See also:  An introduction to Propositional Logics,
Boolean Operators, semiformal and formal descriptions of a propositional logic. informal, semiformal and formal descriptions of a firstorder predicate logic. 
It may be observed in the workings of natural languages that there are certain constructions which have the following features.

For example, the conjunction of the two sentences::
The conjunction of two sentence will be true if, and only if, each of the two sentences from which it was formed is true. 
Other propositional connectives include:

In natural languages, words whose primary role is truth functional often have other roles as well. This is one of many ways in which natural languages fail to be ideal for some logical or technical purposes. To overcome these difficulties formal languages may be helpful. Where a logic is concerned only with sentential connectives it is usually called a propositional logic.  The most well known, and probably the simplest of these logics is known as classical or boolean propositional logic, in which it is assumed that all propositions have a definite truth value; a proposition is either true or it is false. 