Assertion, denial and some cancellation rules in modal logic
type: Item
instance of: scholarly article
title: Assertion, denial and some cancellation rules in modal logic
zbMATH Open document ID: 0651.03010
DOI: 10.1007/BF00247956
author: Timothy Williamson
published in: Journal of Philosophical Logic
publication date: 1988-01-01T00:00:00Z
review text: The author considers that principle that assertability conditions determine truth conditions. In any normal propositional modal logic with Ḻ to mean `it is assertable that', this principle can be formalized as the rule LA\(\leftrightarrow LB/A\leftrightarrow B\) (i.e. from the theoremhood of LA\(\leftrightarrow LB\) to infer \(A\leftrightarrow B)\). This rule is shown to trivialize any system containing either T or S4 in that it enables the proof of LA\(\leftrightarrow A\) for every wff. If however the rule is replaced by LA\(\leftrightarrow LB\), MA\(\leftrightarrow MB/A\leftrightarrow B\), then Sobocinski's K4 is obtained, which is \(S4+p\to (MLp\to Lp)+LMp\to MLp\).
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 4061198
zbMATH Keywords: assertability conditions
zbMATH Keywords: truth conditions
zbMATH Keywords: propositional modal logic
reviewed by: M. J. Cresswell
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4061198