The Index and Core of a Relation. With Applications to the Axiomatics of Relation Algebra
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866911344108765184 |
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| author | Backhouse, Roland Voermans, Ed |
| author_facet | Backhouse, Roland Voermans, Ed |
| contents | We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the axiom to standard axiom systems for point-free reasoning. Examples of the theorems we prove are that a core/index of a difunction is a bijection, and that the so-called ``all or nothing'' axiom used to facilitate pointwise reasoning is derivable from our axiom of choice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_02017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Index and Core of a Relation. With Applications to the Axiomatics of Relation Algebra Backhouse, Roland Voermans, Ed Logic in Computer Science F.3.1; F.4.1 We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the axiom to standard axiom systems for point-free reasoning. Examples of the theorems we prove are that a core/index of a difunction is a bijection, and that the so-called ``all or nothing'' axiom used to facilitate pointwise reasoning is derivable from our axiom of choice. |
| title | The Index and Core of a Relation. With Applications to the Axiomatics of Relation Algebra |
| topic | Logic in Computer Science F.3.1; F.4.1 |
| url | https://arxiv.org/abs/2309.02017 |