Boolean Propositional Logic

See also: An introduction to Propositional Logics,
Boolean Operators,
semi-formal and formal descriptions of a propositional logic.
informal, semi-formal and formal descriptions of a first-order predicate logic.

Sentential Connectives in Natural Languages

It may be observed in the workings of natural languages that there are certain constructions which have the following features.
They are sentential operators
They operate on one or more complete sentences to give a new sentence.
They are truth functional operators
The truth of the resulting sentence can be determined knowing only the truth values of the sentences from which it was constructed.
An example is the construction known as conjunction. This consists in conjoining two sentences with the connective and.

For example, the conjunction of the two sentences::

  • Grass is green
  • Pigs don't fly.
Is the sentence:
  • Grass is green and pigs don't fly.

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:
p or q
known as the disjunction of "p" and "q".
not p
known as the negation of "p".
For the complete range see: Boolean Operators.

Propositional Logics

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.

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