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On a First-Order Bi-Sorted Semantically Closed Language

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Abstract

This paper is about the concept of semantically closed languages. Roughly speaking, those are languages which can name their own sentences and apply to them semantic predicates, such as the truth or satisfaction predicates. Hence, they are “self-referential languages,” in the sense that they are capable of producing sentences about themselves or other sentences in the same language. In section one, we introduce the concept informally; in section two, we provide the formal definition of first-order semantically closed languages, which is the Tarskian definition with some technical modifications. Then, we construct a semantic for this kind of language, and prove that the language is indeed semantically closed (according to Definition 1). Finally, we discuss whether the logic underlying the construction is classical, and future goals of this research.

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Authors and Affiliations

  1. Philosophy Department, University of São Paulo, Rua do Lago 717, São Paulo, SP, Brazil

    Fernanda Birolli Abrahão & Edelcio Gonçalves de Souza

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  1. Fernanda Birolli Abrahão
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  2. Edelcio Gonçalves de Souza
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Correspondence to Fernanda Birolli Abrahão.

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Special Issue: Contemporary Logic in Brazil

Edited by Edward H. Haeusler, Ciro Russo, and Gisele Secco.

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Abrahão, F.B., de Souza, E.G. On a First-Order Bi-Sorted Semantically Closed Language. Stud Logica (2024). https://doi.org/10.1007/s11225-024-10104-6

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  • DOI: https://doi.org/10.1007/s11225-024-10104-6

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