Free Definite Description Theory – Sequent Calculi and Cut Elimination

Logic and Logical Philosophy:1 (forthcoming)
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Abstract

We provide an application of a sequent calculus framework to the formalization of definite descriptions. It is a continuation of research undertaken in [20, 22]. In the present paper a so-called free description theory is examined in the context of different kinds of free logic, including systems applied in computer science and constructive mathematics for dealing with partial functions. It is shown that the same theory in different logics may be formalised by means of different rules and gives results of varying strength. For all presented calculi a constructive cut elimination is provided.

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2020-11-03

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Andrzej Indrzejczak
University of Lodz

References found in this work

[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
Free logics.Ermanno Bencivenga - 2002 - In D. M. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition. Kluwer Academic Publishers. pp. 147--196.
A More Unified Approach to Free Logics.Edi Pavlović & Norbert Gratzl - 2020 - Journal of Philosophical Logic 50 (1):117-148.
More free logic.Scott Lehmann - 2002 - In D. M. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic Vol. 5. Kluwer Academic Publishers. pp. 197-259.

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