PSL University（巴黎文理研究大学）；Inria（法国国家信息与自动化研究所）；University of Bergen（卑尔根大学）；Free University of Bozen-Bolzano（博尔扎诺自由大学）；University of Milano-Bicocca（米兰比可卡大学）
Camille Bourgaux, Ana Ozaki, Rafael Peñaloza, Livia Predoiu
备注：
This is the long version of an IJCAI 2020 paper (23 pages) - v3 fixes glitches in proof of lemma 27 and in claim 30
We address the problem of handling provenance information in ELHr ontologies. We consider a setting recently introduced for ontology-based data access, based on semirings and extending classical data provenance, in which ontology axioms are annotated with provenance tokens. A consequence inherits the provenance of the axioms involved in deriving it, yielding a provenance polynomial as an annotation. We analyse the semantics for the ELHr case and show that the presence of conjunctions poses various difficulties for handling provenance, some of which are mitigated by assuming multiplicative idempotency of the semiring. Under this assumption, we study three problems: ontology completion with provenance, computing the set of relevant axioms for a consequence, and query answering.
We investigate the entailment problem in ELHr ontologies annotated with provenance information. In more detail, we show that subsumption entailment is in NP if provenance is represented with polynomials from the Trio semiring and in PTime if the semiring is not commutative. The proof is based on the construction of a weighted tree automaton which recognises a language that matches with the corresponding provenance polynomial.
A semantic approach to mapping the Provenance Ontology to Basic Formal Ontology
National Center for Ontological Research（国家本体论研究中心）；Conceptual Systems（概念系统公司）；University at Buffalo（布法罗大学）；Summit Knowledge Solutions（顶峰知识解决方案公司）；University of Vienna（维也纳大学）；Institute for Artificial Intelligence and Data Science（人工智能与数据科学研究所）
To appear in Theory and Practice of Logic Programming (TPLP). In this paper we propose an extension of logic programming (LP) where each default literal derived from the well-founded model is associated to a justification represented as an algebraic expression. This expression contains both causal explanations (in the form of proof graphs built with rule labels) and terms under the scope of negation that stand for conditions that enable or disable the application of causal rules. Using some examples, we discuss how these new conditions, we respectively call "enablers" and "inhibitors", are int…
Weighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP(AC)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend …
In distributed environments, access control decisions depend on statements of multiple agents rather than only one central trusted party. However, existing policy languages put few emphasis on authorization provenances. The capability of managing these provenances is important and useful in various security areas such as computer auditing and authorization recycling. Based on our previously proposed logic, we present several case studies of this logic. By doing this, we show its expressiveness and usefulness in security arena.
A model checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that describe the structure. In database theory, provenance analysis by interpretations in commutative semirings has been rather succesful for positive query languages (such a unions of conjunctive queries, positive relational algebra, or datalog). However, it did not really offer an adequate treatment of negation or missing information. Here we propose a new approach…
Semiring provenance is a successful approach to provide detailed information on the combinations of atomic facts that are responsible for the result of a query. In particular, interpretations in general provenance semirings of polynomials or formal power series give precise descriptions of the successful evaluation strategies for the query. While provenance analysis in databases has, for a long time, been largely confined to negation-free query languages, a recent approach extends this to model checking problems for logics with full negation. Algebraically this relies on new quotient semirings…
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the data items that describe the model. Previous work on provenance was, to a large extent, restricted to the negation-free fragment of first-order logic and showed how provenance abstractions can be usefully described as elements of commutative semirings --- most generally as multivariate polynomials with positive integer coefficients. In this paper we introduce a…
Logic programming languages such as Datalog have become popular as Domain Specific Languages (DSLs) for solving large-scale, real-world problems, in particular, static program analysis and network analysis. The logic specifications which model analysis problems, process millions of tuples of data and contain hundreds of highly recursive rules. As a result, they are notoriously difficult to debug. While the database community has proposed several data-provenance techniques that address the Declarative Debugging Challenge for Databases, in the cases of analysis problems, these state-of-the-art t…
We address the problem of providing contextual information about a logical formula (eg provenance, date of validity, or confidence) and representing it within a logical system. In this case, it is needed to rely on a higher order or non standard formalism, or some kind of reification mechanism. We explore the case of reification and formalize the concept of contextualizing logical statements in the case of Description Logics. Then, we define several properties of contextualization that are desirable. No previous approaches satisfy all of the them. Consequently, we define a new way of contextua…
Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse contexts such as databases, quantum mechanics, and statistics by extending first-order logic with atoms that describe dependencies between variables. Combining these two, we propose a unifying approach for analysing the concepts of dependence and independence via a novel semiring team semantics, which subsumes all the previously considered variants for first-ord…
