11: Logic and Inference Rules (Part 2)

Question 1

What is horn logic?

Answer 1

Sub-set of predicate logic that allows efficient reasoning, orthogonal* to description logic

* orthogonal = statistically independent

Question 2

What is SQWRL?

Answer 2

Semantic Query-Enhanced Web Rule Language

A SWRL-based query language that provides SQL-like operators for extracting information from OWL ontologies

Question 3

Which of the following inferred relations in the image is wrong? Why?

Answer 3

female(X), parent(P, X), parent(P, Y) -> sister(X, Y) is wrong

Because X may be Y and we need also notSame(X, Y) to have sister(X, Y)

Question 4

What is first-order logic?

Answer 4

A predicate (Q) can involve more than two instances: Q(a, b, c)

(As opposed to DL, in which a role can involve only two instances)

Question 5

How do you negate a formula?

Answer 5

• Using a proof technique called proof by contradiction
  
  • ​Prove that A follows from B (B -> A)
  • By assuming A is false and deriving a contradiction when combined with B
• We prove that a goal can be answered positively be negating the goal and proving that we get a contradiction using the logic program
  
  • e.g. given the following logic program, we get a logical contradiction

Question 6

What are Description Logic programs (DLP)?

Answer 6

• Can be considered the intersection of Horn logic and description logic
• Allows the combination of the advantages of both approaches
• i.e.
  
  • A modeler may take a DL view, but
  • The implementation may be based on rule technology

Question 7

Using a diagram, show the relation of DLP with other related concepts.

Answer 7

Question 8

In Horn logic, is it possible that you can express that C is a sub-class of the intersection of D₁ and D₂?

Answer 8

Not possible–in Horn logic, the head cannot be combined of atoms and only the tail can be combined of atoms

Question 9

Is it possible, as a pair of rules in Horn logic, to express that the union of C₁ and C₂ is a subclass of D?

Answer 9

Not possible–in Horn logic, the tail cannot have v and can only have ^ which is shown with a comma

Question 10

What are some properties of SWRL?

Answer 10

• If the head of a rule has more than one atom, the rule can be transformed to an equivalent set of rules with one atom in the head
• Expressions, such as restrictions, can appear in the head or body of a rule. This feature adds significant expressive power to OWL, but at the high price of undecidability

Question 11

What is the difference between DLP and SWRL?

Answer 11

• DLP tries to combine the advantages of both languages (description logic and function-free rules) in their common sublanguage, with the goal of computational tractability*
• SWRL takes a more maximalist approach and unites their respective expressivities

* tractability = easily managed