Mathematical Foundation of Computer Science

5.1 INTRODUCTION TO LOGIC

Study of logic is greatly concerned for the verification of reasoning. From a given set of state-
ments the validity of the conclusion drawn from the set of statements would be verified by the
rules provided by the logic. The domain of rules consists of proof of theorems, mathematical
proofs, conclusion of the scientific theories based on certain hypothesis and the theories of
universal laws. Logic is independent of any language or associated set of arguments. Hence,
the rules that encoded the logic are independent to any language so called rules of inference.
Human has feature of sense of mind. Logic provides the shape to the sense of mind.
Consequently, logic is the outcome of sense of mind. Rules of inference provide the computa-
tional tool through which we can check the validity of the argument framed over any lan-
guage. (Fig. 5.1) Logic is a system for formalizing natural language statement so that we can
reason more accurately.

Sense of Mind

Logic

Rules of Inference

Validation of the

Arguments

Conclusion

Fig. 5.1
In this chapter we start our discussion from the beginning that, how we provide the
shape to the logic. In other words, how we represent the rules of inference. A formal language
will be used for this purpose. In a formal language, syntax is well defined and the statements
have not inherited any ambiguous meaning. It is easy to write and manipulate. These features
of the formal language are the prime necessities for the logic representation. Logic is

5 Propositional Logic

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