Analytic implication
type: Item
instance of: scholarly article
title: Analytic implication
zbMATH Open document ID: 0621.03006
author: Kit Fine
published in: Notre Dame Journal of Formal Logic
publication date: 1986-01-01T00:00:00Z
review text: The idea of so-called analytic implication put forward by W. T. Parry may be described informally as follows: a proposition A analytically implies another proposition B iff (1) A necessarily (or strictly) implies B and (2) the ''constitutive content'' of B is contained in the constitutive content of A. In this paper a formalized theory of analytic implication is developed by way of introducing a new relation 'A\(\preccurlyeq B'\) to be read as ''the constitutive content of A is included in that of B''. If this relation is assumed to form a lattice (and moreover to hold necessarily where the underlying logic of necessity is S4), it can be shown that the resulting system for analytic implication to be defined as \((A\to B):=\square (A\supset B)\wedge (B\preccurlyeq A)\) is equivalent to Parry's original system.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 4006232
zbMATH Keywords: entailment
zbMATH Keywords: analytic implication
zbMATH Keywords: formalized theory
reviewed by: Wolfgang Lenzen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093636609
OpenAlex ID: W4250694390
DOI: 10.1305/NDJFL/1093636609
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description: scientific article; zbMATH DE number 4006232