A Framework for Reasoning about Dynamic Axioms in Description Logics

Bartosz Bednarczyk (1) , Stéphane Demri (2, 3) , Alessio Mansutti (2, 3)

1 Uniwersytet Wroclawski = University of Wroclaw
2 LSV - Laboratoire Spécification et Vérification
3 CNRS - Centre National de la Recherche Scientifique

Description logics are well-known logical formalisms for knowledge representation. We propose to enrich knowledge bases (KBs) with dynamic axioms that specify how the satisfaction of statements from the KBs evolves when the interpretation is decomposed or recomposed, providing a natural means to predict the evolution of interpretations. Our dynamic axioms borrow logical con-nectives from separation logics, well-known specification languages to verify programs with dynamic data structures. In the paper, we focus on ALC and EL augmented with dynamic axioms, or to their subclass of positive dynamic axioms. The knowledge base consistency problem in the presence of dynamic axioms is investigated, leading to interesting complexity results, among which the problem for EL with positive dynamic axioms is tractable, whereas EL with dynamic axioms is undecidable.

Mots clés: description logic; description logic ALC; dynamic axiom; update; separation logic; complexity; description logic EL; undecidability; role inclusion; separating conjunction; septraction

Domaines: Informatique [cs]; Intelligence artificielle [cs.AI]; Logique en informatique [cs.LO]

Bartosz Bednarczyk, Stéphane Demri, Alessio Mansutti. A Framework for Reasoning about Dynamic Axioms in Description Logics. Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020, Jan 2021, Yokohama, Japan. ⟨hal-03005848⟩