Propositional Logic Vs Predicate Logic

Proposition vs Predicate Logic

“A branch of philosophy and mathematics that deals with the formal principles, methods and criteria of validity of inference, reasoning and knowledge.” (Dictionary.com)

The primary idea behind logic in computer science is to allow us to know and understand the truth value of a particular premise. This knowledge gives us greater understanding and allows us to make valid conclusions. It is with logic that computer programs are designed and only through logic we check and test the correctness of the program. While there are many kinds of logic, the objective of this paper is to discuss the differences between Proposition and Predicate logic.

Proposition Logic

“A proposition is a declarative sentence (that is,

“Propositional logic dealt quite satisfactorily with sentence components like not, and, or and if . . . then, but the logical aspects of natural and artificial languages are much richer than that. What can we do with modifiers like there exists . . . , all . . . , among . . . and only . . .? Here, propositional logic shows clear limitations and the desire to express more subtle declarative sentences led to the design of predicate logic…” (Michael Huth)

The primary feature with predicate logic is its ability to allow us to express more complicated ideas through logic to allow us to reach a valid conclusion. Predicate Logic is expressed through Quantifiers. It is the Quantifiers that allow the logic to express sentences in Natural language like all, among or only and evaluate scenarios for their truth values.

An example of the use of predicate logic is shown below.

Evaluate and give the truth value for the

(x, y are real numbers).

This is impossible to evaluate using proposition logic as it is not a declarative sentence. However with predicate logic we are able to evaluate it. To disprove this statement we must find an x that is real where there is no available y to make 15.

This is impossible as regardless of the number you choose it is possible.

However if the statement were to change so that the domain is only positive numbers it would become false as once x>16 there is no positive y that would add up to 15.

Proposition and Predicate Logic both have their own uses. Proposition logic is particularly useful in clearing ambiguity of natural language but its strict and narrow nature prevents it from being able to properly express all forms of Natural language. This is where predicate logic is particularly