The Limitations of Propositional Logic & Predicates

The limitations of propositional logic and predicates covered here are as follows:

Limitations of Propositional Logic

Limitation: Propositional Logic does not allow us to conclude the truth of ALL or SOME statements.
Hence, some valid arguments cannot be concluded or translated into purely propositional logic.
It is not possible to mention properties that apply to categories of object, or even about relationships between those properties.
Please read the following examples carefully


Example 1:
Example 2:
Example 3:
Basically, propositional logic is limited to infer statements from general rules.

Predicate Logic

Statements involving variables (e.g. x, y) are neither true nor false when the values of the variables are not specified.
For example:
Predicate Logic allows to make propositions from statements with variables.
A statement with variable has two parts:

Predicates Examples

One Variable

Example 1:Let P(x) denote the statement "x > 3."
What are the truth values of P(4) and P(2)?

Example 2: Let A(x) denote the statement "Computer x is infltrated by a virus." Suppose CS and Business are infilitrated by a virus.
What are truth values of A(CS10), A(CS20), and A(Business)?

Two Variables

We can also have statements that involve more than one variable.
Example 1: Let Q(x, y) denote the statement "x = y + 9."
What are the truth values of the propositions Q(1, 2) and Q(5, 0)?

Example 2: Let Q(x, y) denote the statement "x = y + 3.".
What are the truth values of the propositions Q(3, 2) and Q(7, 0)?

n-ary predicate

In general, a statement involving the n variables x1, x2, . . . , xn can be denoted by
P(xi, x2, . . . , xn).

A statement of the form P(x1, x2, . . . , xn) is the value of the propositional function P at the n-tuple (xi, x2, . . . , xn), and P is also called a n-ary predicate.

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Date of last modification: March 27, 2019