  • Dunn, J.M., “Intuitive semantics for first-degree entailments and ‘coupled trees’”, Philosophical Studies, 29 (1976): 149–168. DOI: 10.1007/BF00373152
  • Dunn, J.M. “A Kripke-style semantics for R-Mingle using a binary accessibility relation”, Studia Logica, 35 (1976): 163–172. DOI: 10.1007/BF02120878
  • Dunn, J.M., “Partiality and its dual”, Studia Logica, 66 (2000), 5–40. DOI: 10.1023/A:1026740726955
  • Dunn, J.M., and R.K. Meyer, “Algebraic completeness results for Dummett’s LC and its extensions”, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 17 (1971), 225–230. DOI: 10.1002/malq.19710170126
  • Gödel, K., “Zum intuitionistischen Aussagenkalkül”, Anzeiger Akademie der Wissenschaffen Wien, Math.-Naturwissensch, Klasse, 69 (1933): 65–66.
  • González, C., “MaTest” (2012), available at Link (Last access 10/10/2013).
  • Łukasiewicz, J., “Die Logik und das Grundlagenproblem”, Les Entretiens de Zürich sur les Fondaments et la Méthode des Sciences Mathématiques, 6–9 (1938), 12: 82–100.
  • Robles. G., “A Routley-Meyer semantics for Gödel 3-valued logic and its paraconsistent counterpart”, Logica Universalis (forthcoming). DOI: 10.1007/s11787-013-0088-7
  • Robles, G., and J.M. Méndez,“A paraconsistent 3-valued logic related to Gödel logic G3”(manuscript).
  • Robles, G., F. Salto, and J.M. Méndez, “Dual equivalent two-valued under-determined and over-determined interpretations for Łukasiewicz’s 3-valued Logic Ł3”, Journal of Philosophical Logic (2013). DOI: 10.1007/s10992-012-9264-0
  • Routley, R., V. Routley, “Semantics of first-degree entailment”, Noûs, 1(1972): 335–359. DOI: 10.2307/2214309
  • Routley, R., R.K. Meyer, V. Plumwood, and R.T. Brady, Relevant Logics and their Rivals, vol. 1, Atascadero, CA: Ridgeview Publishing Co., 1982.
  • Slaney, J., MaGIC, Matrix Generator for Implication Connectives: Version 2.1, Notes and Guide, Canberra: Australian National University, 1995. Link
  • Van Fraasen, B., “Facts and tautological entailments”, The Journal of Philosophy, 67 (1969): 477–487. DOI: 10.2307/2024563
  • Yang, E., “(Star-based) three-valued Kripke-style semantics for pseudo-and weak-Boolean logics”, Logic Journal of the IGPL, 20 (2012): 187–206. DOI: 10.1093/jigpal/jzr030
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-03517793-cd1f-4c0a-a052-456e13cdba2f
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