is a substitution instance of: P & Q and (A ↔ A) ↔ (A ↔ A) is a substitution instance of: (A ↔ A) In some deduction systems for propositional logic, a new...

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

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

in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda...

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

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...

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

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

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...

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

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

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

Transitivity: for every a, b, and c, if a = b and b = c, then a = c. Substitution: Informally, this just means that if a = b, then a can replace b in any...

logic. It is also called (first-order) propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic....

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

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

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...

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...

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...

The Liskov substitution principle (LSP) is a particular definition of a subtyping relation, called strong behavioral subtyping, that was initially introduced...

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...

invalid deductive reasoning is a form of deductive reasoning. Deductive logic studies under what conditions an argument is valid. According to the semantic...

Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often...

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

mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some...

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

operation on proofs is the substitution of one proof for an assumption used in another proof. This is commonly known as a substitution theorem, and can be proved...

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