Two Treatments of Definite Descriptions in Intuitionist Negative Free Logic

08/04/2021
by   Nils Kürbis, et al.
0

Sentences containing definite descriptions, expressions of the form `The F', can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ι 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^ι of intuitionist negative free logic extended by such a quantifier, which was presented in <cit.>, 𝐈𝐍𝐅^ι is first compared to a system of Tennant's and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of 𝐈𝐍𝐅^ι in which the G of ι x[F, G] is restricted to identity. 𝐈𝐍𝐅^ι 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/04/2021

Definite Descriptions in Intuitionist Positive Free Logic

This paper presents rules of inference for a binary quantifier I for the...
research
08/04/2021

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

This paper presents a way of formalising definite descriptions with a bi...
research
08/09/2021

Proof-Theory and Semantics for a Theory of Definite Descriptions

This paper presents a sequent calculus and a dual domain semantics for a...
research
07/15/2021

Tableaux for Free Logics with Descriptions

The paper provides a tableau approach to definite descriptions. We focus...
research
06/29/2021

On Free Description Logics with Definite Descriptions

Definite descriptions are phrases of the form 'the x such that φ', used ...
research
08/16/2023

Non-Rigid Designators in Epistemic and Temporal Free Description Logics (Extended Version)

Definite descriptions, such as 'the smallest planet in the Solar System'...
research
05/19/2019

Is Free Choice Permission Admissible in Classical Deontic Logic?

In this paper, we explore how, and if, free choice permission (FCP) can ...

Please sign up or login with your details

Forgot password? Click here to reset