Partially Finite Model Reasoning in Description Logics Extended Version

2026-04-28

AI Summary

This study addresses the problem of query entailment under partial finite model semantics in description logics: given a knowledge base, a query, and a concept required to be interpreted as a finite set, it investigates whether the query holds in all models satisfying this finiteness constraint. To this end, the work introduces a novel framework for partial finite model reasoning that transcends the traditional dichotomy between finite and infinite model semantics, unifying both cases through techniques for constructing and pruning infinite models. Focusing on the extension of ALC with transitive roles (logic S), the paper establishes that conjunctive query entailment under partial finite semantics lies within 2-EXPTIME by reducing query entailment to query containment, and applies this result to decide query containment under closed predicates.

Abstract

Aiming to harmonise finite and infinite model reasoning, we initiate the study of partially finite models, where the reasoning task comes with a formula that specifies a part of the model that must be finite. We focus on the problem of partially finite query entailment in description logics (DLs): given a knowledge base (KB), a query, and a distinguished concept, decide whether the query holds in all models of the KB that interpret the distinguished concept as a finite set. To break the ground, we work with the DL S, an extension of the basic DL ALC with transitive roles, which is one of the simplest cases where finite and infinite query entailment diverge. Generalising previous results on the finite and infinite cases, we show that also partially finite entailment of conjunctive queries is in 2-exptime for S. The solution involves sophisticated infinite model surgery and goes far beyond combining the arguments for the two special cases. As a direct application, we show how the problem of query containment in the presence of closed predicates can be solved by reduction to partially finite query entailment.

Problem

• partially finite models
• description logics
• query entailment
• finite model reasoning
• conjunctive queries

Innovation

• partially finite models
• description logics
• query entailment
• model surgery
• closed predicates