An inference engine for RDF - Agfa

An inference engine for RDF
The set of all things that have either the property yellow or blue or both needs to
be declared in a superset that has a name.
For a proof of A ∨ ¬A either A has to be proved or ¬A has to be proved (e.g. an
object is yellow or not_yellow only if this has been declared).
This is the consequence of the fact that in the RDF graph everything is
designated by a URI.
A proof of a triple is given when:
a) it is a valid triple
b) it is accepted by the trust system
The BHK-interpretation of constructive logic states:
(Brouwer, Heyting, Kolmogorov) [STANDARD]
a) “ A proof of A and B is given by presenting a proof of A and a proof of B.”
With RDF all triples in a set of triples have between them an implicit
conjunction. If A and B are triples in the RDF database, they are necessarily
true and their conjucntion is thus constructively true too.
b) “ A proof of A or B is given by presenting either a proof of A or a proof of B
or both.”
There is no disjunction defined in RDF. Would it be defined as above(3.2),
then it would be constructive .
c) “ A proof of A Æ B is a procedure which permits us to transform a proof of A
into a proof of B.”
The implication is an extension of RDF. I propose a constructive implication
where (A1, A2, … , An) Æ B is interpreted: if (A1, A2, … An) are true triples
then B is a true triple.
d) “ The constant false has no proof.”
The constant false does not exist in RDF but it could be added .
This constructive approach is chosen for reasons of verifiability. Suppose an
answer to a query is T1 ∨ T2 where T1 and T2 are triples but neither T1 or T2
can be proven. How can such an answer be verified?
When solutions are composed of existing triples then these triples can be
verified i.e. the originating namespace can be queried for a confirmation or
perhaps the triples or their constituents (subject, predicate, object) could be
signed.
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