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...

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

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

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

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

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...

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...

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

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

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

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...

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

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

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

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

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...

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

In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect...

The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India...

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...

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 semantics, the term statement is variously understood to mean either: a meaningful declarative sentence that is true or false,[citation needed]...

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

of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the logical structure of valid arguments. If an argument...

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

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...

first-order logic, without requiring any preliminary reduction of formulae into normal forms. These methods have also been extended to modal logic. Abductive...