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.
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.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.
Domain of discourseIn the formal sciences, the domain of discourse or universe of discourse (borrowing from the mathematical concept of universe) is the set of entities over which certain variables of interest in some formal treatment may range. It is also defined as the collection of objects being discussed in a specific discourse. In model-theoretical semantics, a universe of discourse is the set of entities that a model is based on.
Logical connectiveIn logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is an operator that combines or modifies one or more logical variables or formulas, similarly to how arithmetic connectives like + {\displaystyle +} and − {\displaystyle -} combine or negate arithmetic expressions.
LogicLogic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory.
Property (philosophy)In philosophy and logic (especially metaphysics), a property is a characteristic of an object; for example, a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiated, and often in more than one object.
ExistenceState of being realThe existential quantifier ∃ is often used in logic to express existence.Existence is the state of having being or reality in contrast to nonexistence and nonbeing. Existence is often contrasted with essence: the essence of an entity is its essential features or qualities, which can be understood even if one does not know whether the entity exists. Ontology is the philosophical discipline studying the nature and types of existence.
UnicodeCharacter encoding standardUnicode (also known as The Unicode Standard and TUS) is a character encoding standard maintained by the Unicode Consortium designed to support the use of text in all of the world's writing systems that can be digitized. Version 18.0 defines 172,808 characters and 175 scripts used in various ordinary, literary, academic and technical contexts.
LatexLatex (pl. latices) is an emulsion (stable dispersion) of polymer microparticles in water. Latices are found in nature, but synthetic latices are common as well. In nature, latex is found as a milky fluid, which is present in 10% of all flowering plants (angiosperms) and in some mushrooms (especially species of Lactarius). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums.
Symbol (formal)A formal symbol is a fundamental concept in logic, tokens of which may be marks or a configuration of marks which form a particular pattern.*As an Amazon Associate I earn from qualifying purchases.