Symbolic Logic: Difference between revisions

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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:

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)

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

Modal logic -- also deontic logic, temporal logic:

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-The three main systems studied in symbolic logic are propositional calculus, predicate calculus and modal logics.
+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:
-Propositional calculus
+* classical -- the normal traditional system
-Predicate calculus -- First-order, higher-order
+* many-valued -- permits sentences to be more than just true or false, but also have intermediate truth values
-Modal Logics -- deal with possibility, various systems: B, T, S4, S5; also deontic logic, temporal logic
+* 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
+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