A logic of graded attributes
Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries repr...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Belohlavek, Radim [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2015 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2015 |
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| Übergeordnetes Werk: |
Enthalten in: Archive for mathematical logic - Springer Berlin Heidelberg, 1988, 54(2015), 7-8 vom: 10. Juli, Seite 785-802 |
|---|---|
| Übergeordnetes Werk: |
volume:54 ; year:2015 ; number:7-8 ; day:10 ; month:07 ; pages:785-802 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00153-015-0440-0 |
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OLC2060249813 |
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| 520 | |a Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. | ||
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10.1007/s00153-015-0440-0 doi (DE-627)OLC2060249813 (DE-He213)s00153-015-0440-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Belohlavek, Radim verfasserin aut A logic of graded attributes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. Attribute implication Fuzzy logic Graded-style completeness Pavelka-style logic Vychodil, Vilem aut Enthalten in Archive for mathematical logic Springer Berlin Heidelberg, 1988 54(2015), 7-8 vom: 10. Juli, Seite 785-802 (DE-627)130412910 (DE-600)623073-8 (DE-576)015915948 0933-5846 nnns volume:54 year:2015 number:7-8 day:10 month:07 pages:785-802 https://doi.org/10.1007/s00153-015-0440-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4700 AR 54 2015 7-8 10 07 785-802 |
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10.1007/s00153-015-0440-0 doi (DE-627)OLC2060249813 (DE-He213)s00153-015-0440-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Belohlavek, Radim verfasserin aut A logic of graded attributes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. Attribute implication Fuzzy logic Graded-style completeness Pavelka-style logic Vychodil, Vilem aut Enthalten in Archive for mathematical logic Springer Berlin Heidelberg, 1988 54(2015), 7-8 vom: 10. Juli, Seite 785-802 (DE-627)130412910 (DE-600)623073-8 (DE-576)015915948 0933-5846 nnns volume:54 year:2015 number:7-8 day:10 month:07 pages:785-802 https://doi.org/10.1007/s00153-015-0440-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4700 AR 54 2015 7-8 10 07 785-802 |
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10.1007/s00153-015-0440-0 doi (DE-627)OLC2060249813 (DE-He213)s00153-015-0440-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Belohlavek, Radim verfasserin aut A logic of graded attributes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. Attribute implication Fuzzy logic Graded-style completeness Pavelka-style logic Vychodil, Vilem aut Enthalten in Archive for mathematical logic Springer Berlin Heidelberg, 1988 54(2015), 7-8 vom: 10. Juli, Seite 785-802 (DE-627)130412910 (DE-600)623073-8 (DE-576)015915948 0933-5846 nnns volume:54 year:2015 number:7-8 day:10 month:07 pages:785-802 https://doi.org/10.1007/s00153-015-0440-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4700 AR 54 2015 7-8 10 07 785-802 |
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10.1007/s00153-015-0440-0 doi (DE-627)OLC2060249813 (DE-He213)s00153-015-0440-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Belohlavek, Radim verfasserin aut A logic of graded attributes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. Attribute implication Fuzzy logic Graded-style completeness Pavelka-style logic Vychodil, Vilem aut Enthalten in Archive for mathematical logic Springer Berlin Heidelberg, 1988 54(2015), 7-8 vom: 10. Juli, Seite 785-802 (DE-627)130412910 (DE-600)623073-8 (DE-576)015915948 0933-5846 nnns volume:54 year:2015 number:7-8 day:10 month:07 pages:785-802 https://doi.org/10.1007/s00153-015-0440-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4700 AR 54 2015 7-8 10 07 785-802 |
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10.1007/s00153-015-0440-0 doi (DE-627)OLC2060249813 (DE-He213)s00153-015-0440-0-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Belohlavek, Radim verfasserin aut A logic of graded attributes 2015 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2015 Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. Attribute implication Fuzzy logic Graded-style completeness Pavelka-style logic Vychodil, Vilem aut Enthalten in Archive for mathematical logic Springer Berlin Heidelberg, 1988 54(2015), 7-8 vom: 10. Juli, Seite 785-802 (DE-627)130412910 (DE-600)623073-8 (DE-576)015915948 0933-5846 nnns volume:54 year:2015 number:7-8 day:10 month:07 pages:785-802 https://doi.org/10.1007/s00153-015-0440-0 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_24 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4277 GBV_ILN_4700 AR 54 2015 7-8 10 07 785-802 |
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A logic of graded attributes |
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Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. © Springer-Verlag Berlin Heidelberg 2015 |
| abstractGer |
Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. © Springer-Verlag Berlin Heidelberg 2015 |
| abstract_unstemmed |
Abstract We present a logic for reasoning about attribute dependencies in data involving degrees such as a degree to which an object is red or a degree to which two objects are similar. The dependencies are of the form A ⇒ B and can be interpreted in two ways: first, in data tables with entries representing degrees to which objects (rows) have attributes (columns); second, in database tables where each domain is equipped with a similarity relation. We assume that the degrees form a scale equipped with operations representing many-valued logical connectives. If 0 and 1 are the only degrees, the algebra of degrees becomes the two-element Boolean algebra and the two interpretations become well-known dependencies in Boolean data and functional dependencies of relational databases. In a setting with general scales, we obtain a new kind of dependencies with naturally arising degrees of validity, degrees of entailment, and related logical concepts. The deduction rules of the proposed logic are inspired by Armstrong rules and make it possible to infer dependencies to degrees—the degrees of provability. We provide a soundness and completeness theorem for such a setting asserting that degrees of entailment coincide with degrees of provability, prove the independence of deduction rules, and present further observations. © Springer-Verlag Berlin Heidelberg 2015 |
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| title_short |
A logic of graded attributes |
| url |
https://doi.org/10.1007/s00153-015-0440-0 |
| remote_bool |
false |
| author2 |
Vychodil, Vilem |
| author2Str |
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| doi_str |
10.1007/s00153-015-0440-0 |
| up_date |
2024-07-04T00:55:31.481Z |
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7.400937 |