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In first-order logic, it is often used as a rule for the existential quantifier in formal proofs. Example: "Rover loves to wag his tail. Therefore, something loves to wag its tail." Example: "Alice made herself a cup of tea. Therefore, Alice made someone a cup of tea." Example: "Alice made herself a cup of tea.
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, [1] and continued to develop the method until his death in 1914. They include both a separate graphical notation for logical statements and a logical calculus, a formal ...
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
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 ...
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 ...
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 ...
Term logic treated All, Some and No in the 4th century BC, in an account also touching on the alethic modalities. In 1827, George Bentham published his Outline of a New System of Logic: With a Critical Examination of Dr. Whately's Elements of Logic, describing the principle of the quantifier, but the book was not widely circulated. [12]
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.