Rule of replacement

Transformation rules
Propositional calculus
Rules of inference
Modus ponens / Modus tollens Biconditional introduction / elimination Conjunction introduction / elimination Disjunction introduction / elimination Disjunctive / Hypothetical syllogism Constructive / Destructive dilemma Absorption Modus ponendo tollens
Rules of replacement
Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology Negation introduction
Predicate logic
Universal generalization / instantiation Existential generalization / instantiation

In logic, a rule of replacement^[1]^[2]^[3] is a transformation rule that may be applied to only a particular segment of an expression. A logical system may be constructed so that it uses either axioms, rules of inference, or both as transformation rules for logical expressions in the system. Whereas a rule of inference is always applied to a whole logical expression, a rule of replacement may be applied to only a particular segment. Within the context of a logical proof, logically equivalent expressions may replace each other. Rules of replacement are used in propositional logic to manipulate propositions.

References

↑ Copi, Irving M.; Cohen, Carl (2005). Introduction to Logic. Prentice Hall.
↑ Hurley, Patrick (1991). A Concise Introduction to Logic 4th edition. Wadsworth Publishing.
↑ Moore and Parker
↑ not admitted in intuitionistic logic

This article is issued from Wikipedia - version of the 11/8/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.