David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Notre Dame Journal of Formal Logic 50 (3):275-301 (2009)
We present $\in_I$-Logic (Epsilon-I-Logic), a non-Fregean intuitionistic logic with a truth predicate and a falsity predicate as intuitionistic negation. $\in_I$ is an extension and intuitionistic generalization of the classical logic $\in_T$ (without quantifiers) designed by Sträter as a theory of truth with propositional self-reference. The intensional semantics of $\in_T$ offers a new solution to semantic paradoxes. In the present paper we introduce an intuitionistic semantics and study some semantic notions in this broader context. Also we enrich the quantifier-free language by the new connective < that expresses reference between statements and yields a finer characterization of intensional models. Our results in the intuitionistic setting lead to a clear distinction between the notion of denotation of a sentence and the here-proposed notion of extension of a sentence (both concepts are equivalent in the classical context). We generalize the Fregean Axiom to an intuitionistic version not valid in $\in_I$. A main result of the paper is the development of several model constructions. We construct intensional models and present a method for the construction of standard models which contain specific (self-)referential propositions
|Keywords||truth theory non-Fregean logics self-reference intuitionistic logic semantic paradoxes intensional semantics extension intension denotation|
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Steffen Lewitzka (2015). Denotational Semantics for Modal Systems S3–S5 Extended by Axioms for Propositional Quantifiers and Identity. Studia Logica 103 (3):507-544.
Steffen Lewitzka (2011). ?K: A Non-Fregean Logic of Explicit Knowledge. Studia Logica 97 (2):233-264.
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