Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

5.1 Introduction
Production systems, covered in chapter 3, has been successfully used for
reasoning in many intelligent systems [1],[6]. Because of its inherent
simplicity, it has been widely accepted as a fundamental tool to knowledge
representation. The efficiency of production systems, however, degrades with
the increase in complexity of knowledge in real world problems. For instance,
a production system does not support simple rules like if ((X is a son of Y )
OR ( X is a daughter of Y)) then (Y is a father of X). The logic of
propositions (also called propositional logic) is an alternative form of
knowledge representation, which overcomes some of the weakness of
production systems. For instance, it can join simple sentences or clauses by
logical connectives to represent more complex sentences. Due to the usage of
logical connectives, propositional logic is sometimes called logical calculus.
However, it needs mention that such logic has no relevance with Calculus, the
popularly known branch of mathematics. This chapter will be devoted to
representing knowledge with propositional logic. Generally, the reasoning
problems in propositional logic are formulated in the form of mathematical
theorems. For instance, given two facts : i) Birds fly, ii) Parrot is a bird, and
one has to infer that parrot flies. This can be formally stated in the form of a
theorem: given the premises birds fly and parrot is a bird, prove that parrot
flies. We can now employ tools of propositional logic to prove (or disprove)
the theorem. The chapter presents various tools and techniques for theorem
proving by propositional logic.
Predicate Logic (also called first order predicate logic or simply first
order logic or predicate calculus) has similar formalisms like the propositional
logic. It is more versatile than the propositional counterpart for its added
features. For instance, it includes two quantifiers, namely, the essential
quantifier (∀) and the existential quantifier (∃) that are capable of handling
more complex knowledge.
The chapter is organized as follows. It starts with a set of formal
definitions and presents the methodology of knowledge representation by
propositional logic. It then covers the semantic and syntactic methods of
theorem proving by propositional logic. Next predicate logic is introduced
from the first principles, and a method to represent large sentences in clause
form is described. Later two fundamental properties of predicate calculus: the
unification algorithm and the resolution principle, which are useful for
theorem proving, are introduced. The issues of soundness and completeness
are discussed briefly in the chapter.