Frege Structures for Partial Applicative Theories

Abstract

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-theoretic strength.

DOI: 10.1093/logcom/9.5.683

Cite this paper

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