Characterizing implications of injective partial orders. (English) Zbl 1213.68597

Priss, Uta (ed.) et al., Conceptual structures: Knowledge architectures for smart applications. 15th international conference on conceptual structures, ICCS 2007, Sheffield, UK, July 22–27, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73680-6/pbk). Lecture Notes in Computer Science 4604. Lecture Notes in Artificial Intelligence, 492-495 (2007).
Summary: It is known that implications in powerset-based closure systems correspond to Horn approximations in propositional logic frameworks. Here we focus on the problem of implications between injective partial orders. We set up the definitions that allow one to apply standard constructions of implications, and formally characterize the propositional theory obtained. We describe also some experimental applications of our development.
For the entire collection see [Zbl 1122.68010].


68T30 Knowledge representation
03B05 Classical propositional logic
06A15 Galois correspondences, closure operators (in relation to ordered sets)
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