Paper Info
Title
Basic propositional logic and the weak excluded middle
Abstract
We study basic propositional logic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{(BPC)}}$</tex> augmented with the law of the weak excluded middle <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{(WEM)}}$</tex> , i.e. <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{BPW}} = \operatorname{\textbf{BPC}} + \operatorname{\textbf{WEM}}$</tex> . We show that the variety of the algebraic models of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{BPW}}$</tex> is canonical, and its Kripke completeness is proved via cononicity. Moreover, it is also proved that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{BPW}}$</tex> has the finite model property and is decidable. It is shown that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{BPC}}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{BPW}}$</tex> have the same behaviour on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\bot $</tex> -free formulas and that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{CPC}}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\operatorname{\textbf{BPW}}$</tex> have the same behaviour on the negated formulas.
Year
DOI
Venue
2019
10.1093/jigpal/jzy052
Logic Journal of The Igpl \/ Bulletin of The Igpl
Keywords
Field
DocType
Basic propositional logic,weak excluded middle,Kripke models,Visser algebras
Law of excluded middle,Propositional calculus,Calculus,Mathematics
Journal
Volume
Issue
ISSN
27
2
1367-0751
Citations 
PageRank 
References 
0
0.34
7
Authors
2
Name
Order
Citations
PageRank
Majid Alizadeh1215.60
Mohammad Ardeshir28217.78