Contraexamples in difference posets and orthoalgebras View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1994-01

AUTHORS

Zdenka Riečanová, Daniel Bršel

ABSTRACT

We show that every orthoalgebra (difference orthoposet) uniquely determines a difference orthoalgebraic structure. We give examples of posets on which there exist more than one difference operation. In spite of that, every finite chain is a uniquely determined difference poset. On a difference poset there need not exist any orthoalgebraic operation, but the category of difference orthoposets is isomorphic with the category of orthoalgebras. But a difference poset which is also an orthoposet need not be a difference orthoposet. Moreover, there exist complete lattices on which there does not exist any difference operation. Finally, we show that difference operations and orthoalgebraic operations need not be extendable on a MacNeille completion of the base poset. More... »

PAGES

133-141

References to SciGraph publications

  • 1956-10. Zur Kennzeichnung der Dedekind-MacNeilleschen HÜlle einer geordneten HÜlle in ARCHIV DER MATHEMATIK
  • 1981. What are Quantum Logics and What Ought They to be? in CURRENT ISSUES IN QUANTUM LOGIC
  • 1992-05. Filters and supports in orthoalgebras in INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00671618

    DOI

    http://dx.doi.org/10.1007/bf00671618

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1052652300


    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/2008/0102", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Applied Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia", 
              "id": "http://www.grid.ac/institutes/grid.440789.6", 
              "name": [
                "Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Rie\u010danov\u00e1", 
            "givenName": "Zdenka", 
            "id": "sg:person.014366525167.69", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014366525167.69"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia", 
              "id": "http://www.grid.ac/institutes/grid.440789.6", 
              "name": [
                "Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Br\u0161el", 
            "givenName": "Daniel", 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/978-1-4613-3228-2_3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025561636", 
              "https://doi.org/10.1007/978-1-4613-3228-2_3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf00678545", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050899565", 
              "https://doi.org/10.1007/bf00678545"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01900297", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050039277", 
              "https://doi.org/10.1007/bf01900297"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "1994-01", 
        "datePublishedReg": "1994-01-01", 
        "description": "We show that every orthoalgebra (difference orthoposet) uniquely determines a difference orthoalgebraic structure. We give examples of posets on which there exist more than one difference operation. In spite of that, every finite chain is a uniquely determined difference poset. On a difference poset there need not exist any orthoalgebraic operation, but the category of difference orthoposets is isomorphic with the category of orthoalgebras. But a difference poset which is also an orthoposet need not be a difference orthoposet. Moreover, there exist complete lattices on which there does not exist any difference operation. Finally, we show that difference operations and orthoalgebraic operations need not be extendable on a MacNeille completion of the base poset.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/bf00671618", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1053677", 
            "issn": [
              "0020-7748", 
              "1572-9575"
            ], 
            "name": "International Journal of Theoretical Physics", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "1", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "33"
          }
        ], 
        "keywords": [
          "difference posets", 
          "examples of posets", 
          "orthoalgebras", 
          "posets", 
          "difference operation", 
          "finite chains", 
          "complete lattice", 
          "MacNeille completion", 
          "orthoposets", 
          "operation", 
          "lattice", 
          "structure", 
          "chain", 
          "categories", 
          "spite", 
          "completion", 
          "example", 
          "difference orthoalgebraic structure", 
          "orthoalgebraic structure", 
          "determined difference poset", 
          "orthoalgebraic operation", 
          "difference orthoposets", 
          "category of orthoalgebras", 
          "base poset", 
          "Contraexamples"
        ], 
        "name": "Contraexamples in difference posets and orthoalgebras", 
        "pagination": "133-141", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1052652300"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/bf00671618"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/bf00671618", 
          "https://app.dimensions.ai/details/publication/pub.1052652300"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2021-12-01T19:07", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/article/article_234.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/bf00671618"
      }
    ]
     

    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/bf00671618'

    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/bf00671618'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf00671618'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf00671618'


     

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

    101 TRIPLES      22 PREDICATES      54 URIs      43 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/bf00671618 schema:about anzsrc-for:01
    2 anzsrc-for:0102
    3 schema:author N84f39c83ec77473ba56a0ba1527eb490
    4 schema:citation sg:pub.10.1007/978-1-4613-3228-2_3
    5 sg:pub.10.1007/bf00678545
    6 sg:pub.10.1007/bf01900297
    7 schema:datePublished 1994-01
    8 schema:datePublishedReg 1994-01-01
    9 schema:description We show that every orthoalgebra (difference orthoposet) uniquely determines a difference orthoalgebraic structure. We give examples of posets on which there exist more than one difference operation. In spite of that, every finite chain is a uniquely determined difference poset. On a difference poset there need not exist any orthoalgebraic operation, but the category of difference orthoposets is isomorphic with the category of orthoalgebras. But a difference poset which is also an orthoposet need not be a difference orthoposet. Moreover, there exist complete lattices on which there does not exist any difference operation. Finally, we show that difference operations and orthoalgebraic operations need not be extendable on a MacNeille completion of the base poset.
    10 schema:genre article
    11 schema:inLanguage en
    12 schema:isAccessibleForFree false
    13 schema:isPartOf N3a6c7b91b7da419d8b990b29a5c96235
    14 N85044f59551c42c2b1ad819a89490394
    15 sg:journal.1053677
    16 schema:keywords Contraexamples
    17 MacNeille completion
    18 base poset
    19 categories
    20 category of orthoalgebras
    21 chain
    22 complete lattice
    23 completion
    24 determined difference poset
    25 difference operation
    26 difference orthoalgebraic structure
    27 difference orthoposets
    28 difference posets
    29 example
    30 examples of posets
    31 finite chains
    32 lattice
    33 operation
    34 orthoalgebraic operation
    35 orthoalgebraic structure
    36 orthoalgebras
    37 orthoposets
    38 posets
    39 spite
    40 structure
    41 schema:name Contraexamples in difference posets and orthoalgebras
    42 schema:pagination 133-141
    43 schema:productId Na4f14c34afdc4a888defaed69f95a6f4
    44 Nc00970c5ae984cf5a8d5c1ee11b38977
    45 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052652300
    46 https://doi.org/10.1007/bf00671618
    47 schema:sdDatePublished 2021-12-01T19:07
    48 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    49 schema:sdPublisher N9ee3e49c597b48e09d9bed3d3f331023
    50 schema:url https://doi.org/10.1007/bf00671618
    51 sgo:license sg:explorer/license/
    52 sgo:sdDataset articles
    53 rdf:type schema:ScholarlyArticle
    54 N3a6c7b91b7da419d8b990b29a5c96235 schema:volumeNumber 33
    55 rdf:type schema:PublicationVolume
    56 N44870728efbd425cb71e4782a4a8efe5 schema:affiliation grid-institutes:grid.440789.6
    57 schema:familyName Bršel
    58 schema:givenName Daniel
    59 rdf:type schema:Person
    60 N5ee81323285a413d9af455f89aa71361 rdf:first N44870728efbd425cb71e4782a4a8efe5
    61 rdf:rest rdf:nil
    62 N84f39c83ec77473ba56a0ba1527eb490 rdf:first sg:person.014366525167.69
    63 rdf:rest N5ee81323285a413d9af455f89aa71361
    64 N85044f59551c42c2b1ad819a89490394 schema:issueNumber 1
    65 rdf:type schema:PublicationIssue
    66 N9ee3e49c597b48e09d9bed3d3f331023 schema:name Springer Nature - SN SciGraph project
    67 rdf:type schema:Organization
    68 Na4f14c34afdc4a888defaed69f95a6f4 schema:name dimensions_id
    69 schema:value pub.1052652300
    70 rdf:type schema:PropertyValue
    71 Nc00970c5ae984cf5a8d5c1ee11b38977 schema:name doi
    72 schema:value 10.1007/bf00671618
    73 rdf:type schema:PropertyValue
    74 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Mathematical Sciences
    76 rdf:type schema:DefinedTerm
    77 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
    78 schema:name Applied Mathematics
    79 rdf:type schema:DefinedTerm
    80 sg:journal.1053677 schema:issn 0020-7748
    81 1572-9575
    82 schema:name International Journal of Theoretical Physics
    83 schema:publisher Springer Nature
    84 rdf:type schema:Periodical
    85 sg:person.014366525167.69 schema:affiliation grid-institutes:grid.440789.6
    86 schema:familyName Riečanová
    87 schema:givenName Zdenka
    88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014366525167.69
    89 rdf:type schema:Person
    90 sg:pub.10.1007/978-1-4613-3228-2_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025561636
    91 https://doi.org/10.1007/978-1-4613-3228-2_3
    92 rdf:type schema:CreativeWork
    93 sg:pub.10.1007/bf00678545 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050899565
    94 https://doi.org/10.1007/bf00678545
    95 rdf:type schema:CreativeWork
    96 sg:pub.10.1007/bf01900297 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050039277
    97 https://doi.org/10.1007/bf01900297
    98 rdf:type schema:CreativeWork
    99 grid-institutes:grid.440789.6 schema:alternateName Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia
    100 schema:name Department of Mathematics, Faculty of Electrical Engineering, Slovak Technical University, CS-812 19, Bratislava, Slovakia
    101 rdf:type schema:Organization
     




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


    ...