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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.
In mathematical logic, a Lindström quantifier is a generalized polyadic quantifier. Lindström quantifiers generalize first-order quantifiers, such as the existential quantifier, the universal quantifier, and the counting quantifiers. They were introduced by Per Lindström in 1966.
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.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃ x " or " ∃( x ...
Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified statement " ∃ x {\displaystyle \exists x} such that … {\displaystyle \ldots } " can be viewed as a question "When is there an x {\displaystyle x} such that … {\displaystyle \ldots ...
existential generalization A rule of inference allowing the conclusion that something exists with a certain property, based on the existence of a particular example. existential import The implication that something exists by the assertion of a particular kind of statement, especially relevant in traditional syllogistic logic. existential ...
A generalization to infinite domains and infinite signs is easy. A generalization to infinite predicates needs no explanation. A convenient fact is that this logic can also accommodate the domain of the null set, as quantificational claims will not need to assume an element in the domain.
The decision problem for the existential theory of the reals is the algorithmic problem of testing whether a given sentence belongs to this theory; equivalently, for strings that pass the basic syntactical checks (they use the correct symbols with the correct syntax, and have no unquantified variables) it is the problem of testing whether the ...