Boolean and classical restriction categories
| Autor: | Robin Cockett, Ernie Manes |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Mathematical Structures in Computer Science. 19:357-416 |
| ISSN: | 1469-8072 0960-1295 |
| DOI: | 10.1017/s0960129509007543 |
| Popis: | A restriction category is an abstract category of partial maps. A Boolean restriction category is a restriction category that supports classical (Boolean) reasoning. Such categories are models of loop-free dynamic logic that is deterministic in the sense that < α > Q ⊂ [α]Q. Classical restriction categories are restriction categories with a locally Boolean structure: it is shown that they are precisely full subcategories of Boolean restriction categories. In particular, a Boolean restriction category may be characterised as a classical restriction category with finite coproducts in which all restriction idempotents split.Every restriction category admits a restriction embedding into a Boolean restriction category. Thus, every abstract category of partial maps admits a conservative extension that supports classical reasoning. An explicit construction of the classical completion of a restriction category is given. |
| Databáze: | OpenAIRE |
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