Search results
Results from the WOW.Com Content Network
The order of quantifiers is critical to meaning, as is illustrated by the following two propositions: For every natural number n, there exists a natural number s such that s = n 2. This is clearly true; it just asserts that every natural number has a square. The meaning of the assertion in which the order of quantifiers is reversed is different:
A quantifier that operates within a specific domain or set, as opposed to an unbounded or universal quantifier that applies to all elements of a particular type. branching quantifier A type of quantifier in formal logic that allows for the expression of dependencies between different quantified variables, representing more complex relationships ...
Logic is the study of proof and deduction as manifested in language (abstracting from any underlying psychological or biological processes). [1] Logic is not a closed, completed science, and presumably, it will never stop developing: the logical analysis can penetrate into varying depths of the language [2] (sentences regarded as atomic, or splitting them to predicates applied to individual ...
An atomic term is an upper case Latin letter, I and S excepted, followed by a numerical superscript called its degree, or by concatenated lower case variables, collectively known as an argument list. The degree of a term conveys the same information as the number of variables following a predicate letter.
Along with numerals, and special-purpose words like some, any, much, more, every, and all, they are quantifiers. Quantifiers are a kind of determiner and occur in many constructions with other determiners, like articles: e.g., two dozen or more than a score. Scientific non-numerical quantities are represented as SI units.
Thus, for example, quantifiers over sets of individuals may range over only a subset of the powerset of the set of individuals. HOL with these semantics is equivalent to many-sorted first-order logic, rather than being stronger than first-order logic. In particular, HOL with Henkin semantics has all the model-theoretic properties of first-order ...
An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
In semantics and mathematical logic, a quantifier is a way that an argument claims that an object with a certain property exists or that no object with a certain property exists. Not to be confused with Category:Quantification (science) .