In mathematics, a proof is a demonstration that if some fundamental statements are assumed to be true, then some mathematical statement is necessarily true. Proofs are obtained from deductive reasoning, rather than from inductive or empirical arguments; a proof must demonstrate that a statement is always true (occasionally by listing all possible cases and showing that it holds in each), rather than enumerate many confirmatory cases.
more from Wikipedia
Uninterpreted function
In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and arity. Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra).
more from Wikipedia
Craig interpolation
In mathematical logic, Craig's interpolation theorem is a result about the relationship between different logical theories. Roughly stated, the theorem says that if a formula ¿ implies a formula ¿ then there is a third formula ¿, called an interpolant, such that every nonlogical symbol in ¿ occurs both in ¿ and ¿, ¿ implies ¿, and ¿ implies ¿. The theorem was first proved for first-order logic by William Craig in 1957. Variants of the theorem hold for other logics, such as propositional logic.
more from Wikipedia
First-order logic
First-order logic is a formal system used in mathematics, philosophy, linguistics, and computer science. It is also known as first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less precise term). First-order logic is distinguished from propositional logic by its use of quantified variables.
more from Wikipedia
Model checking
In computer science, model checking refers to the following problem: Given a model of a system, test automatically whether this model meets a given specification. Typically, the systems one has in mind are hardware or software systems, and the specification contains safety requirements such as the absence of deadlocks and similar critical states that can cause the system to crash. Model checking is a technique for automatically verifying correctness properties of finite-state systems.
more from Wikipedia
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of operations that combine numbers. In common usage, it refers to the simpler properties when using the traditional operations of addition, subtraction, multiplication and division with smaller values of numbers.
more from Wikipedia
Exponentiation
Exponentiation is a mathematical operation, written as b, involving two numbers, the base b and the exponent (or index or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors, each of which is equal to b (the product itself can also be called power): just as multiplication by a positive integer corresponds to repeated addition: The exponent is usually shown as a superscript to the right of the base.
more from Wikipedia
Logic
Logic (from the Greek ¿¿¿¿¿¿ logik¿) is the philosophical study of valid reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science. It examines general forms that arguments may take, which forms are valid, and which are fallacies. In philosophy, the study of logic is applied in most major areas: metaphysics, ontology, epistemology, and ethics.
more from Wikipedia