Standard completeness theorem for \(\Pi\)MTL (Q1778060)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Standard completeness theorem for \(\Pi\)MTL |
scientific article; zbMATH DE number 2171981
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Standard completeness theorem for \(\Pi\)MTL |
scientific article; zbMATH DE number 2171981 |
Statements
Standard completeness theorem for \(\Pi\)MTL (English)
0 references
26 May 2005
0 references
\(\Pi\)MTL is a schematic extension of the monoidal t-norm-based logic (MTL) by a new connective that is in \([0, 1]\) interpreted by the ordinary product of reals. It is proved that \(\Pi\)MTL satisfies the standard completeness theorem, namely, that a formula of \(\Pi\)MTL is provable iff it is true in a degree 1 in all \(\Pi\)MTL-chains in \([0, 1]\) with finitely many Archimedean classes. From the algebraic point of view this means that the class of \(\Pi\)MTL-algebras in \([0, 1]\) generates the variety of all \(\Pi\)MTL-algebras.
0 references
fuzzy logic in narrow sense
0 references
product logic
0 references
MTL-logic
0 references
left-continuous t-norm
0 references
0 references
