Visual Reasoning with Diagrams by Amirouche Moktefi & Sun-Joo Shin

Author:Amirouche Moktefi & Sun-Joo Shin
Language: eng
Format: epub
Publisher: Springer Basel, Basel

9.4 Relation to Description Logic

The ∀∃-form ∀∃(c,r,d) has the counterpart sentence c⊑∃r.d in description logic (DL), cf. e.g. [4, 15] for logico-algebraic and predicate logical accounts of DL.

More generally DL offers a fragment of FOL comprising classical negation supported by consistency (satisfiability) check facilities. DL comprise operators for forming new classes corresponding to the boolean operators in FOL. One may notice that the CRL relationship ∀∀(c,r,d) is different from the DL sentence c⊑∀r.d, the latter being ∀x(c(x)→∀y(r(x,y)→d(y))).

DL is biased towards a set-theoretic, extensional understanding of classes supported by the usual set operations on classes as sets. By contrast CRL supports a graph conception of class relationships in the vein of semantic networks. As such CRL is biased towards an intensional understanding of classes as objects possessing and inheriting properties via class-class relationships. Furthermore the CRL metalogic level supports classes and relationships as first class citizens which can be quantified over as it appears in the devised inference rules.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.