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logicowlontologydiscrete-mathematicsreasoning

What should be the outcome of this ontology?

I am learning web ontology and Description logic. I came across this and was quite confused about what should be the answer:

This is the knowledge base. Where Parent(X,Y) means X is parent of Y.

Parent(X,Y).
Parent(Y,Z).
Parent(X,Z).
Parent(Z,M).
Manager(Y).
¬Manager(M).

Does these facts imply fact:

X∈(∃Parent.(Manager⊓∃Parent.¬Manager))

P.S this is not homework.

Solution

  • Short answer, no.

    What can be inferred:

    ∃Parent.⊤ (X has some parent, namely Y and Z) ∃Parent.Manager (X has some parent that is a manager, namely Y but not Z) ∃Parent.(Manager ⊓ ∃Parent.⊤) (X has some parent that is a manager and has a parent, namely Y)

    Z is not a manager, thus you could only infer ∃Parent.∃Parent.⊤ (X has some parent (Y and Z) that has a parent ∃Parent.∃Parent.¬Manager (X has some parent (Z) that has a parent (M) which is not a manager)