Mathematical Foundation of Computer Science

DHARM

PROPOSITIONAL LOGIC 103

manuscripted in symbolic form (object language). Arguments are prepared in natural language
(English/Hindi) but their representation (symbolic logic) need object language and so they are
ready for validation checking computation.

Object Language

Natural Language

Fig. 5.2

Section 5.2 starts with discussion of statements and symbolization of statements.

5.2 Symbolization of Statements..........................................................................................

A statement is a declarative sentence. It assigns one and only one of the two possible truth
values true or false. A statement is of two types. A statement is said to be atomic statement if it
can not be decomposable further into simple statement/s. Atomic statements are denoted by
distinct symbols like,
A, B, C, ................X, Y, Z.
a, b, c, ...................x, y, z.
A1, A2, .........................
B1, B2,..........................
Etc...
These symbols are called propositional variables. Second type of statements are com-
pound statements. If a statement is formed over composition of several statements through
connectives like conjunction, disjunction, negation and implication etc. then it is a compound
statement. In other words statements are closed under connectives. In the latter section, we
shall discuss the connectives in more detail. The compound statement is denoted by the string
of symbols, connectives and parenthesis. Parenthesis is used to restrict the scope of the con-
nective over symbols. The compound statement also assigns one and only one of the two possi-
ble truth values true or false. That will be the out come of the truth value attain from all the
statements of the compound statement.
Therefore, set of statements both atomic and composite, formed language called object
language so that we can symbolize the statements.

Example 5.1. Illustrates the meaning of the statement.

1. India is a developing country.


2. L K Adwani is the leader of USA.


3. Henry Nikolas will be the richest person after 10 years.


4. False never encumbered truth.


5. It will rain today.


6. Leave the room


7. Bring my coat and tie.