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  2. List of rules of inference - Wikipedia

    en.wikipedia.org/wiki/List_of_rules_of_inference

    Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.

  3. Conjunction elimination - Wikipedia

    en.wikipedia.org/wiki/Conjunction_elimination

    In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, [1] or simplification) [2] [3] [4] is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.

  4. Category:Rules of inference - Wikipedia

    en.wikipedia.org/wiki/Category:Rules_of_inference

    Download as PDF; Printable version; ... Pages in category "Rules of inference" ... Simplification of disjunctive antecedents;

  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. Armstrong's axioms - Wikipedia

    en.wikipedia.org/wiki/Armstrong's_axioms

    The set of inference rules is said to be complete if the following holds: F + ⊆ F A ∗ {\displaystyle F^{+}\subseteq F_{A}^{*}} more simply put, we are able to derive by A {\displaystyle A} all the functional dependencies that are logically implied by F {\displaystyle F} .

  7. Rule of inference - Wikipedia

    en.wikipedia.org/wiki/Rule_of_inference

    But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. rules such that there is an effective procedure for determining whether any given formula is the ...

  8. Modus ponens - Wikipedia

    en.wikipedia.org/wiki/Modus_ponens

    Enderton, for example, observes that "modus ponens can produce shorter formulas from longer ones", [9] and Russell observes that "the process of the inference cannot be reduced to symbols. Its sole record is the occurrence of ⊦q [the consequent] ... an inference is the dropping of a true premise; it is the dissolution of an implication". [10]

  9. Universal instantiation - Wikipedia

    en.wikipedia.org/wiki/Universal_instantiation

    In predicate logic, universal instantiation [1] [2] [3] (UI; also called universal specification or universal elimination, [citation needed] and sometimes confused with dictum de omni) [citation needed] is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class.