Predicate (logic)In logic, a predicate is a non-logical symbol that represents a property or a relation, though, formally, does not need to represent anything at all. For instance, in the first-order formulaP(a){\displaystyle P(a)}, the symbol P{\displaystyle P} is a predicate that applies to the individual constanta{\displaystyle a} which evaluates to either true or false.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.
Propositional logicPropositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called first-order propositional logic to contrast it with System F, but it is distinct from first-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them.
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.
Finitary relationIn mathematics, a finitary relation over a sequence of sets X1, ..., Xn is a subset of the Cartesian productX1 × ... × Xn; that is, it is a set of n-tuples(x1, ..., xn), each being a sequence of elements xi in the corresponding Xi. Typically, the relation describes a possible connection between the elements of an n-tuple.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathematics – is mostly concerned with those that are relevant to mathematics as a whole.
ArithmeticBranch of elementary mathematicsThe main arithmetic operations are addition, subtraction, multiplication, and division.Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. Arithmetic systems can be distinguished based on the type of numbers they operate on.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
PhilosophyStudy of general and fundamental questionsThe statue The Thinker by Auguste Rodin is a symbol of philosophical thought.
LinguisticsLinguistics is the scientific study of language. Specific areas of linguistic description and analysis are syntax (rules governing the structure of sentences), semantics (meaning), morphology (structure of words), phonetics (speech sounds and equivalent manual gestures in sign languages), phonology (the abstract sound system of a particular language, and analogous systems of sign languages), and pragmatics (how the context of use contributes to meaning).
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.Formal systemA formal system (or deductive system) is an abstract structure and formalization of an axiomatic system used for deducing, using rules of inference, theorems from axioms. In 1921, David Hilbert proposed to use formal systems as the foundation of knowledge in mathematics. However, in 1931 Kurt Gödel proved that any consistent formal system sufficiently powerful to express basic arithmetic cannot prove its own completeness.*As an Amazon Associate I earn from qualifying purchases.