How Hard is it to Decide if a Fact is Relevant to a Query?

We consider the following fundamental problem: given a database D, Boolean conjunctive query (CQ) q, and fact f in D, decide whether f is relevant to q wrt. D, i.e., does f belong to a minimal subset S of D such that S |= q. Despite being of central importance to query answer explanation, the combined complexity of deciding query relevance has not been studied in detail, leaving open what makes this problem hard, and which restrictions can yield lower complexity. Relevance has already been shown to be harder than query evaluation: namely, $Σ^p_2$-complete for CQs, even over a binary signature. We further observe that NP-hardness applies already to (acyclic) chain CQs. Our work identifies self-joins (multiple atoms with the same relation) as the culprit. Indeed, we prove that if we forbid or bound the occurrence of self-joins, then relevance has the same complexity as query evaluation, namely, NP (without structural restrictions) and LogCFL (for bounded hypertreewidth classes). In the ontology setting, we establish an analogous result for ontology-mediated queries consisting of a CQ and DL-Lite_R ontology, namely that relevance is no harder than query answering provided that we bound the interaction width (which generalizes both self-join width and a recently introduced 'interaction-free' condition). Our results thus pinpoint what makes relevance harder than query evaluation and identify natural classes of queries which admit efficient relevance computation.

Inferring High-Level Events from Timestamped Data: Complexity and Medical Applications

In this paper, we develop a novel logic-based approach to detecting high-level temporally extended events from timestamped data and background knowledge. Our framework employs logical rules to capture existence and termination conditions for simple temporal events and to combine these into meta-events. In the medical domain, for example, disease episodes and therapies are inferred from timestamped clinical observations, such as diagnoses and drug administrations stored in patient records, and can be further combined into higher-level disease events. As some incorrect events might be inferred, we use constraints to identify incompatible combinations of events and propose a repair mechanism to select preferred consistent sets of events. While reasoning in the full framework is intractable, we identify relevant restrictions that ensure polynomial-time data complexity. Our prototype system implements core components of the approach using answer set programming. An evaluation on a lung cancer use case supports the interest of the approach, both in terms of computational feasibility and positive alignment of our results with medical expert opinions. While strongly motivated by the needs of the healthcare domain, our framework is purposely generic, enabling its reuse in other areas.

Using ASP(Q) to Handle Inconsistent Prioritized Data

We explore the use of answer set programming (ASP) and its extension with quantifiers, ASP(Q), for inconsistency-tolerant querying of prioritized data, where a priority relation between conflicting facts is exploited to define three notions of optimal repairs (Pareto-, globally- and completion-optimal). We consider the variants of three well-known semantics (AR, brave and IAR) that use these optimal repairs, and for which query answering is in the first or second level of the polynomial hierarchy for a large class of logical theories. Notably, this paper presents the first implementation of globally-optimal repair-based semantics, as well as the first implementation of the grounded semantics, which is a tractable under-approximation of all these optimal repair-based semantics. Our experimental evaluation sheds light on the feasibility of computing answers under globally-optimal repair semantics and the impact of adopting different semantics, approximations, and encodings.

Data Complexity of Querying Description Logic Knowledge Bases under Cost-Based Semantics

In this paper, we study the data complexity of querying inconsistent weighted description logic (DL) knowledge bases under recently-introduced cost-based semantics. In a nutshell, the idea is to assign each interpretation a cost based upon the weights of the violated axioms and assertions, and certain and possible query answers are determined by considering all (resp. some) interpretations having optimal or bounded cost. Whereas the initial study of cost-based semantics focused on DLs between $\mathcal{EL}_\bot$ and $\mathcal{ALCO}$, we consider DLs that may contain inverse roles and role inclusions, thus covering prominent DL-Lite dialects. Our data complexity analysis goes significantly beyond existing results by sharpening several lower bounds and pinpointing the precise complexity of optimal-cost certain answer semantics (no non-trivial upper bound was known). Moreover, while all existing results show the intractability of cost-based semantics, our most challenging and surprising result establishes that if we consider $\text{DL-Lite}^\mathcal{H}_\mathsf{bool}$ ontologies and a fixed cost bound, certain answers for instance queries and possible answers for conjunctive queries can be computed using first-order rewriting and thus enjoy the lowest possible data complexity ($\mathsf{TC}_0$).

A Rule-Based Approach to Specifying Preferences over Conflicting Facts and Querying Inconsistent Knowledge Bases

Repair-based semantics have been extensively studied as a means of obtaining meaningful answers to queries posed over inconsistent knowledge bases (KBs). While several works have considered how to exploit a priority relation between facts to select optimal repairs, the question of how to specify such preferences remains largely unaddressed. This motivates us to introduce a declarative rule-based framework for specifying and computing a priority relation between conflicting facts. As the expressed preferences may contain undesirable cycles, we consider the problem of determining when a set of preference rules always yields an acyclic relation, and we also explore a pragmatic approach that extracts an acyclic relation by applying various cycle removal techniques. Towards an end-to-end system for querying inconsistent KBs, we present a preliminary implementation and experimental evaluation of the framework, which employs answer set programming to evaluate the preference rules, apply the desired cycle resolution techniques to obtain a priority relation, and answer queries under prioritized-repair semantics.

Inconsistency Handling in DatalogMTL

In this paper, we explore the issue of inconsistency handling in DatalogMTL, an extension of Datalog with metric temporal operators. Since facts are associated with time intervals, there are different manners to restore consistency when they contradict the rules, such as removing facts or modifying their time intervals. Our first contribution is the definition of relevant notions of conflicts (minimal explanations for inconsistency) and repairs (possible ways of restoring consistency) for this setting and the study of the properties of these notions and the associated inconsistency-tolerant semantics. Our second contribution is a data complexity analysis of the tasks of generating a single conflict / repair and query entailment under repair-based semantics.

Shapley Revisited: Tractable Responsibility Measures for Query Answers

The Shapley value, originating from cooperative game theory, has been employed to define responsibility measures that quantify the contributions of database facts to obtaining a given query answer. For non-numeric queries, this is done by considering a cooperative game whose players are the facts and whose wealth function assigns 1 or 0 to each subset of the database, depending on whether the query answer holds in the given subset. While conceptually simple, this approach suffers from a notable drawback: the problem of computing such Shapley values is #P-hard in data complexity, even for simple conjunctive queries. This motivates us to revisit the question of what constitutes a reasonable responsibility measure and to introduce a new family of responsibility measures -- weighted sums of minimal supports (WSMS) -- which satisfy intuitive properties. Interestingly, while the definition of WSMSs is simple and bears no obvious resemblance to the Shapley value formula, we prove that every WSMS measure can be equivalently seen as the Shapley value of a suitably defined cooperative game. Moreover, WSMS measures enjoy tractable data complexity for a large class of queries, including all unions of conjunctive queries. We further explore the combined complexity of WSMS computation and establish (in)tractability results for various subclasses of conjunctive queries.

Queries With Exact Truth Values in Paraconsistent Description Logics

We present a novel approach to querying classical inconsistent description logic (DL) knowledge bases by adopting a~paraconsistent semantics with the four Belnapian values: exactly true ($\mathbf{T}$), exactly false ($\mathbf{F}$), both ($\mathbf{B}$), and neither ($\mathbf{N}$). In contrast to prior studies on paraconsistent DLs, we allow truth value operators in the query language, which can be used to differentiate between answers having contradictory evidence and those having only positive evidence. We present a reduction to classical DL query answering that allows us to pinpoint the precise combined and data complexity of answering queries with values in paraconsistent $\mathcal{ALCHI}$ and its sublogics. Notably, we show that tractable data complexity is retained for Horn DLs. We present a comparison with repair-based inconsistency-tolerant semantics, showing that the two approaches are incomparable.

Abductive Reasoning in a Paraconsistent Framework

We explore the problem of explaining observations starting from a classically inconsistent theory by adopting a paraconsistent framework. We consider two expansions of the well-known Belnap--Dunn paraconsistent four-valued logic $\mathsf{BD}$: $\mathsf{BD}_\circ$ introduces formulas of the form $\circ\phi$ (the information on $\phi$ is reliable), while $\mathsf{BD}_\triangle$ augments the language with $\triangle\phi$'s (there is information that $\phi$ is true). We define and motivate the notions of abduction problems and explanations in $\mathsf{BD}_\circ$ and $\mathsf{BD}_\triangle$ and show that they are not reducible to one another. We analyse the complexity of standard abductive reasoning tasks (solution recognition, solution existence, and relevance / necessity of hypotheses) in both logics. Finally, we show how to reduce abduction in $\mathsf{BD}_\circ$ and $\mathsf{BD}_\triangle$ to abduction in classical propositional logic, thereby enabling the reuse of existing abductive reasoning procedures.

Cost-Based Semantics for Querying Inconsistent Weighted Knowledge Bases

In this paper, we explore a quantitative approach to querying inconsistent description logic knowledge bases. We consider weighted knowledge bases in which both axioms and assertions have (possibly infinite) weights, which are used to assign a cost to each interpretation based upon the axioms and assertions it violates. Two notions of certain and possible answer are defined by either considering interpretations whose cost does not exceed a given bound or restricting attention to optimal-cost interpretations. Our main contribution is a comprehensive analysis of the combined and data complexity of bounded cost satisfiability and certain and possible answer recognition, for description logics between ELbot and ALCO.