In logic and philosophy, a propositional statement is a sentence or expression that is either true or false. Generally speaking, a statement is propositional because it makes a proposition about the world; that is, it asserts a truth. This doesn’t mean the statement is true but only that it contains an assertion of some kind. Even saying something as simple as “the sky is blue” is a propositional statement, because it's assuming a logical connection between the sky and the color blue.
Understanding Truth Value
According to the computer science department at the University of Texas, Austin, the truth value of a propositional statement can be either true or false depending on the logical validity of the statement. For example, the statement “all dogs are cats” contains a general assertion about dogs that is logically inconsistent: Dogs cannot be both dogs and cats at the same time. The truth value of this statement, then, would be false. A propositional statement that is always true is called a tautology, while a propositional statement that is always false is called a contradiction. For instance, the statement “I will eat my dinner or I will not” is a tautology, because it allows for either instance and therefore is always true.