62 research outputs found
Current and Future Challenges in Knowledge Representation and Reasoning
Knowledge Representation and Reasoning is a central, longstanding, and active
area of Artificial Intelligence. Over the years it has evolved significantly;
more recently it has been challenged and complemented by research in areas such
as machine learning and reasoning under uncertainty. In July 2022 a Dagstuhl
Perspectives workshop was held on Knowledge Representation and Reasoning. The
goal of the workshop was to describe the state of the art in the field,
including its relation with other areas, its shortcomings and strengths,
together with recommendations for future progress. We developed this manifesto
based on the presentations, panels, working groups, and discussions that took
place at the Dagstuhl Workshop. It is a declaration of our views on Knowledge
Representation: its origins, goals, milestones, and current foci; its relation
to other disciplines, especially to Artificial Intelligence; and on its
challenges, along with key priorities for the next decade
Query Rewriting with Disjunctive Existential Rules and Mappings
We consider the issue of answering unions of conjunctive queries (UCQs) with
disjunctive existential rules and mappings. While this issue has already been
well studied from a chase perspective, query rewriting within UCQs has hardly
been addressed yet. We first propose a sound and complete query rewriting
operator, which has the advantage of establishing a tight relationship between
a chase step and a rewriting step. The associated breadth-first query rewriting
algorithm outputs a minimal UCQ-rewriting when one exists. Second, we show that
for any ``truly disjunctive'' nonrecursive rule, there exists a conjunctive
query that has no UCQ-rewriting. It follows that the notion of finite
unification sets (fus), which denotes sets of existential rules such that any
UCQ admits a UCQ-rewriting, seems to have little relevance in this setting.
Finally, turning our attention to mappings, we show that the problem of
determining whether a UCQ admits a UCQ-rewriting through a disjunctive mapping
is undecidable. We conclude with a number of open problems.Comment: This report contains the paper accepted at KR 2023 and an appendix
with full proofs. 24 page
Deciding FO-rewritability of Regular Languages and Ontology-Mediated Queries in Linear Temporal Logic
Our concern is the problem of determining the data complexity of answering an ontology-mediated query (OMQ) formulated in linear temporal logic LTL over (Z,<) and deciding whether it is rewritable to an FO(<)-query, possibly with some extra predicates. First, we observe that, in line with the circuit complexity and FO-definability of regular languages, OMQ answering in AC0, ACC0 and NC1 coincides with FO(<,≡)-rewritability using unary predicates x ≡ 0 (mod n), FO(<,MOD)-rewritability, and FO(RPR)-rewritability using relational primitive recursion, respectively. We prove that, similarly to known PSᴘᴀᴄᴇ-completeness of recognising FO(<)-definability of regular languages, deciding FO(<,≡)- and FO(<,MOD)-definability is also PSᴘᴀᴄᴇ-complete (unless ACC0 = NC1). We then use this result to show that deciding FO(<)-, FO(<,≡)- and FO(<,MOD)-rewritability of LTL OMQs is ExᴘSᴘᴀᴄᴇ-complete, and that these problems become PSᴘᴀᴄᴇ-complete for OMQs with a linear Horn ontology and an atomic query, and also a positive query in the cases of FO(<)- and FO(<,≡)-rewritability. Further, we consider FO(<)-rewritability of OMQs with a binary-clause ontology and identify OMQ classes, for which deciding it is PSᴘᴀᴄᴇ-, Π2p- and coNP-complete
Decidability of Querying First-Order Theories via Countermodels of Finite Width
We propose a generic framework for establishing the decidability of a wide
range of logical entailment problems (briefly called querying), based on the
existence of countermodels that are structurally simple, gauged by certain
types of width measures (with treewidth and cliquewidth as popular examples).
As an important special case of our framework, we identify logics exhibiting
width-finite finitely universal model sets, warranting decidable entailment for
a wide range of homomorphism-closed queries, subsuming a diverse set of
practically relevant query languages. As a particularly powerful width measure,
we propose Blumensath's partitionwidth, which subsumes various other commonly
considered width measures and exhibits highly favorable computational and
structural properties. Focusing on the formalism of existential rules as a
popular showcase, we explain how finite partitionwidth sets of rules subsume
other known abstract decidable classes but -- leveraging existing notions of
stratification -- also cover a wide range of new rulesets. We expose natural
limitations for fitting the class of finite unification sets into our picture
and provide several options for remedy
The Stable Model Semantics of Datalog with Metric Temporal Operators
We introduce negation under the stable model semantics in DatalogMTL - a
temporal extension of Datalog with metric temporal operators. As a result, we
obtain a rule language which combines the power of answer set programming with
the temporal dimension provided by metric operators. We show that, in this
setting, reasoning becomes undecidable over the rational timeline, and
decidable in EXPSPACE in data complexity over the integer timeline. We also
show that, if we restrict our attention to forward-propagating programs,
reasoning over the integer timeline becomes PSPACE-complete in data complexity,
and hence, no harder than over positive programs; however, reasoning over the
rational timeline in this fragment remains undecidable. Under consideration in
Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
A tetrachotomy of ontology-mediated queries with a covering axiom
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Î 2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL
A tetrachotomy of ontology-mediated queries with a covering axiom
Our concern is the problem of efficiently determining the data complexity of answering queries mediated by descrip- tion logic ontologies and constructing their optimal rewritings to standard database queries. Originated in ontology- based data access and datalog optimisation, this problem is known to be computationally very complex in general, with no explicit syntactic characterisations available. In this article, aiming to understand the fundamental roots of this difficulty, we strip the problem to the bare bones and focus on Boolean conjunctive queries mediated by a simple cov- ering axiom stating that one class is covered by the union of two other classes. We show that, on the one hand, these rudimentary ontology-mediated queries, called disjunctive sirups (or d-sirups), capture many features and difficulties of the general case. For example, answering d-sirups is Î 2p-complete for combined complexity and can be in AC0 or L-, NL-, P-, or coNP-complete for data complexity (with the problem of recognising FO-rewritability of d-sirups be- ing 2ExpTime-hard); some d-sirups only have exponential-size resolution proofs, some only double-exponential-size positive existential FO-rewritings and single-exponential-size nonrecursive datalog rewritings. On the other hand, we prove a few partial sufficient and necessary conditions of FO- and (symmetric/linear-) datalog rewritability of d- sirups. Our main technical result is a complete and transparent syntactic AC0 / NL / P / coNP tetrachotomy of d-sirups with disjoint covering classes and a path-shaped Boolean conjunctive query. To obtain this tetrachotomy, we develop new techniques for establishing P- and coNP-hardness of answering non-Horn ontology-mediated queries as well as showing that they can be answered in NL
28th International Symposium on Temporal Representation and Reasoning (TIME 2021)
The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond
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