Kürbis, N;
(2021)
Proof-Theory and Semantics for a Theory of Definite Descriptions.
In: Das, A and Negri, S, (eds.)
TABLEAUX 2021: Automated Reasoning with Analytic Tableaux and Related Methods.
(pp. 95-111).
Springer: Cham, Switzerland.
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Abstract
This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown to be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive.
Type: | Book chapter |
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Title: | Proof-Theory and Semantics for a Theory of Definite Descriptions |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1007/978-3-030-86059-2_6 |
Publisher version: | https://doi.org/10.1007/978-3-030-86059-2_6 |
Language: | English |
Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Definite descriptions, Positive free logic, Proof theory, Sequent calculus, Cut elimination, Dual domain semantics |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL SLASH UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > Dept of Philosophy |
URI: | https://discovery.ucl.ac.uk/id/eprint/10132750 |
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