On Classical Decidable Logics extended with Percentage Quantifiers and Arithmetics

Publikation: Beitrag in Buch/Konferenzbericht/Sammelband/GutachtenBeitrag in KonferenzbandBeigetragenBegutachtung

Beitragende

Abstract

During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of restriction imposed on formulae from the language. Despite the success of the mentioned logics in areas like formal verification and knowledge representation, such first-order fragments are too weak to express even the simplest statistical constraints, required for modelling of influence networks or in statistical reasoning. In this work we investigate the extensions of these classical decidable logics with percentage quantifiers, specifying how frequently a formula is satisfied in the indented model. We show, surprisingly, that all the mentioned decidable fragments become undecidable under such extension, sharpening the existing results in the literature. Our negative results are supplemented by decidability of the two-variable guarded fragment with even more expressive counting, namely Presburger constraints. Our results can be applied to infer decidability of various modal and description logics, e.g. Presburger Modal Logics with Converse or ALCI, with expressive cardinality constraints.

Details

OriginalspracheEnglisch
TitelProceedings of the 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)
Redakteure/-innenMikołaj Bojańczyk, Chandra Chekuri
Herausgeber (Verlag)Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Band213
ISBN (elektronisch)9783959772150
PublikationsstatusVeröffentlicht - 1 Dez. 2021
Peer-Review-StatusJa

Externe IDs

Scopus 85122473826

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

  • (Un)decidability, Fragments of first-order logic, Guarded fragment, Knowledge representation, Satisfiability, Statistical reasoning, Two-variable fragment