On the Computational Meaning of AxiomsReport as inadecuate

On the Computational Meaning of Axioms - Download this document for free, or read online. Document in PDF available to download.

1 IHPST - Institut d-Histoire et de Philosophie des Sciences et des Techniques 2 IHES - Institut des Hautes Etudes Scientifiques

Abstract : An anti-realist theory of meaning suitable for both logical and proper axioms is investigated. As opposed to other anti-realist accounts, like Dummett-Prawitz verificationism, the standard framework of classical logic is not called into question. In particular, semantical features are not limited solely to inferential ones, but also computational aspects play an essential role in the process of determination of meaning. In order to deal with such computational aspects, a relaxation of syntax is shown to be necessary. This leads to a general kind of proof theory, where the objects of study are not typed objects like deductions, but rather untyped ones, in which formulas have been replaced by geometrical configurations.

Keywords : Typed vs. untyped proof-objects Proof theory Anti-realist theory of meaning Axioms Computational interpretation of proofs Typed vs. untyped proof-objects.

Author: Alberto Naibo - Mattia Petrolo - Thomas Seiller -

Source: https://hal.archives-ouvertes.fr/


Related documents