Inference in first-order logic

Outline

Universal instantiation (UI)

Existential instantiation (EI)

Reduction to propositional inference

Reduction contd.

Reduction contd.

Problems with propositionalization

Unification

Unification

Unification

Unification

Unification

Unification

The unification algorithm

The unification algorithm

Generalized Modus Ponens (GMP)

Soundness of GMP

Example knowledge base

Example knowledge base contd.

Forward chaining algorithm

Forward chaining proof

Forward chaining proof

Forward chaining proof

Properties of forward chaining

Efficiency of forward chaining

Hard matching example

Backward chaining algorithm

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Properties of backward chaining

Logic programming: Prolog

Prolog

Resolution: brief summary

Conversion to CNF

Conversion to CNF contd.

Resolution proof: definite clauses