First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated Queries Article Swipe
Alessandro Artale
,
Roman Kontchakov
,
Alisa Kovtunova
,
Vladislav Ryzhikov
,
Frank Wolter
,
Michael Zakharyaschev
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2111.06806
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2111.06806
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 first-order 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 FOE with the standard congruence predicates t \equiv 0 mod n, for any fixed n > 1, and FO(RPR) that admits relational primitive recursion. In terms of circuit complexity, FOE- and FO(RPR)-rewritability guarantee answering OMQs in uniform AC0 and NC1, 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.
Related Topics
Concepts
Decidability
Description logic
Ontology language
Computer science
Theoretical computer science
Web Ontology Language
Linear temporal logic
Ontology
Recursion (computer science)
Consistency (knowledge bases)
Temporal logic
Mathematics
Discrete mathematics
Programming language
Artificial intelligence
Semantic Web
Philosophy
Epistemology
Metadata
- Type
- preprint
- Language
- en
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4226099549
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4226099549Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2111.06806Digital Object Identifier
- Title
-
First-Order Rewritability and Complexity of Two-Dimensional Temporal Ontology-Mediated QueriesWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-11-12Full publication date if available
- Authors
-
Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter, Michael ZakharyaschevList of authors in order
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2111.06806Direct OA link when available
- Concepts
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Decidability, Description logic, Ontology language, Computer science, Theoretical computer science, Web Ontology Language, Linear temporal logic, Ontology, Recursion (computer science), Consistency (knowledge bases), Temporal logic, Mathematics, Discrete mathematics, Programming language, Artificial intelligence, Semantic Web, Philosophy, EpistemologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.LTL | 28, 157, 168 |
| abstract_inverted_index.Our | 33, 55 |
| abstract_inverted_index.The | 255 |
| abstract_inverted_index.and | 13, 49, 78, 104, 117, 125, 143, 159, 178, 216, 268 |
| abstract_inverted_index.any | 99 |
| abstract_inverted_index.are | 60, 258 |
| abstract_inverted_index.for | 58, 68, 79, 98, 186, 194, 244 |
| abstract_inverted_index.its | 85 |
| abstract_inverted_index.mod | 96 |
| abstract_inverted_index.one | 227 |
| abstract_inverted_index.our | 187 |
| abstract_inverted_index.the | 20, 73, 80, 89, 145, 164, 171, 183, 190, 212, 241, 265 |
| abstract_inverted_index.> | 102 |
| abstract_inverted_index.< | 77 |
| abstract_inverted_index.(and | 223 |
| abstract_inverted_index.FOE- | 116 |
| abstract_inverted_index.Horn | 217, 271 |
| abstract_inverted_index.Krom | 215 |
| abstract_inverted_index.NC1, | 126 |
| abstract_inverted_index.OMQs | 121, 148, 158, 246, 248 |
| abstract_inverted_index.also | 181, 207 |
| abstract_inverted_index.data | 3 |
| abstract_inverted_index.even | 225 |
| abstract_inverted_index.from | 19 |
| abstract_inverted_index.full | 229 |
| abstract_inverted_index.lift | 238 |
| abstract_inverted_index.main | 34 |
| abstract_inverted_index.only | 269 |
| abstract_inverted_index.onto | 155 |
| abstract_inverted_index.over | 29 |
| abstract_inverted_index.role | 201, 218 |
| abstract_inverted_index.show | 208 |
| abstract_inverted_index.some | 239 |
| abstract_inverted_index.that | 43, 106 |
| abstract_inverted_index.time | 31, 69 |
| abstract_inverted_index.with | 24, 66, 88, 149, 198, 249 |
| abstract_inverted_index.OMQs. | 169 |
| abstract_inverted_index.While | 189 |
| abstract_inverted_index.based | 259 |
| abstract_inverted_index.data, | 7, 179 |
| abstract_inverted_index.final | 235 |
| abstract_inverted_index.fixed | 100 |
| abstract_inverted_index.leads | 220 |
| abstract_inverted_index.logic | 27, 65 |
| abstract_inverted_index.might | 203 |
| abstract_inverted_index.query | 14 |
| abstract_inverted_index.sorts | 67 |
| abstract_inverted_index.step, | 236 |
| abstract_inverted_index.study | 263 |
| abstract_inverted_index.terms | 112 |
| abstract_inverted_index.that, | 209 |
| abstract_inverted_index.three | 131 |
| abstract_inverted_index.(OMQs) | 42 |
| abstract_inverted_index.Aiming | 0 |
| abstract_inverted_index.First, | 133 |
| abstract_inverted_index.\equiv | 94 |
| abstract_inverted_index.access | 4 |
| abstract_inverted_index.admits | 107, 228 |
| abstract_inverted_index.atomic | 150, 245 |
| abstract_inverted_index.define | 135 |
| abstract_inverted_index.design | 9 |
| abstract_inverted_index.domain | 81 |
| abstract_inverted_index.family | 23 |
| abstract_inverted_index.linear | 25 |
| abstract_inverted_index.logics | 18 |
| abstract_inverted_index.models | 267 |
| abstract_inverted_index.query. | 54 |
| abstract_inverted_index.rather | 210 |
| abstract_inverted_index.recent | 161 |
| abstract_inverted_index.steps. | 132 |
| abstract_inverted_index.target | 56 |
| abstract_inverted_index.Boolean | 200 |
| abstract_inverted_index.DL-Lite | 22 |
| abstract_inverted_index.FO(RPR) | 105 |
| abstract_inverted_index.circuit | 114 |
| abstract_inverted_index.concern | 35, 270 |
| abstract_inverted_index.consist | 44 |
| abstract_inverted_index.involve | 173 |
| abstract_inverted_index.lifting | 256 |
| abstract_inverted_index.ordered | 71 |
| abstract_inverted_index.problem | 185 |
| abstract_inverted_index.proceed | 129 |
| abstract_inverted_index.queries | 41, 151 |
| abstract_inverted_index.results | 162, 243, 257 |
| abstract_inverted_index.uniform | 123 |
| abstract_inverted_index.Booleans | 230 |
| abstract_inverted_index.FO(<) | 62 |
| abstract_inverted_index.built-in | 74 |
| abstract_inverted_index.consider | 182 |
| abstract_inverted_index.deciding | 174 |
| abstract_inverted_index.discrete | 30 |
| abstract_inverted_index.in-depth | 262 |
| abstract_inverted_index.instance | 53, 253 |
| abstract_inverted_index.instants | 70 |
| abstract_inverted_index.ontology | 12, 48, 141, 196 |
| abstract_inverted_index.positive | 51, 251 |
| abstract_inverted_index.queries. | 254 |
| abstract_inverted_index.relation | 76 |
| abstract_inverted_index.standard | 90 |
| abstract_inverted_index.temporal | 6, 11, 26, 52, 252 |
| abstract_inverted_index.(Z,<). | 32 |
| abstract_inverted_index.answering | 120 |
| abstract_inverted_index.canonical | 266 |
| abstract_inverted_index.combining | 17 |
| abstract_inverted_index.concepts. | 232 |
| abstract_inverted_index.employing | 160 |
| abstract_inverted_index.expected, | 205 |
| abstract_inverted_index.extension | 86 |
| abstract_inverted_index.guarantee | 119 |
| abstract_inverted_index.hierarchy | 137 |
| abstract_inverted_index.languages | 15, 57, 142, 197 |
| abstract_inverted_index.primitive | 109 |
| abstract_inverted_index.(extended) | 21 |
| abstract_inverted_index.congruence | 91 |
| abstract_inverted_index.expressive | 199, 250 |
| abstract_inverted_index.inclusions | 202, 219 |
| abstract_inverted_index.languages. | 188 |
| abstract_inverted_index.ontologies | 177 |
| abstract_inverted_index.precedence | 75 |
| abstract_inverted_index.predicates | 92 |
| abstract_inverted_index.recursion. | 110 |
| abstract_inverted_index.relational | 108 |
| abstract_inverted_index.two-sorted | 61 |
| abstract_inverted_index.DL-Lite/LTL | 140 |
| abstract_inverted_index.complexity, | 115 |
| abstract_inverted_index.consistency | 175, 184, 193 |
| abstract_inverted_index.first-order | 37, 64 |
| abstract_inverted_index.individuals | 83 |
| abstract_inverted_index.investigate | 144 |
| abstract_inverted_index.ontologies. | 272 |
| abstract_inverted_index.projections | 154, 172 |
| abstract_inverted_index.restriction | 213 |
| abstract_inverted_index.constructing | 153 |
| abstract_inverted_index.decidability | 222 |
| abstract_inverted_index.FO-rewritings | 59 |
| abstract_inverted_index.propositional | 167 |
| abstract_inverted_index.respectively. | 127 |
| abstract_inverted_index.rewritability | 38, 242 |
| abstract_inverted_index.surprisingly, | 211 |
| abstract_inverted_index.ontology-based | 2 |
| abstract_inverted_index.undecidability | 191 |
| abstract_inverted_index.two-dimensional | 10 |
| abstract_inverted_index.FO-rewritability | 146, 165 |
| abstract_inverted_index.ontology-mediated | 40 |
| abstract_inverted_index.FO(RPR)-rewritability | 118 |
| abstract_inverted_index.ExpSpace-completeness), | 224 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 6 |
| citation_normalized_percentile |