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Data Complexity of Query Answering in Description Logics (Extended Abstract)

AAAI Conferences

We study the data complexity of answering conjunctive queries over Description Logic knowledge bases constituted by a TBox and an ABox. In particular, we are interested in characterizing the FO- rewritability and the polynomial tractability boundaries of conjunctive query answering, depending on the expressive power of the DL used to express the knowledge base. What emerges from our complexity analysis is that the Description Logics of the DL-Lite family are essentially the maximal logics allowing for conjunctive query answering through standard database technology.


Rudolph

AAAI Conferences

Recently, the field of knowledge representation is drawing a lot of inspiration from database theory. In particular, in the area of description logics and ontology languages, interest has shifted from satisfiability checking to query answering, with various query notions adopted from databases, like (unions of) conjunctive queries or different kinds of path queries. Likewise, the finite model semantics is being established as a viable and interesting alternative to the traditional semantics based on unrestricted models. In this paper, we investigate diverse database-inspired reasoning problems for very expressive description logics (all featuring the worrisome trias of inverses, counting, and nominals) which have in common that role paths of unbounded length can be described (in the knowledge base or of the query), leading to a certain non-locality of the reasoning problem. We show that for all the cases considered, undecidability can be established by very similar means. Most notably, we show undecidability of finite entailment of unions of conjunctive queries for a fragment of SHOIQ (the logic underlying the OWL DL ontology language), and undecidability of finite entailment of conjunctive queries for a fragment of SROIQ (the logical basis of the more recent and popular OWL 2 DL standard).


Undecidability Results for Database-Inspired Reasoning Problems in Very Expressive Description Logics

AAAI Conferences

Recently, the field of knowledge representation is drawing a lot of inspiration from database theory. In particular, in the area of description logics and ontology languages, interest has shifted from satisfiability checking to query answering, with various query notions adopted from databases, like (unions of) conjunctive queries or different kinds of path queries. Likewise, the finite model semantics is being established as a viable and interesting alternative to the traditional semantics based on unrestricted models. In this paper, we investigate diverse database-inspired reasoning problems for very expressive description logics (all featuring the worrisome trias of inverses, counting, and nominals) which have in common that role paths of unbounded length can be described (in the knowledge base or of the query), leading to a certain non-locality of the reasoning problem. We show that for all the cases considered, undecidability can be established by very similar means. Most notably, we show undecidability of finite entailment of unions of conjunctive queries for a fragment of SHOIQ (the logic underlying the OWL DL ontology language), and undecidability of finite entailment of conjunctive queries for a fragment of SROIQ (the logical basis of the more recent and popular OWL 2 DL standard).


Conjunctive Query Answering for the Description Logic SHIQ

Journal of Artificial Intelligence Research

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.


Conjunctive Query Answering for the Description Logic SHIQ

arXiv.org Artificial Intelligence

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood if transitive roles are admitted in the query. In this paper, we consider unions of conjunctive queries over knowledge bases formulated in the prominent DL SHIQ and allow transitive roles in both the query and the knowledge base. We show decidability of query answering in this setting and establish two tight complexity bounds: regarding combined complexity, we prove that there is a deterministic algorithm for query answering that needs time single exponential in the size of the KB and double exponential in the size of the query, which is optimal. Regarding data complexity, we prove containment in co-NP.