First-Order Rewritability of Frontier-Guarded Ontology-Mediated Queries

Barceló, Pablo; Berger, Gérald; Lutz, Carsten; Pieris, Andréas

doi:10.24963/ijcai.2018/236

Cited by 11 publications

(11 citation statements)

References 6 publications

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“…This means that there is little hope for our dichotomy to be decidable over arbitrary Datalog queries, but on its own it does not imply undecidability, so the question remains open. However, our dichotomy is effective for query languages for which boundedness is decidable, e.g., monadic Datalog, its generalization GN-Datalog [BTCCB15], C2RPQs [BFR19], or ontology-mediated query answering with guarded existential rules [BBLP18].…”

Section: Results Statementmentioning

confidence: 99%

The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

Amarilli¹,

Ceylan²

2022

Logical Methods in Computer Science

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We study the problem of query evaluation on probabilistic graphs, namely, tuple-independent probabilistic databases over signatures of arity two. We focus on the class of queries closed under homomorphisms, or, equivalently, the infinite unions of conjunctive queries. Our main result states that the probabilistic query evaluation problem is #P-hard for all unbounded queries from this class. As bounded queries from this class are equivalent to a union of conjunctive queries, they are already classified by the dichotomy of Dalvi and Suciu (2012). Hence, our result and theirs imply a complete data complexity dichotomy, between polynomial time and #P-hardness, on evaluating homomorphism-closed queries over probabilistic graphs. This dichotomy covers in particular all fragments of infinite unions of conjunctive queries over arity-two signatures, such as negation-free (disjunctive) Datalog, regular path queries, and a large class of ontology-mediated queries. The dichotomy also applies to a restricted case of probabilistic query evaluation called generalized model counting, where fact probabilities must be 0, 0.5, or 1. We show the main result by reducing from the problem of counting the valuations of positive partitioned 2-DNF formulae, or from the source-to-target reliability problem in an undirected graph, depending on properties of minimal models for the query.

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Section: Results Statementmentioning

confidence: 99%

The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

Amarilli¹,

Ceylan²

2022

Logical Methods in Computer Science

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“…(non-uniform approach) How complex is it to decide, given an arbitrary DL-Lite ✷ bool/horn OMAQ or OMPIQ, whether it is FO(<)-, FO(<, ≡)or FO(RPR)-rewritable? For atemporal OMQs with DL-ontologies, this non-uniform approach to OBDA has been actively developed since the mid 2010s (Bienvenu, ten Cate, Lutz, & Wolter, 2014;Bienvenu, Hansen, Lutz, & Wolter, 2016;Barceló, Berger, Lutz, & Pieris, 2018). In the temporal case, first steps have recently been made for LTL OMQs in (Ryzhikov, Savateev, & Zakharyaschev, 2021).…”

Section: Discussionmentioning

confidence: 99%

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

Artale¹,

Kontchakov²,

Kovtunova³

et al. 2021

Preprint

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Aiming at ontology-based data access to temporal data, we design two-dimensional temporal ontology and query languages by combining logics from the (extended) DL-Lite family with linear temporal logic LTL over discrete time (Z, <). Our main concern is firstorder rewritability of ontology-mediated queries (OMQs) that consist of a 2D ontology and a positive temporal instance query. Our target languages for FO-rewritings are two-sorted FO(<)-first-order logic with sorts for time instants ordered by the built-in precedence relation < and for the domain of individuals-its extension FO(<, ≡) with the standard congruence predicates t ≡ 0 (mod n), for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FO(<, ≡)and FO(RPR)rewritability guarantee answering OMQs in uniform AC 0 and NC 1 , respectively.We proceed in three steps. First, we define a hierarchy of 2D DL-Lite/LTL ontology languages and investigate the FO-rewritability of OMQs with atomic queries by constructing projections onto 1D LTL OMQs and employing recent results on the FO-rewritability of propositional LTL OMQs. As the projections involve deciding consistency of ontologies and data, we also consider the consistency problem for our languages. While the undecidability of consistency for 2D ontology languages with expressive Boolean role inclusions might be expected, we also show that, rather surprisingly, the restriction to Krom and Horn role inclusions leads to decidability (and ExpSpace-completeness), even if one admits full Booleans on concepts. As a final step, we lift some of the rewritability results for atomic OMQs to OMQs with expressive positive temporal instance queries. The lifting results are based on an in-depth study of the canonical models and only concern Horn ontologies.

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“…That Theorem 7 does not hold for such CQs is demonstrated by 5 in Example 1 (cf. Claim 7.1 (3)), 6 in Example 4 (cf. Claim 7.1 (4)), and 7 , 8 below (cf.…”

Section: Monadic D-sirups With a Ditree Cqmentioning

confidence: 98%

Deciding Boundedness of Monadic Sirups

Kikot

Kurucz

Podolskii

et al. 2021

Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems

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We show that deciding boundedness (aka FO-rewritability) of monadic single rule datalog programs (sirups) is 2ExpTime-hard, which matches the upper bound known since 1988 and finally settles a long-standing open problem. We obtain this result as a byproduct of an attempt to classify monadic 'disjunctive sirups'-Boolean conjunctive queries with unary and binary predicates mediated by a disjunctive rule ( ) ∨ ( ) ← ( )-according to the data complexity of their evaluation. Apart from establishing that deciding FO-rewritability of disjunctive sirups with a dag-shaped is also 2ExpTime-hard, we make substantial progress towards obtaining a complete FO/L-hardness dichotomy of disjunctive sirups with ditree-shaped .

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First-Order Rewritability of Frontier-Guarded Ontology-Mediated Queries

Cited by 11 publications

References 6 publications

The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

The Dichotomy of Evaluating Homomorphism-Closed Queries on Probabilistic Graphs

First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries

Deciding Boundedness of Monadic Sirups

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