# Frege Structures for Partial Applicative Theories

@article{Kahle1999FregeSF, title={Frege Structures for Partial Applicative Theories}, author={Reinhard Kahle}, journal={J. Log. Comput.}, year={1999}, volume={9}, pages={683-700} }

Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories. To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. Both approaches are compatible with the traditional formalizations of Frege structures and preserve the main results, namely abstraction and the proof…

## 8 Citations

### Truth in Applicative Theories

- PhilosophyStud Logica
- 2001

This work presents as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation of Frege structures, and presents the proof-theoretic results for these theories and shows their syntACTical expressive power.

### A feasible theory of truth over combinatory algebra

- Philosophy, Computer ScienceAnn. Pure Appl. Log.
- 2014

### On Applicative Theories

- Mathematics
- 1999

Systems of explicit mathematics were introduced in Feferman [7, 9] in order to give a logical account to Bishop-style constructive mathematics, and they soon turned out to be very important for the…

### Sets, Truth, and Recursion

- Philosophy
- 2015

We discuss some philosophical aspects of an intensional set theory based on an axiomatic truth theory. This set theory gains its justification from natural truth axioms combined with standard…

### Applicative Theories and Explicit Mathematics

- Mathematics
- 2003

[5] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive µ-operator. [6] Solomon Feferman and Gerhard Jäger. Systems of explicit mathematics with non-constructive…

### THE UNIVERSAL SET AND DIAGONALIZATION IN FREGE STRUCTURES

- PhilosophyThe Review of Symbolic Logic
- 2011

The resulting set theory is discussed with respect to its historical and philosophical significance and includes the treatment of diagonalization in the presence of a universal set.

### Extraction of Programs for Exact Real Number Computation Using Agda

- Mathematics, Computer Science
- 2011

This thesis contains the to the authors' knowledge first research project to extract in the theorem prover Agda programs from proofs involving postulated axioms using postulated data types and functions in Agda without giving any computational rules.

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