Sentential Logic: 10 Tutorials

Logical System

Indicative sentences in a natural language, English, for instance, are either true or false. For example, 'There are 35 State Governors in the U.S.A.' is an indicative sentence (which happens to be false). Such sentences express statements or propositions. Not all pieces of language express propositions. For example, the question 'What day is it today?' is not either true or false (although reasonable answers to it will be either true or false); again, the greeting 'Have a nice day!' is not either true or false.

Statements or propositions or sentences can be atomic or compound. 'There are 35 State Governors in the U.S.A.' expresses an atomic proposition; whereas 'There are 35 State Governors in the U.S.A. and there is one President of the U.S.A. ' expresses a compound proposition composed of two atomic propositions (one false one and one true one).

Propositional logic considers reasoning involving atomic and compound propositions. We will see later, when considering predicate logic, that propositional logic is a relatively coarse instrument. It ignores details which can be important. However, ignoring detail allows the resultant theory to be simple, elegant, and easy to understand. And it is a good representation for many cases.

It is also a good place to start when learning logic.