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  1. 2 Bulletin of the Section of Logic

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  1. 2 Kürbis N.

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  1. 2 2019

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A Binary Quantifier for Definite Descriptions in Intuitionist Negative Free Logic: Natural Deduction and Normalisation

100%
Kürbis N.
Bulletin of the Section of Logic
|
2019
|
tom 48
|
nr 2
81-97
EN
This paper presents a way of formalising definite descriptions with a binary quantifier ℩, where ℩x[F, G] is read as `The F is G'. Introduction and elimination rules for ℩ in a system of intuitionist negative free logic are formulated. Procedures for removing maximal formulas of the form ℩x[F, G] are given, and it is shown that deductions in the system can be brought into normal form.
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Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

75%
Kürbis N.
Bulletin of the Section of Logic
|
2019
|
tom 48
|
nr 4
EN
Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantier that forms a formula out of two predicates, where ℩x[F;G] is read as `The F is G'. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INF℩ of intuitionist negative free logic extended by such a quantier, which was presented in [4], INF℩ is first compared to a system of Tennant's and an axiomatic treatment of a term forming ℩ operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INF℩ in which the G of ℩x[F;G] is restricted to identity. INF℩ is then compared to an intuitionist version of a system of Lambert's which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion.
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