Best solving modal equations
type: Item
instance of: scholarly article
title: Best solving modal equations
zbMATH Open document ID: 0949.03010
DOI: 10.1016/S0168-0072(99)00032-9
author: Silvio Ghilardi
published in: Annals of Pure and Applied Logic
publication date: 2000-12-06T00:00:00Z
review text: Classical propositional calculus enjoys the following property: for every formula \(A\), if there is a substitution \(\sigma\), such that \(\sigma(A)\) is provable, then there is ``the best'' substitution with this property. But for other logical calculi, for some modal calculi in particular, this property is not valid. However in many systems, like K4, S4, S4Grz, GL, etc., there are finitely many ``best substitutions'' for any formula admitting at least a unifier. In other words if an equation is solvable in the free algebra, then there are finitely many ``best solutions''. The author shows that such solutions can be effectively computed.
Mathematics Subject Classification ID: 03B35
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 08B20
zbMATH DE Number: 1423280
zbMATH Keywords: modal logic
zbMATH Keywords: \(E\)-unification
zbMATH Keywords: equations in free algebras
Wikidata QID: Q56474448
reviewed by: Nail Zamov
MaRDI profile type: Publication
cites work: Q4285787
cites work: Logics containing K4. Part I
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cites work: Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus
cites work: Unification theory
full work available at URL: s0168-0072(99)00032-9
OpenAlex ID: W2077847391
DBLP publication ID: journals/apal/Ghilardi00
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description: scientific article; zbMATH DE number 1423280