An algebraic study of exactness in partial contexts. (English) Zbl 1316.03041
Summary: DMF’s are the natural algebraic tool for modelling reasoning with Körner’s partial predicates. We provide two representation theorems for DMF’s which give rise to two adjunctions, the first between DMF and the category of sets and the second between DMF and the category of distributive lattices with minimum. Then we propose a logic \(\mathcal L_{\{1\}}\) for dealing with exactness in partial contexts, which belongs neither to the Leibniz, nor to the Frege hierarchies, and carry on its study with techniques of abstract algebraic logic. Finally a fully adequate and algebraizable Gentzen system for \(\mathcal L_{\{1\}}\) is given.
MSC:
| 03G27 | Abstract algebraic logic |
| 03G10 | Logical aspects of lattices and related structures |
| 06D30 | De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects) |
| 68T30 | Knowledge representation |
Keywords:
partial predicates; abstract algebraic logic; algebraic logic; DMF lattice; Kleene lattice; fixed pointReferences:
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