|Summary||Propositional logic is the simpler of the two modern classical logics. It ignores entirely the structure within propositions. In classical propositional logic, molecular or compound propositions are built up from atomic propositions by means of the connectives, whose meaning is given by their truth tables. The principle by which the meaning or truth conditions of compound propositions can be recovered by this "building up" process is known as compositionality.
This leaf node is a sub-category of classical logic. As such, non-standard propositional logics are not normally classified in this category—unless a comparison between classical logic and another logic is being drawn or one is reduced to the other—although restrictions of propositional logic in which nothing not a theorem in ordinary propositional logic is a theorem in the restriction do fit here. Also appropriate here are modest extensions of propositional logic, provided that Boole's three laws of thought are not violated, viz. a proposition is either true or false, not neither, and not both.
Meta-theoretical results for propositional logic are also generally classified as "proof theory," "model theory," "mathematical logic," etc.
|Key works||See below.|
|Introductions||Because of the age of propositional logic there are literally hundreds of introductions to logic which cover this subject reasonably well. Instructors will have their own favorites.
In selecting a book for classroom use, I recommend checking one thing: how much meta-theory is included, so that the book is neither below nor above the level students can handle.
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David Bourget (London)
David Chalmers (ANU, NYU)
Rafael De Clercq
Catarina Dutilh Novaes
John Simpson Wilkins
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