# Interpreting descriptions in intensional type theory

@article{Carlstrm2005InterpretingDI, title={Interpreting descriptions in intensional type theory}, author={Jesper Carlstr{\"o}m}, journal={Journal of Symbolic Logic}, year={2005}, volume={70}, pages={488 - 514} }

Abstract Natural deduction systems with indefinite and definite descriptions (ε-terms and ι-terms) are presented, and interpreted in Martin-LÖf's intensional type theory. The interpretations are formalizations of ideas which are implicit in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of ‘the element such that the property holds’ and refer by that phrase to the element constructed in the existence proof. In particular, we…

## 4 Citations

A Presuppositional Analysis of Definite Descriptions in Proof Theory

- Computer Science, PhilosophyJSAI
- 2007

A proof-theoretic analysis of presuppositions in natural language, focusing on the interpretation of definite descriptions, and shows how to treat presupposition projection and accommodation within the proof- theoretic framework.

Free Definite Description Theory – Sequent Calculi and Cut Elimination

- Computer Science
- 2020

It is shown that the same theory in different logics may be formalised by means of different rules and gives results of varying strength.

Toward the Formulation of Presupposition by Illative Combinatory Logic

- PhilosophyLACL
- 2012

One proof is based on soundness and the other on cut-elimination, which makes use of different resources but also together reveals what the consistency of predicate calculus indeed depends on.

A novel approach to equality

- MathematicsSynthese
- 2021

A new type of formalization of classical first-order logic with equality is introduced on the basis of the sequent calculus. It serves to justify the claim that equality is a logical constant…

## References

SHOWING 1-10 OF 30 REFERENCES

Collection Principles in Dependent Type Theory

- PhilosophyTYPES
- 2000

We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond…

Intuitionistic Predicate Calculus with ε-Symbol

- Philosophy
- 1971

predicate calculus with ?-symbol used in Maehara [5] contains incompletely the ?-terms in the usual sense . In this paper, we treat an intuitionistic predicate calculus with ?-symbol containing all…

Choice in Dynamic Linking

- Computer ScienceFoSSaCS
- 2004

A computational interpretation for Hilbert’s choice operator (e) is introduced, which yields a typed foundation for dynamic linking in software systems and defines and investigates operational semantics.

Subsets, Quotients and Partial Functions in Martin-Löf's Type Theory

- Mathematics, PhilosophyTYPES
- 2002

The method used is not to make any changes to the type theory itself, but to view the new concepts as defined ones, with subsets as propositional functions.

A General Theory of Completeness Proofs

- Philosophy
- 1970

The purpose of the following treatise is to remark the fact that the method developed in Schiitte [6] is able to give a unification to completeness proofs for several formal systems of logic.…

Type-Theoretical Grammar

- Linguistics
- 1995

1. Preliminary remarks 2. Gradual introduction to type theory 3. Logical operators in English 4. Anaphoric expressions 5. Temporal reference 6. Text and discourse 7. Context and possible worlds 8.…

Programming in Martin-Löf's Type Theory

- Mathematics
- 1990

data type, 179 abstraction, 14 Abstraction rule, 143 absurdity, 43 append, 68 application, 13 Application rule, 143 apply, 48, 148 arity of an expression, 18 Assumption rule, 123, 142 AUTOMATH, 8…

Intuitionistic type theory

- PhilosophyStudies in proof theory
- 1984

These lectures were given in Padova and Munich later in the same year as part of the meeting on Konstruktive Mengenlehre und Typentheorie which was organized in Munich by Prof. Helmut Schwichtenberg.

Introduction to Mathematical Philosophy

- Philosophy
- 1919

Bertrand Russell is the most important philosopher of mathematics of the twentieth century. The author of The Principles of Mathematics and, with Alfred Whitehead, the massive Principia Mathematica ,…