Appendix:Glossary of logic in Wiktionary, the free dictionary. This is a glossary of logic. Logic is the study of the principles of valid reasoning and This is a glossary of logic. Logic is the study of the principles of valid reasoning and argumentation. first-order logic A formal logical system involving quantifiers "for all" and "there exists," which can quantify over individuals but not over predicates or functions. intuitionistic logic A system of logic that reflects the principles of intuitionism, rejecting the law of excluded… paraconsistent logic A non-classical logic that allows for contradictions to exist without deriving absurdity, useful in modeling inconsistent but non-trivial systems. pure first-order logic The system of first-order logic that contains no function symbols or identity, only predicate symbols.

logic, equality is a primitive predicate (a statement that may have free variables) with the reflexive property (called the law of identity), and the In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. Equality between A and B is denoted with an equals sign as A = B, and read "A equals B". A written expression of equality is called an equation or identity depending on the context. Two objects that are not equal are said to be distinct Function application is also sometimes included in the axioms of equality, but isn't necessary as it can be deduced from the other two axioms, and similarly for symmetry and transitivity (see § Derivations of basic properties). In first-order logic, these are axiom schemas (usually, see below), each of which specify an infinite set of axioms. If a theory has a predicate that satisfies the law of identity and substitution property, it is common to say that it "has equality", or is "a theory with equality". The use of "equality" here somewhat of a misnomer in that any system with equality can be modeled by a theory without standard identity, and with indiscernibles. Those two axioms are strong enough, however, to be isomorphic to a model with identity; that is, if a system has a predicate satisfying those axioms without standard equality, there is a model of that system with standard equality. This can be done by defining a new domain whose objects are the equivalence classes of the original "equality". If a model is interpreted to have equality then those properties are enough, since if x {\displaystyle x} has all the same properties as y , {\displaystyle y,} and x {\displaystyle x} has the property of being equal to x , {\displaystyle x,} then y {\displaystyle y} has the property of being equal to x . {\displaystyle x.}