Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement. The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both. However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another.
The Language of Propositional Logic
Tautologies, Logical Equivalence and Validity
Deduction: Rules of Inference and Replacement
Axiomatic Systems and the Propositional Calculus
Meta-Theoretic Results for the Propositional Calculus
Other Forms of Propositional Logic
References and Further Reading
Syntax and Formation Rules of PL
Truth Functions and Truth Tables
Definability of the Operators and the Languages PL' and PL''
Conditional and Indirect Proofs
