A substitution is a syntactic transformation on formal expressions. To apply a substitution to an expression means to consistently replace its variable...

abstract machines, predicate logic, and symbolic computation. A simple example of a lambda calculus with explicit substitution is "λx", which adds one new...

Z),} therefore X = Z . {\displaystyle X=Z.} Substitution: See Substitution (logic) § Proof of substitution in ZFC. Function application: Given a = b {\displaystyle...

propositional logic, or valid sentences of predicate logic that can be reduced to propositional tautologies by substitution. Propositional logic begins with...

{\displaystyle B'} yields B {\displaystyle B} after substitution, then attempts to prove A {\displaystyle A} by substitution. chaining forward: given expression A →...

Rhetoric -- Subjective logic -- Substitution (logic) -- Substructural logic -- Sufficient condition -- Sum of Logic -- Sunk costs -- Supertask -- Supervaluationism...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics,...

In logic and philosophy, S5 is one of five systems of modal logic proposed by Clarence Irving Lewis and Cooper Harold Langford in their 1932 book Symbolic...

up substitution in Wiktionary, the free dictionary. Substitution may refer to: Substitution (poetry), a variation in poetic scansion Substitution (theatre)...

instead of quantifying over substitution instances. Some authors also admit propositional variables in first-order logic, which must then also be interpreted...

Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell...

the substituted x was supposed to be free but ended up being bound. The correct substitution in this case is λz.x, up to α-equivalence. Substitution is...

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...

subtype of an immutable point, whereas Liskov substitution principle forbids this. Liskov substitution principle explains a property, "If for each object...

V} . Then a substitution σ {\displaystyle \sigma } is subsumed by another substitution τ {\displaystyle \tau } if there is a substitution θ {\displaystyle...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes...

(term). Unifying the two produces the substitution X ↦ a Discarding the unified predicates, and applying this substitution to the remaining predicates (just...

e. if u = tσ for some renaming substitution σ. In that case, u is a renaming of t, too, since a renaming substitution σ has an inverse σ−1, and t = uσ−1...

with a rule of substitution, as this article does. The use of "Hilbert-style" and similar terms to describe axiomatic proof systems in logic is due to the...

redirect targets Substitution instance – Concept in logicPages displaying short descriptions of redirect targets Theory (mathematical logic) – Set of sentences...

In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true...

Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as...

denotes the substitution of each x {\displaystyle x} in φ {\displaystyle \varphi } by a t {\displaystyle t} ; see also First-order logic.[citation needed]...

In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. Second-order logic...

contains logic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of logic symbols. In logic, a set...

terms belong to logic, and not those given in concrete terms. The concrete terms man, mortal, and so forth are analogous to the substitution values of the...

showing what substitution of equals for equals is being used. This premise is theorem ( 3.9 ) {\textstyle (3.9)} with the substitution p := q {\textstyle...

In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to...

In logic and deductive reasoning, an argument is sound if it is both valid in form and has no false premises. Soundness has a related meaning in mathematical...