Dynamic effect algebras and their representations
Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chajda, Ivan [verfasserIn] Paseka, Jan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2012 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 16(2012), 10 vom: 12. Mai, Seite 1733-1741 |
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| Übergeordnetes Werk: |
volume:16 ; year:2012 ; number:10 ; day:12 ; month:05 ; pages:1733-1741 |
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| DOI / URN: |
10.1007/s00500-012-0857-x |
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| 520 | |a Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. | ||
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10.1007/s00500-012-0857-x doi (DE-627)SPR006479847 (SPR)s00500-012-0857-x-e DE-627 ger DE-627 rakwb eng Chajda, Ivan verfasserin aut Dynamic effect algebras and their representations 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. Effect algebra (dpeaa)DE-He213 Lattice effect algebra (dpeaa)DE-He213 Tense operators (dpeaa)DE-He213 Dynamic effect algebra (dpeaa)DE-He213 Paseka, Jan verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 16(2012), 10 vom: 12. Mai, Seite 1733-1741 (DE-627)SPR006469531 nnns volume:16 year:2012 number:10 day:12 month:05 pages:1733-1741 https://dx.doi.org/10.1007/s00500-012-0857-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 16 2012 10 12 05 1733-1741 |
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10.1007/s00500-012-0857-x doi (DE-627)SPR006479847 (SPR)s00500-012-0857-x-e DE-627 ger DE-627 rakwb eng Chajda, Ivan verfasserin aut Dynamic effect algebras and their representations 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. Effect algebra (dpeaa)DE-He213 Lattice effect algebra (dpeaa)DE-He213 Tense operators (dpeaa)DE-He213 Dynamic effect algebra (dpeaa)DE-He213 Paseka, Jan verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 16(2012), 10 vom: 12. Mai, Seite 1733-1741 (DE-627)SPR006469531 nnns volume:16 year:2012 number:10 day:12 month:05 pages:1733-1741 https://dx.doi.org/10.1007/s00500-012-0857-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 16 2012 10 12 05 1733-1741 |
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10.1007/s00500-012-0857-x doi (DE-627)SPR006479847 (SPR)s00500-012-0857-x-e DE-627 ger DE-627 rakwb eng Chajda, Ivan verfasserin aut Dynamic effect algebras and their representations 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. Effect algebra (dpeaa)DE-He213 Lattice effect algebra (dpeaa)DE-He213 Tense operators (dpeaa)DE-He213 Dynamic effect algebra (dpeaa)DE-He213 Paseka, Jan verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 16(2012), 10 vom: 12. Mai, Seite 1733-1741 (DE-627)SPR006469531 nnns volume:16 year:2012 number:10 day:12 month:05 pages:1733-1741 https://dx.doi.org/10.1007/s00500-012-0857-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 16 2012 10 12 05 1733-1741 |
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10.1007/s00500-012-0857-x doi (DE-627)SPR006479847 (SPR)s00500-012-0857-x-e DE-627 ger DE-627 rakwb eng Chajda, Ivan verfasserin aut Dynamic effect algebras and their representations 2012 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. Effect algebra (dpeaa)DE-He213 Lattice effect algebra (dpeaa)DE-He213 Tense operators (dpeaa)DE-He213 Dynamic effect algebra (dpeaa)DE-He213 Paseka, Jan verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 16(2012), 10 vom: 12. Mai, Seite 1733-1741 (DE-627)SPR006469531 nnns volume:16 year:2012 number:10 day:12 month:05 pages:1733-1741 https://dx.doi.org/10.1007/s00500-012-0857-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 16 2012 10 12 05 1733-1741 |
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Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. |
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Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. |
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Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006479847</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002736.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2012 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-012-0857-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006479847</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-012-0857-x-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Chajda, Ivan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dynamic effect algebras and their representations</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2012</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract For lattice effect algebras, the so-called tense operators were already introduced by Chajda and Kolařík. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that in every effect algebra can be introduced tense operators which, for non-complete lattice effect algebras, can be only partial mappings. An effect algebra equipped with tense operators reflects changes of quantum events from past to future. A crucial problem concerning tense operators is their representation. Having an effect algebra with tense operators, we can ask if there exists a frame such that each of these operators can be obtained by our construction. We solve this problem for (strict) dynamic effect algebras having a full set of homorphisms into a complete lattice effect algebra.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Effect algebra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lattice effect algebra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tense operators</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamic effect algebra</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Paseka, Jan</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Soft Computing</subfield><subfield code="d">Springer-Verlag, 2003</subfield><subfield code="g">16(2012), 10 vom: 12. Mai, Seite 1733-1741</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:16</subfield><subfield code="g">year:2012</subfield><subfield code="g">number:10</subfield><subfield code="g">day:12</subfield><subfield code="g">month:05</subfield><subfield code="g">pages:1733-1741</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-012-0857-x</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">16</subfield><subfield code="j">2012</subfield><subfield code="e">10</subfield><subfield code="b">12</subfield><subfield code="c">05</subfield><subfield code="h">1733-1741</subfield></datafield></record></collection>
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