Structural completeness in propositional logics of dependence (Q334998)
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: Structural completeness in propositional logics of dependence |
scientific article; zbMATH DE number 6646572
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Structural completeness in propositional logics of dependence |
scientific article; zbMATH DE number 6646572 |
Statements
Structural completeness in propositional logics of dependence (English)
0 references
1 November 2016
0 references
The paper studies three logics of dependence: \textsf{PD}, \textsf{InqL} and \textsf{PT}. None of these logics is closed under uniform substitutions, but they are closed under substitutions of a particular type: flat substitutions which map propositional variables to flat formulas. A flat formula is a classical formula satisfying the condition \(X \models \varphi \Leftrightarrow \forall v, \{v\} \models \varphi\). In a natural way, admissibility of a rule can be defined in terms of flat substitutions. It is proven that all three aforementioned logics are closed and structurally complete relative to flat substitutions.
0 references
propositional logic
0 references
dependence logic
0 references
inquisitive logic
0 references
inference rule
0 references
admissible rule
0 references
structural completeness
0 references
