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b) OWL2 is a subset of HOL language. For example in OWL2 Functional Style, we have proposition [2]SubClassOf( C1 C2 )
where C1 C2 are unary predicates, i.e. SubClassOf is a binary predicate on unary predicates - this is a HOL language feature.
"Translation into First-Order Logic. Since the semantic conditions of OWL 2 Full have the form of FOL formulae, its semantics can directly be axiomatisized [sic] as a FOL theory. Further, every RDF graph can be written as a FOL axiom consisting of a conjunction of ternary atomic formulae, with existentially quantified variables for the blank nodes. The details of the translation can be found in [7]. As a concrete FOL syntax, we use the TPTP language [8], which is understood by the majority of existing FOL reasoners" (p. 2)
I would have thought it would be trivial to find a clear statement like this somewhere on the W3C site, but either it's not there, or my search skills were not sufficient to find it.
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On 1 Jan 2022, at 11:46, Patrick Browne <patrickb...@gmail.com> wrote:
I am studying Conceptual Graphs (CGs) with a view to using them in my research as a visual presentation of First Order Logic with equality (FOL=).
I have posted two questions, Question 1 and Question 2, to AI StackExchange.
In his seminal book (page 86), Sowa provides a mapping Φ from CGs to FOL. I also require a mapping Φ inverse. This is more difficult than I first thought due to the differing structuring mechanisms in the sources and targets of the mappings for my particular case. I am using CafeOBJ to present FOL theories, where structuring is based on the Theory of Institutions (TOI). From my limited knowledge of CGs it seems that the concepts are structured using a Lattice of Theories.
Obviously, members of this forum would be in a unique position to answer such questions. Any assistance would be greatly appreciated and would help remove my misconceptions.
Regards,
Patrick Browne--
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