Term (logic)

termstermfirst-order termsconstantexpressionexpressionsfinite termsfirst-order termliterally similarsubterm
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.wikipedia
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Variable (mathematics)

variablesvariableunknown
A first-order term is recursively constructed from constant symbols, variables and function symbols.
In mathematical logic, a variable is either a symbol representing an unspecified term of the theory, or a basic object of the theory, which is manipulated without referring to its possible intuitive interpretation.

Uninterpreted function

empty theoryfree theoryfunction letter
A first-order term is recursively constructed from constant symbols, variables and function symbols.
Function symbols are used, together with constants and variables, to form terms.

First-order logic

predicate logicfirst-orderpredicate calculus
A first-order term is recursively constructed from constant symbols, variables and function symbols.
also term structure vs. representation.

Well-formed formula

formulamathematical formulaformulas
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

Coefficient

coefficientsleading coefficientfactor
In the context of polynomials, sometimes term is used for a monomial with a coefficient: to 'collect like terms' in a polynomial is the operation of making it a linear combination of distinct monomials.
In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression.

Polynomial

polynomial functionpolynomialsmultivariate polynomial
In the context of polynomials, sometimes term is used for a monomial with a coefficient: to 'collect like terms' in a polynomial is the operation of making it a linear combination of distinct monomials.
That is, a polynomial can either be zero or can be written as the sum of a finite number of non-zero terms.

Series (mathematics)

infinite seriesseriespartial sum
A series is often represented as the sum of a sequence of terms.
In modern terminology, any (ordered) infinite sequence of terms (that is, numbers, functions, or anything that can be added) defines a series, which is the operation of adding the a_i one after the other.

Like terms

Combining like termsgrouping
In the context of polynomials, sometimes term is used for a monomial with a coefficient: to 'collect like terms' in a polynomial is the operation of making it a linear combination of distinct monomials.
In algebra, like terms are terms that have the same variables and powers.

Rewriting

term rewritingterm rewriting systemrewrite system
Besides in logic, terms play important roles in universal algebra, and rewriting systems.
To this end, each such number has to be encoded as a term.

Ground expression

ground termgroundground atom
A term that doesn't contain any variables is called a ground term; a term that doesn't contain multiple occurrences of a variable is called a linear term.
In mathematical logic, a ground term of a formal system is a term that does not contain any free variables.

Unification (computer science)

unificationmost general unifierE-unification
The syntactic first-order unification problem { y = cons(2,y) } has no solution over the set of finite terms; however, it has the single solution { y ↦ cons(2,cons(2,cons(2,...))) } over the set of infinite trees.

Substitution (logic)

substitutionsubstitution instancesubstituting
In contrast, a term t is called a renaming, or a variant, of a term u if the latter resulted from consistently renaming all variables of the former, i.e. if u = tσ for some renaming substitution σ.
A substitution is called a ground substitution if it maps all variables of its domain to ground, i.e. variable-free, terms.

Encompassment ordering

encompassment preorder
the containment, or encompassment, preorder on the set of terms, is defined by :s ≤ t if a subterm of t is a substitution instance of s.

Noun phrase

noun phrasesNPnominal phrase
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

Sentence (linguistics)

sentencesentencesdeclarative sentence
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

Mathematical logic

formal logicsymbolic logiclogic
In analogy to natural language, where a noun phrase refers to an object and a whole sentence refers to a fact, in mathematical logic, a term denotes a mathematical object and a formula denotes a mathematical fact.

Recursive definition

inductive definitionrecursively definedinductively defined
A first-order term is recursively constructed from constant symbols, variables and function symbols.

Predicate (mathematical logic)

predicatepredicatespredication
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.

Atomic formula

atomatomicatomic expressions
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.

Truth

trueTruth theorytheory of truth
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.

False (logic)

falseFalsityfalsehood
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.

Principle of bivalence

bivalentBivalencetwo-valued logic
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.

Interpretation (logic)

interpretationintended interpretationinterpretations
An expression formed by applying a predicate symbol to an appropriate number of terms is called an atomic formula, which evaluates to true or false in bivalent logics, given an interpretation.