Living without Beth and Craig: Definitions and Interpolants in the Guarded and Two-Variable Fragments

In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an explicit definition of a relation follows from the validity of a...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science S. 1 - 14
Hauptverfasser: Jung, Jean Christoph, Wolter, Frank
Format: Tagungsbericht
Sprache:Englisch
Veröffentlicht: IEEE 29.06.2021
Schlagworte:
Complexity theory
Computer science
Interpolation
Upper bound
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:In logics with the Craig interpolation property (CIP) the existence of an interpolant for an implication follows from the validity of the implication. In logics with the projective Beth definability property (PBDP), the existence of an explicit definition of a relation follows from the validity of a formula expressing its implicit definability. The two-variable fragment, FO 2 , and the guarded fragment, GF, of first-order logic both fail to have the CIP and the PBDP. We show that nevertheless in both fragments the existence of interpolants and explicit definitions is decidable. In GF, both problems are 3EXPTIME-complete in general, and 2EXPTIME-complete if the arity of relation symbols is bounded by a constant c ≥ 3. In FO 2 , we prove a CON2EXPTIME upper bound and a 2EXPTIME lower bound for both problems. Thus, both for GF and FO 2 existence of interpolants and explicit definitions are decidable but harder than validity (in case of FO 2 under standard complexity assumptions).
DOI:10.1109/LICS52264.2021.9470585