First Order Logic and Logical Inference

The rule of Universal Instantiation (UI for short) says that we can infer any sentence obtained by substituting a ground term (a term without variables) for the variable.

• True

• False

What among the following could the universal instantiation of ___________ For all x King(x) ^ Greedy(x) => Evil(x)

• King(John) ^ Greedy(John) => Evil(John)

• King(y) ^ Greedy(y) => Evil(y)

• King(Richard) ^ Greedy(Richard) => Evil(Richard)

• All of the mentioned

Lifted inference rules require finding substitutions that make different logical expressions looks identical.

• Existential Instantiation

• Universal Instantiation

• Unification

• Modus Ponen

Which of the following is not the style of inference?

• Forward Chaining

• Backward Chaining

• Resolution Refutation

• Modus Ponen

In order to utilize generalized Modus Ponens, all sentences in the KB must be in the form of Horn sentences.

• True

• False

For resolution to apply, all sentences must be in conjunctive normal form, a conjunction of disjunctions of literals.

• True

• False

What are the two basic types of inferences?

• Reduction to propositional logic, Manipulate rules directly

• Reduction to propositional logic, Apply modus ponen

• Apply modus ponen, Manipulate rules directly

• Convert every rule to Horn Clause, Reduction to propositional logic

Which among the following could the Existential instantiation of ∃x Crown(x) ^ OnHead(x, Johnny)?

• Crown(John) ^ OnHead(John, Jonny)

• Crown(y) ^ OnHead(y, y, x)

• Crown(x) ^ OnHead(x, Jonny)

• None of the mentioned

Translate the following statement into FOL. "For every a, if a is a PhD student, then a has a master degree"

• ∀ a PhD(a) -> Master(a)

• ∃ a PhD(a) -> Master(a)

• A is true, B is true

• A is false, B is false

There exist only two types of quantifiers, Universal Quantification and Existential Quantification.

• True

• False