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In the sentence above, the possessive pronoun her is a free variable. It may refer to the previously mentioned Lisa or to any other female. In other words, her book could be referring to Lisa's book (an instance of coreference ) or to a book that belongs to a different female (e.g. Jane's book).
In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.
If a formula does not contain free variables, and so is a sentence, then the initial variable assignment does not affect its truth value. In other words, a sentence is true according to M and μ {\displaystyle \mu } if and only if it is true according to M and every other variable assignment μ ′ {\displaystyle \mu '} .
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.
the occurrence of both x and y in C(y, x) is free, while the occurrence of x and y in B(y, x) is bound (i.e. non-free). Syntax tree of the formula ((,)) (,), illustrating scope and variable capture. Bound and free variable occurrences are colored in red and green, respectively.
For a fixed signature σ, the set of all formulas of dependence logic and their respective sets of free variables () are defined as follows: Any atomic formula ϕ {\displaystyle \phi } is a formula, and Free ( ϕ ) {\displaystyle {\mbox{Free}}(\phi )} is the set of all variables occurring in it;
In mathematical logic, a ground term of a formal system is a term that does not contain any variables. Similarly, a ground formula is a formula that does not contain any variables. In first-order logic with identity with constant symbols a {\displaystyle a} and b {\displaystyle b} , the sentence Q ( a ) ∨ P ( b ) {\displaystyle Q(a)\lor P(b ...