Search results
Results from the WOW.Com Content Network
In predicate logic, generalization (also universal generalization, universal introduction, [1] [2] [3] GEN, UG) is a valid inference rule. It states that if ...
In the following rules, (/) is exactly like except for having the term wherever has the free variable . Universal Generalization (or Universal Introduction) (/) _Restriction 1: is a variable which does not occur in .
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.
In symbolic logic, the universal quantifier symbol (a turned "A" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell.
Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for all members of the domain. [2] [3] Some sources use the term existentialization to refer to existential quantification. [4] Quantification in general is covered in the article on quantification (logic).
In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula.For instance, the universal quantifier in the first order formula () expresses that everything in the domain satisfies the property denoted by .
These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...
In predicate logic, existential generalization [1] [2] (also known as existential introduction, ∃I) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition.