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2. Template:Transformation rules - Wikipedia

   en.wikipedia.org/wiki/Template:Transformation_rules

   Transformation rules; Propositional calculus; Rules of inference; Implication introduction / elimination (modus ponens) Biconditional introduction / elimination; Conjunction introduction / elimination; Disjunction introduction / elimination; Disjunctive / hypothetical syllogism; Constructive / destructive dilemma

3. List of rules of inference - Wikipedia

   en.wikipedia.org/wiki/List_of_rules_of_inference

   A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.

4. Rule of replacement - Wikipedia

   en.wikipedia.org/wiki/Rule_of_replacement

   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 ...

5. De Morgan's laws - Wikipedia

   en.wikipedia.org/wiki/De_Morgan's_laws

   De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.

6. Exportation (logic) - Wikipedia

   en.wikipedia.org/wiki/Exportation_(logic)

   Exportation [1] [2] [3] [4] is a valid rule of replacement in propositional logic.The rule allows conditional statements having conjunctive antecedents to be replaced ...

7. Measure-preserving dynamical system - Wikipedia

   en.wikipedia.org/wiki/Measure-preserving...

   The definition of a measure-preserving dynamical system can be generalized to the case in which T is not a single transformation that is iterated to give the dynamics of the system, but instead is a monoid (or even a group, in which case we have the action of a group upon the given probability space) of transformations T s : X → X ...

8. List of formulas in Riemannian geometry - Wikipedia

   en.wikipedia.org/wiki/List_of_formulas_in...

   The gradient of a function is obtained by raising the index of the differential , whose components are given by: =; =; =, = = The divergence of a vector field with components is

9. Graph rewriting - Wikipedia

   en.wikipedia.org/wiki/Graph_rewriting

   The basic idea is that if the state of a computation can be represented as a graph, further steps in that computation can then be represented as transformation rules on that graph. Such rules consist of an original graph, which is to be matched to a subgraph in the complete state, and a replacing graph, which will replace the matched subgraph.