A new axiomatization of Belnap's conditional assertion
type: Item
instance of: scholarly article
title: A new axiomatization of Belnap's conditional assertion
zbMATH Open document ID: 0592.03015
author: Daniel H. Cohen
published in: Notre Dame Journal of Formal Logic
publication date: 1986-01-01T00:00:00Z
review text: A conditional assertion, as distinguished from the assertion of a conditional, asserts just its consequent, provided that the antecedent condition of assertion is met. If that condition is not met, there is no assertion at all. Nonassertive subformulas make no contribution to truth- functional compounds of which they are a part. This feature enables conditional assertions, in conjunction with standard, unrestricted quantifiers, to effect restricted quantification. However, it also means that classically valid schemata will have non-true and even falsifiable instances. This paper provides an axiomatization of the never-false formulas of the language (and, by a result of \textit{J. M. Dunn} [J. Philos. Logic 4, 383-397 (1975; Zbl 0329.02006)], also of the always-true formulas). The key technical innovation is the definition of a function from formulas to formulas, such that the latter are true just when the former are assertive (true or false), and false otherwise. This makes it possible to specify a decidable axiom set using ''impure'', conditioned axiom schemata - there is no single logical form that all instances of a schemata share - or, alternatively, to provide actual axioms with a conditioned, i.e. restrictive, rule of substitution.
Mathematics Subject Classification ID: 03B60
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 3950492
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093636531
OpenAlex ID: W1998166524
DOI: 10.1305/NDJFL/1093636531
description: scientific article; zbMATH DE number 3950492