Inference in PL and FOL

Outline: PL Inference

Proof methods

Efficient propositional inference

The DPLL algorithm

The DPLL algorithm

The WalkSAT algorithm

The WalkSAT algorithm

Hard satisfiability problems

Hard satisfiability problems

Hard satisfiability problems

Proof methods

Resolution

Resolution example

The power of false

Applying inference rules

Inference

Completeness

Resolution

Resolution

Completeness of Resolution

Completeness of Resolution (cont)

Other Reasoning Patterns

Forward and backward chaining

Forward chaining

Forward chaining algorithm

Forward chaining example

Forward chaining example

Forward chaining example

Forward chaining example

Forward chaining example

Forward chaining example

Forward chaining example

Forward chaining example

Proof of completeness

Backward chaining example

Backward chaining example

Backward chaining example

Inference in first-order logic

Outline

Universal instantiation (UI)

Existential instantiation (EI)

Reduction to propositional inference

Reduction contd.

Reduction con’td.

Problems with propositionalization

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

Backward chaining algorithm

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Backward chaining example

Prolog Inference

Properties of backward chaining

Prolog Execution

Prolog Execution

Procedural Prolog Programming

A Singaporean example

Summary