Model Comparison Games for Horn Description Logics

Horn description logics are syntactically defined fragments of standard description logics that fall within the Horn fragment of first-order logic and for which ontology-mediated query answering is in PTIME for data complexity. They were independently introduced in modal logic to capture the intersection of Horn first-order logic with modal logic. In this paper, we introduce model comparison games for the basic Horn description logic hornALC (corresponding to the basic Horn modal logic) and use them to obtain an Ehrenfeucht-Fra ̈ısse ́ type definability result and a van Benthem style expressive completeness result for hornALC. We also establish a finite model theory version of the latter. The Ehrenfeucht-Fra ̈ısse ́ type definability result is used to show that checking hornALC indistinguishability of models is EXPTIME-complete, which is in sharp contrast to ALC indistinguishability (i.e., bisimulation equivalence) checkable in PTIME. In addition, we explore the behavior of Horn fragments of more expressive description and modal logics by defining a Horn guarded fragment of first-order logic and introducing model comparison games for it

Reverse engineering queries in ontology-enriched systems: the case of expressive horn description logic ontologies

We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples? We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE

Model Comparison Games for Horn Description Logics

Horn description logics are syntactically defined fragments of standard description logics that fall within the Horn fragment of first-order logic and for which ontology-mediated query answering is in PTime for data complexity. They were independently introduced in modal logic to capture the intersection of Horn first-order logic with modal logic. In this paper, we introduce model comparison games for the basic Horn description logic hornALC (corresponding to the basic Horn modal logic) and use them to obtain an Ehrenfeucht-Fra\"iss\'e type definability result and a van Benthem style expressive completeness result for hornALC. We also establish a finite model theory version of the latter. The Ehrenfeucht-Fra\"iss\'e type definability result is used to show that checking hornALC indistinguishability of models is ExpTime-complete, which is in sharp contrast to ALC indistinguishability (i.e., bisimulation equivalence) checkable in PTime. In addition, we explore the behavior of Horn fragments of more expressive description and modal logics by defining a Horn guarded fragment of first-order logic and introducing model comparison games for it

Topics in Knowledge Bases: Epistemic Ontologies and Secrecy-preserving Reasoning

Applications of ontologies/knowledge bases (KBs) in many domains (healthcare, national security, intelligence) have become increasingly important. In this dissertation, we focus on developing techniques for answering queries posed to KBs under the open world assumption (OWA). In the first part of this dissertation, we study the problem of query answering in KBs that contain epistemic information, i.e., knowledge of different experts. We study ALCKm, which extends the description logic ALC by adding modal operators of the basic multi-modal logic Km. We develop a sound and complete tableau algorithm for answering ALCKm queries w.r.t. an ALCKm knowledge base with an acyclic TBox. We then consider answering ALCKm queries w.r.t. an ALCKm knowledge base in which the epistemic operators correspond to those of classical multi-modal logic S4m and provide a sound and complete tableau algorithm. Both algorithms can be implemented in PSpace. In the second part, we study problems that allow autonomous entities or organizations (collectively called querying agents) to be able to selectively share information. In this scenario, the KB must make sure its answers are informative but do not disclose sensitive information. Most of the work in this area has focused on access control mechanisms that prohibit access to sensitive information (secrets). However, such an approach can be too restrictive in that it prohibits the use of sensitive information in answering queries against knowledge bases even when it is possible to do so without compromising secrets. We investigate techniques for secrecy-preserving query answering (SPQA) against KBs under the OWA. We consider two scenarios of increasing difficulty: (a) a KB queried by a single agent; and (b) a KB queried by multiple agents where the secrecy policies can differ across the different agents and the agents can selectively communicate the answers that they receive from the KB with each other subject to the applicable answer sharing policies. We consider classes of KBs that are of interest from the standpoint of practical applications (e.g., description logics and Horn KBs). Given a KB and secrets that need to be protected against the querying agent(s), the SPQA problem aims at designing a secrecy-preserving reasoner that answers queries without compromising secrecy under OWA. Whenever truthfully answering a query risks compromising secrets, the reasoner is allowed to hide the answer to the query by feigning ignorance, i.e., answering the query as Unknown . Under the OWA, the querying agent is not able to infer whether an Unknown answer to a query is obtained because of the incomplete information in the KB or because secrecy protection mechanism is being applied. In each scenario, we provide a general framework for the problem. In the single-agent case, we apply the general framework to the description logic EL and provide algorithms for answering queries as informatively as possible without compromising secrecy. In the multiagent case, we extend the general framework for the single-agent case. To model the communication between querying agents, we use a communication graph, a directed acyclic graph (DAG) with self-loops, where each node represents an agent and each edge represents the possibility of information sharing in the direction of the edge. We discuss the relationship between secrecy-preserving reasoners and envelopes (used to protect secrets) and present a special case of the communication graph that helps construct tight envelopes in the sense that removing any information from them will leave some secrets vulnerable. To illustrate our general idea of constructing envelopes, Horn KBs are considered

Worst-case Optimal Query Answering for Greedy Sets of Existential Rules and Their Subclasses

The need for an ontological layer on top of data, associated with advanced reasoning mechanisms able to exploit the semantics encoded in ontologies, has been acknowledged both in the database and knowledge representation communities. We focus in this paper on the ontological query answering problem, which consists of querying data while taking ontological knowledge into account. More specifically, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called tuple-generating dependencies, Datalog+/- rules, or forall-exists-rules. Our contribution is twofold. First, we introduce the class of greedy bounded-treewidth sets (gbts) of rules, which covers guarded rules, and their most well-known generalizations. We provide a generic algorithm for query entailment under gbts, which is worst-case optimal for combined complexity with or without bounded predicate arity, as well as for data complexity and query complexity. Secondly, we classify several gbts classes, whose complexity was unknown, with respect to combined complexity (with both unbounded and bounded predicate arity) and data complexity to obtain a comprehensive picture of the complexity of existential rule fragments that are based on diverse guardedness notions. Upper bounds are provided by showing that the proposed algorithm is optimal for all of them