Showing papers by "Franz Baader published in 2019"

Expressive cardinality constraints on ALCSCC concepts

Abstract: In two previous publications we have, on the one hand, extended the description logic (DL) ALCQ by more expressive number restrictions using numerical and set constraints expressed in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). The resulting DL was called ALCSCC. On the other hand, we have extended the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general cardinality constraints expressed in QFBAPA, which we called extended cardinality constraints. Here, we combine the two extensions, i.e., we consider extended cardinality constraints on ALCSCC concepts. We show that this does not increase the complexity of reasoning, which is NExpTime-complete both for extended cardinality constraints in ALC and ALCSCC. The same is true for a restricted version of such cardinality constraints, where the complexity of reasoning decreases to ExpTime, not just for ALC, but also for ALCSCC.

Satisfiability Checking and Conjunctive Query Answering in Description Logics with Global and Local Cardinality Constraints.

Abstract: We introduce and investigate the expressive description logic (DL) ALCSCC, in which the global and local cardinality constraints introduced in previous papers can be mixed. On the one hand, we prove that this does not increase the complexity of satisfiability checking and other standard inference problems. On the other hand, the satisfiability problem becomes undecidable if inverse roles are added to the languages. In addition, even without inverse roles, conjunctive query entailment in this DL turns out to be undecidable. We prove that decidability of querying can be regained if global and local constraints are not mixed and the global constraints are appropriately restricted. The latter result is based on a locally-acyclic model construction, and it reduces query entailment to ABox consistency in the restricted setting, i.e., to ABox consistency w.r.t. restricted cardinality constraints in ALCSCC, for which we can show an ExpTime upper bound.

On the Expressive Power of Description Logics with Cardinality Constraints on Finite and Infinite Sets

Abstract: In recent work we have extended the description logic (DL) \(\mathcal {ALC\!Q}\) by means of more expressive number restrictions using numerical and set constraints stated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). It has been shown that reasoning in the resulting DL, called \(\mathcal {ALCSCC}\), is PSpace-complete without a TBox and ExpTime-complete w.r.t. a general TBox. The semantics of \(\mathcal {ALCSCC}\) is defined in terms of finitely branching interpretations, that is, interpretations where every element has only finitely many role successors. This condition was needed since QFBAPA considers only finite sets. In this paper, we first introduce a variant of \(\mathcal {ALCSCC}\), called \(\mathcal {ALCSCC} ^\infty \), in which we lift this requirement (inexpressible in first-order logic) and show that the complexity results for \(\mathcal {ALCSCC}\) mentioned above are preserved. Nevertheless, like \(\mathcal {ALCSCC}\), \(\mathcal {ALCSCC} ^\infty \) is not a fragment of first-order logic. The main contribution of this paper is to give a characterization of the first-order fragment of \(\mathcal {ALCSCC} ^\infty \). The most important tool used in the proof of this result is a notion of bisimulation that characterizes this fragment.

Privacy-Preserving Ontology Publishing for \(\mathcal {EL} \) Instance Stores

Abstract: We make a first step towards adapting an existing approach for privacy-preserving publishing of linked data to Description Logic (DL) ontologies. We consider the case where both the knowledge about individuals and the privacy policies are expressed using concepts of the DL \(\mathcal {EL} \), which corresponds to the setting where the ontology is an \(\mathcal {EL} \) instance store. We introduce the notions of compliance of a concept with a policy and of safety of a concept for a policy, and show how optimal compliant (safe) generalizations of a given \(\mathcal {EL}\) concept can be computed. In addition, we investigate the complexity of the optimality problem.

Expressive cardinality restrictions on concepts in a description logic with expressive number restrictions

Abstract: In two previous publications we have, on the one hand, extended the description logic (DL) ALCQ by more expressive number restrictions using numerical and set constraints expressed in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA). The resulting DL was called ALCSCC. On the other hand, we have extended the terminological formalism of the well-known description logic ALC from concept inclusions (CIs) to more general cardinality constraints expressed in QFBAPA, which we called extended cardinality constraints. Here, we combine the two extensions, i.e., we consider extended cardinality constraints on ALCSCC concepts. We show that this does not increase the complexity of reasoning, which is NExpTime-complete both for extended cardinality constraints in the DL ALC and in its extension ALCSCC. The same is true for a restricted version of such cardinality constraints, where the complexity of reasoning decreases to ExpTime, not just for ALC, but also for ALCSCC.

The Complexity of the Consistency Problem in the Probabilistic Description Logic \(\mathcal {ALC} ^\mathsf {ME}\)

Abstract: The probabilistic Description Logic \(\mathcal {ALC} ^\mathsf {ME}\) is an extension of the Description Logic \(\mathcal {ALC} \) that allows for uncertain conditional statements of the form “if C holds, then D holds with probability p,” together with probabilistic assertions about individuals. In \(\mathcal {ALC} ^\mathsf {ME}\), probabilities are understood as an agent’s degree of belief. Probabilistic conditionals are formally interpreted based on the so-called aggregating semantics, which combines a statistical interpretation of probabilities with a subjective one. Knowledge bases of \(\mathcal {ALC} ^\mathsf {ME}\) are interpreted over a fixed finite domain and based on their maximum entropy (\(\mathsf {ME}\)) model. We prove that checking consistency of such knowledge bases can be done in time polynomial in the cardinality of the domain, and in exponential time in the size of a binary encoding of this cardinality. If the size of the knowledge base is also taken into account, the combined complexity of the consistency problem is NP-complete for unary encoding of the domain cardinality and NExpTime-complete for binary encoding.

Counting Strategies for the Probabilistic Description Logic $$\mathcal {ALC}^\mathsf {ME}$$ Under the Principle of Maximum Entropy

Abstract: We present \(\mathcal {ALC}^\mathsf {ME}\), a probabilistic variant of the Description Logic \(\mathcal {ALC}\) that allows for representing and processing conditional statements of the form “if E holds, then F follows with probability p” under the principle of maximum entropy. Probabilities are understood as degrees of belief and formally interpreted by the aggregating semantics. We prove that both checking consistency and drawing inferences based on approximations of the maximum entropy distribution is possible in \(\mathcal {ALC}^\mathsf {ME}\) in time polynomial in the domain size. A major problem for probabilistic reasoning from such conditional knowledge bases is to count models and individuals. To achieve our complexity results, we develop sophisticated counting strategies on interpretations aggregated with respect to the so-called conditional impacts of types, which refine their conditional structure.

Automatic Translation of Clinical Trial Eligibility Criteria into Formal Queries.

Abstract: Selecting patients for clinical trials is very labor-intensive. Our goal is to develop an automated system that can support doctors in this task. This paper describes a major step towards such a system: the automatic translation of clinical trial eligibility criteria from natural language into formal, logic-based queries. First, we develop a semantic annotation process that can capture many types of clinical trial criteria. Then, we map the annotated criteria to the formal query language. We have built a prototype system based on state-of-the-art NLP tools such as Word2Vec, Stanford NLP tools, and the MetaMap Tagger, and have evaluated the quality of the produced queries on a number of criteria from clinicaltrials.gov. Finally, we discuss some criteria that were hard to translate, and give suggestions for how to formulate eligibility criteria to make them easier to translate automatically.

Mixing Description Logics in Privacy-Preserving Ontology Publishing

Abstract: In previous work, we have investigated privacy-preserving publishing of Description Logic (DL) ontologies in a setting where the knowledge about individuals to be published is an \(\mathcal {EL} \) instance store, and both the privacy policy and the possible background knowledge of an attacker are represented by concepts of the DL \(\mathcal {EL}\). We have introduced the notions of compliance of a concept with a policy and of safety of a concept for a policy, and have shown how, in the context mentioned above, optimal compliant (safe) generalizations of a given \(\mathcal {EL}\) concept can be computed. In the present paper, we consider a modified setting where we assume that the background knowledge of the attacker is given by a DL different from the one in which the knowledge to be published and the safety policies are formulated. In particular, we investigate the situations where the attacker’s knowledge is given by an \(\mathcal {FL}_0 \) or an \(\mathcal {FLE} \) concept. In both cases, we show how optimal safe generalizations can be computed. Whereas the complexity of this computation is the same (ExpTime) as in our previous results for the case of \(\mathcal {FL}_0 \), it turns out to be actually lower (polynomial) for the more expressive DL \(\mathcal {FLE} \).