Search results
Results from the WOW.Com Content Network
Given a structure or interpretation, a sentence will have a fixed truth value. A theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. The study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability ...
Left to right: tree structure of the term (n⋅(n+1))/2 and n⋅((n+1)/2) Given a set V of variable symbols, a set C of constant symbols and sets F n of n-ary function symbols, also called operator symbols, for each natural number n ≥ 1, the set of (unsorted first-order) terms T is recursively defined to be the smallest set with the following properties: [1]
For example, assuming a function declaration :, and a constant declaration :, the term is perfectly valid and has the sort . In order to supply the information that the mother of a dog is a dog in turn, another declaration mother : dog dog {\displaystyle {\text{mother}}:{\text{dog}}\longrightarrow {\text{dog}}} may be issued; this is called ...
In discrete mathematics, dominance order (synonyms: dominance ordering, majorization order, natural ordering) is a partial order on the set of partitions of a positive integer n that plays an important role in algebraic combinatorics and representation theory, especially in the context of symmetric functions and representation theory of the ...
The domain of a structure is an arbitrary set; it is also called the underlying set of the structure, its carrier (especially in universal algebra), its universe (especially in model theory, cf. universe), or its domain of discourse. In classical first-order logic, the definition of a structure prohibits the empty domain. [citation needed] [5]
In mathematics, a structure on a set (or on some sets) refers to providing it (or them) with certain additional features (e.g. an operation, relation, metric, or topology). Τhe additional features are attached or related to the set (or to the sets), so as to provide it (or them) with some additional meaning or significance.
Concerns that mathematics had not been built on a proper foundation led to the development of axiomatic systems for fundamental areas of mathematics such as arithmetic, analysis, and geometry. In logic, the term arithmetic refers to the theory of the natural numbers.
A fundamental structure in mathematics and logic that consists of two elements arranged in a specific order, typically represented as (a, b). ostensive definition A definition that explains the meaning of a term or symbol by pointing to examples and counterexamples of the concept it represents.