Universal instantiationIn predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a validrule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory.
Rule of inferenceRules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as the logical structure of valid arguments. If an argument with true premises follows a rule of inference then the conclusion cannot be false.
Existential quantificationIn predicate logic, an existential quantification is a type of quantifier which asserts the existence of an object with a given property. It is usually denoted by the logical operatorsymbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"), read as "there exists", "there is at least one", or "for some".
First-order logicType of logical systemIn mathematics, philosophy, linguistics, and computer science, first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
ReferenceIn logic, a reference is a relationship between objects in which one object designates, or acts as a means by which to connect to or link to, another object. The first object in this relation is said to refer to the second object. It is called a name for the second object. The next object, the one to which the first object refers, is called the referent of the first object. A name is usually a phrase or expression, or some other symbolic representation.
Existential instantiationIn predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form (∃x)ϕ(x){\displaystyle (\exists x)\phi (x)}, one may infer ϕ(c){\displaystyle \phi (c)} for a new constant symbol c. The rule has the restrictions that the constant c introduced by the rule must be a new term that has not occurred earlier in the proof, and it also must not occur in the conclusion of the proof.Validity (logic)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 and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion.
Willard Van Orman QuineWillard Van Orman Quine ( ; June 25, 1908 – December 25, 2000) was an American logician and philosopher in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". He held the Edgar Pierce Chair of Philosophy at Harvard University from 1956 to 1978. Quine was a teacher of logic and set theory.
Fitch notationFitch notation, also known as Fitch diagrams (named after Frederic Fitch), is a method of presenting natural deduction proofs in propositional calculus and first-order logics using a structured, line-by-line format that explicitly shows assumptions, inferences, and their scope. It was invented by Frederic Brenton Fitch in the 1930s and later popularized through his textbook Symbolic Logic (1952).Quantifier (logic)In mathematical logic, quantifiers are formal counterparts of natural-language adjectives like all, some, most, few, etc. which indicate the number of objects satisfying a given property. More precisely, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula.
Universal quantificationIn mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain.*As an Amazon Associate I earn from qualifying purchases.