Correia Semantics Revisited

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• 作者：Thomas Macaulay Ferguson
• 关键词：Analytic containment ; Correia semantics ; Many ; valued logic
• 刊名：Studia Logica
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：104
• 期：1
• 页码：145-173
• 全文大小：651 KB
• 参考文献：1.Angell R. B.: Three systems of first degree entailment. Journal of Symbolic Logic 42(1), 147 (1977)
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  22.Jennings, R. E., and Y. Chen, Articular models for first-degree paraconsistent systems, in Proceedings of the 9th IEEE International Conference on Cognitive Informatics (ICCI 2010), IEEE Computer Society, Los Alamitos, CA, 2010, pp. 904–907.
  23.Jennings, R. E., Y. Chen, and J. Sahasrabudhe, On a new idiom in the study of entailment, Logica Universalis 5(1):101–113, 2011.
  24.Kleene, S. C., Introduction to Metamathematics, North-Holland Publishing Company, Amsterdam, 1952.
  25.Parry, W. T., Ein Axiomensystem für eine neue Art von Implikation (analytische Implikation), Ergebnisse eines mathematischen Kolloquiums 4:5–6, 1933.
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• 作者单位：Thomas Macaulay Ferguson (1)
  
  1. Department of Philosophy, City University of New York Graduate Center, 365 Fifth Avenue, New York, USA
  
• 刊物类别：Humanities, Social Sciences and Law
• 刊物主题：Philosophy
  Logic
  Mathematical Logic and Foundations
  Computational Linguistics
  
• 出版者：Springer Netherlands
• ISSN：1572-8730

文摘

Despite a renewed interest in Richard Angell’s logic of analytic containment (\({\mathsf{AC}}\)), the first semantics for \({\mathsf{AC}}\) introduced by Fabrice Correia has remained largely unexamined. This paper describes a reasonable approach to Correia semantics by means of a correspondence with a nine-valued semantics for \({\mathsf{AC}}\). The present inquiry employs this correspondence to provide characterizations of a number of propositional logics intermediate between \({\mathsf{AC}}\) and classical logic. In particular, we examine Correia’s purported characterization of classical logic with respect to his semantics, showing the condition Correia cites in fact characterizes the “logic of paradox” \({\mathsf{LP}}\) and provide a correct characterization. Finally, we consider some remarks on related matters, such as the applicability of the present correspondence to the analysis of the system \({\mathsf{AC}^{\ast}}\) and an intriguing relationship between Correia’s models and articular models for first degree entailment. Keywords Analytic containment Correia semantics Many-valued logic