An operational logic of proofs with positive and negative information
type: Item
instance of: scholarly article
title: An operational logic of proofs with positive and negative information
zbMATH Open document ID: 0947.03077
DOI: 10.1023/A:1005298816666
author: Duccio Luchi
author: Franco Montagna
published in: Studia Logica
publication date: 2000-11-05T00:00:00Z
review text: As a generalization of provability logic, which deals with formal provability, Artemov introduced a dynamic logic in order to study the concept of proof in a formal way. Inspired by this idea, the authors investigate some natural operations on proofs based on the arithmetical interpretation and formalize some fragment of such kind of logic of proofs, which then is shown to be complete and decidable with respect to the arithmetical interpretation. An important advantage of the system in this paper compared to Artemov's original logic is that it is given by considering not only positive but also negative imformations on proofs such as ``not being a proof'', for instance.
reviewed by: Osamu Sonobe
Mathematics Subject Classification ID: 03F45
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F07
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 1420244
zbMATH Keywords: provability logic
zbMATH Keywords: logic of proofs
zbMATH Keywords: proof theory
zbMATH Keywords: arithmetical interpretation
MaRDI profile type: Publication
full work available at URL: a:1005298816666
OpenAlex ID: W1517928606
description: scientific article; zbMATH DE number 1420244