Symbolic Logic

Symbolic logic is divided into propositional calculus, predicate calculus and modal logics.

Propositional caluclus deals with the logic of individual sentences. There are a number of different systems of propositional calculus:

• classical -- the normal traditional system

• many-valued -- permits sentences to be more than just true or false, but also have intermediate truth values

• paraconsistent -- permits inconsistent sentences. Does not have ex contradictione quodlibet (from a contradiction anything follows)

• infinitary -- permits sentences to be infinitely long

• intuitionistic --

• relevant -- has only relevant implication

• substructural -- systems of logic weaker than classical logic

Predicate calculus deals with the logic of predication and quantification. Systems include:

• lower-order --

• higher-order -- permits quantification and predication of predicates

Modal logic -- also deontic logic, temporal logic:

• various systems: B, T, S4, S5