On matrices and K-relations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2021-07-15

AUTHORS

Robert Brijder, Marc Gyssens, Jan Van den Bussche

ABSTRACT

We show that the matrix query language MATLANG corresponds to a natural fragment of the positive relational algebra on K-relations. The fragment is defined by introducing a composition operator and restricting K-relation arities to 2. We then proceed to show that MATLANG can express all matrix queries expressible in the positive relational algebra on K-relations, when intermediate arities are restricted to 3. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to first-order logic with three variables. More... »

PAGES

1-30

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10472-021-09760-4

DOI

http://dx.doi.org/10.1007/s10472-021-09760-4

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1139733080


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium", 
          "id": "http://www.grid.ac/institutes/grid.12155.32", 
          "name": [
            "Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Brijder", 
        "givenName": "Robert", 
        "id": "sg:person.01124236701.65", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01124236701.65"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium", 
          "id": "http://www.grid.ac/institutes/grid.12155.32", 
          "name": [
            "Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Gyssens", 
        "givenName": "Marc", 
        "id": "sg:person.016126431027.84", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016126431027.84"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium", 
          "id": "http://www.grid.ac/institutes/grid.12155.32", 
          "name": [
            "Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Van den Bussche", 
        "givenName": "Jan", 
        "id": "sg:person.012021464533.34", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012021464533.34"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-3-030-39951-1_3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1124370144", 
          "https://doi.org/10.1007/978-3-030-39951-1_3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00370681", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032494380", 
          "https://doi.org/10.1007/bf00370681"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-21676-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109712412", 
          "https://doi.org/10.1007/978-3-662-21676-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-011-5694-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1042156914", 
          "https://doi.org/10.1007/978-94-011-5694-3"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2021-07-15", 
    "datePublishedReg": "2021-07-15", 
    "description": "We show that the matrix query language MATLANG corresponds to a natural fragment of the positive relational algebra on K-relations. The fragment is defined by introducing a composition operator and restricting K-relation arities to 2. We then proceed to show that MATLANG can express all matrix queries expressible in the positive relational algebra on K-relations, when intermediate arities are restricted to 3. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to first-order logic with three variables.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s10472-021-09760-4", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1043955", 
        "issn": [
          "1012-2443", 
          "1573-7470"
        ], 
        "name": "Annals of Mathematics and Artificial Intelligence", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }
    ], 
    "keywords": [
      "first-order logic", 
      "natural fragments", 
      "relational algebra", 
      "relation", 
      "logic", 
      "binary relations", 
      "arity", 
      "classical logic", 
      "situation", 
      "queries", 
      "fragments", 
      "positive relational algebra", 
      "algebra", 
      "composition operators", 
      "numerical data", 
      "data", 
      "operators", 
      "matrix queries", 
      "model", 
      "variables", 
      "matrix", 
      "analogues", 
      "matrix query language MATLANG", 
      "query language MATLANG", 
      "language MATLANG", 
      "MATLANG", 
      "relation arities", 
      "intermediate arities"
    ], 
    "name": "On matrices and K-relations", 
    "pagination": "1-30", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1139733080"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10472-021-09760-4"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10472-021-09760-4", 
      "https://app.dimensions.ai/details/publication/pub.1139733080"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T19:02", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_885.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s10472-021-09760-4"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10472-021-09760-4'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10472-021-09760-4'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10472-021-09760-4'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10472-021-09760-4'


 

This table displays all metadata directly associated to this object as RDF triples.

110 TRIPLES      22 PREDICATES      55 URIs      43 LITERALS      4 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10472-021-09760-4 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N35b7c08fca1449a983e2d5890e099506
4 schema:citation sg:pub.10.1007/978-3-030-39951-1_3
5 sg:pub.10.1007/978-3-662-21676-7
6 sg:pub.10.1007/978-94-011-5694-3
7 sg:pub.10.1007/bf00370681
8 schema:datePublished 2021-07-15
9 schema:datePublishedReg 2021-07-15
10 schema:description We show that the matrix query language MATLANG corresponds to a natural fragment of the positive relational algebra on K-relations. The fragment is defined by introducing a composition operator and restricting K-relation arities to 2. We then proceed to show that MATLANG can express all matrix queries expressible in the positive relational algebra on K-relations, when intermediate arities are restricted to 3. Thus we offer an analogue, in a model with numerical data, to the situation in classical logic, where the algebra of binary relations is equivalent to first-order logic with three variables.
11 schema:genre article
12 schema:inLanguage en
13 schema:isAccessibleForFree false
14 schema:isPartOf sg:journal.1043955
15 schema:keywords MATLANG
16 algebra
17 analogues
18 arity
19 binary relations
20 classical logic
21 composition operators
22 data
23 first-order logic
24 fragments
25 intermediate arities
26 language MATLANG
27 logic
28 matrix
29 matrix queries
30 matrix query language MATLANG
31 model
32 natural fragments
33 numerical data
34 operators
35 positive relational algebra
36 queries
37 query language MATLANG
38 relation
39 relation arities
40 relational algebra
41 situation
42 variables
43 schema:name On matrices and K-relations
44 schema:pagination 1-30
45 schema:productId N7c1e29627329409fbd52241764441fb9
46 Nf486e9f9f2e64f3587551094fa9845fb
47 schema:sameAs https://app.dimensions.ai/details/publication/pub.1139733080
48 https://doi.org/10.1007/s10472-021-09760-4
49 schema:sdDatePublished 2022-01-01T19:02
50 schema:sdLicense https://scigraph.springernature.com/explorer/license/
51 schema:sdPublisher Nb390d33f3d8a4baa8505d02308fc3a85
52 schema:url https://doi.org/10.1007/s10472-021-09760-4
53 sgo:license sg:explorer/license/
54 sgo:sdDataset articles
55 rdf:type schema:ScholarlyArticle
56 N2328e0035cf44453adc76d076173f3ab rdf:first sg:person.016126431027.84
57 rdf:rest Nd0f2438e38ed4e64a0ed94eb50620111
58 N35b7c08fca1449a983e2d5890e099506 rdf:first sg:person.01124236701.65
59 rdf:rest N2328e0035cf44453adc76d076173f3ab
60 N7c1e29627329409fbd52241764441fb9 schema:name doi
61 schema:value 10.1007/s10472-021-09760-4
62 rdf:type schema:PropertyValue
63 Nb390d33f3d8a4baa8505d02308fc3a85 schema:name Springer Nature - SN SciGraph project
64 rdf:type schema:Organization
65 Nd0f2438e38ed4e64a0ed94eb50620111 rdf:first sg:person.012021464533.34
66 rdf:rest rdf:nil
67 Nf486e9f9f2e64f3587551094fa9845fb schema:name dimensions_id
68 schema:value pub.1139733080
69 rdf:type schema:PropertyValue
70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
71 schema:name Mathematical Sciences
72 rdf:type schema:DefinedTerm
73 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
74 schema:name Pure Mathematics
75 rdf:type schema:DefinedTerm
76 sg:journal.1043955 schema:issn 1012-2443
77 1573-7470
78 schema:name Annals of Mathematics and Artificial Intelligence
79 schema:publisher Springer Nature
80 rdf:type schema:Periodical
81 sg:person.01124236701.65 schema:affiliation grid-institutes:grid.12155.32
82 schema:familyName Brijder
83 schema:givenName Robert
84 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01124236701.65
85 rdf:type schema:Person
86 sg:person.012021464533.34 schema:affiliation grid-institutes:grid.12155.32
87 schema:familyName Van den Bussche
88 schema:givenName Jan
89 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012021464533.34
90 rdf:type schema:Person
91 sg:person.016126431027.84 schema:affiliation grid-institutes:grid.12155.32
92 schema:familyName Gyssens
93 schema:givenName Marc
94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016126431027.84
95 rdf:type schema:Person
96 sg:pub.10.1007/978-3-030-39951-1_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1124370144
97 https://doi.org/10.1007/978-3-030-39951-1_3
98 rdf:type schema:CreativeWork
99 sg:pub.10.1007/978-3-662-21676-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109712412
100 https://doi.org/10.1007/978-3-662-21676-7
101 rdf:type schema:CreativeWork
102 sg:pub.10.1007/978-94-011-5694-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1042156914
103 https://doi.org/10.1007/978-94-011-5694-3
104 rdf:type schema:CreativeWork
105 sg:pub.10.1007/bf00370681 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032494380
106 https://doi.org/10.1007/bf00370681
107 rdf:type schema:CreativeWork
108 grid-institutes:grid.12155.32 schema:alternateName Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium
109 schema:name Faculty of Sciences, Hasselt University, Martelarenlaan 42, 3500, Hasselt, Belgium
110 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...