# 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

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.

### Expression (mathematics)

expressionmathematical expressionexpressions

### Equation

equationsmathematical equationunknown

### 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.