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An abstract structure is a set of rules, properties and relationships that is defined independently of any physical objects. Abstract structures are studied in philosophy, computer science and mathematics. Indeed, modern mathematics has been defined in a very general sense as the study of abstract structures (by the Bourbaki group: see discussion there, at algebraic structure and also structure).
An abstract structure may be represented (perhaps with some degree of approximation) by one or more physical objects - this is called an implementation or instantiation of the abstract structure. But the abstract structure itself is defined in a way that is not dependent on the properties of any particular implementation.
The rules of chess are an abstract structure, because their definition is independent of any particular chess set or board or chess notation. In this abstract structure, the king, for example, is defined as a piece that can move one square in any direction (except that it may not move onto a square that is under attack by an enemy piece). The king is not defined as a tall piece with a small cross on top, because it could be represented instead by the letter K, a computer icon, or a small figurine of Captain Kirk. Because chess is an abstract structure, it is possible in principle to play a game of chess that is entirely mental (provided that you and your opponent have very good memories !).
Other board games such as draughts and go are also examples of abstract structures. Most sports, on the other hand, are not abstract structures because their rules depend on the physical properties of the pitch, ball or other playing equipment.
An abstract structure has a richer structure than a conceptA concept is an abstract, universal psychical entity that serves to designate a category or class of entities, events or relations. A concept is the element of a proposition rather in the way that a word is the element of a sentence. Concepts are abstract or an ideaAn idea ( Greek: iota;δ&alpha is the result of thinking. Thought, Concept) Idea is the term used in both popular and philosophical terminology with the general sense of "mental picture" or "understanding". Today many people believe that ideas are a. An abstract structure must include precise rules of behaviour which can be used to determine whether a candidate implementation actually matches the abstract structure in question. Thus we may debate how well a particular government fits the concept of democracyA democracy is a form of government under which the power to alter the laws and structures of government lies with the voting citizenry (referred to as "the people", because in modern times it usually consists of all people over 18 years of age), and all, but there is no room for debate over whether a given sequence of moves is or is not a valid game of chess.
A sort algorithm is an abstract structure, but a recipeThis article discusses culinary recipes . For a discussion of the semiconductor IC recipes used by the semiconductor fabs, see, for example, integrated circuit. A recipe is a set of instructions (an algorithm) that show how to prepare or make something, e is not, because it depends on the properties and quantities of its ingredients.
A simple melodyIn music, a melody is a series of linear events or a succession, not a simultaneity as in a chord. However, this succession must contain change of some kind and be perceived as a single entity (possibly gestalt) to be called a melody. Most specifically th is an abstract structure, but an orchestrationFor the use of the term "orchestration" in computer science, see orchestration (computers Orchestration or arrangement is the study and practice of arranging music for an orchestra or musical ensemble. In practical terms it consists of deciding which inst is not, because it depends on the properties of particular instruments.
Euclidean geometryEuclidean geometry In mathematics, Euclidean geometry is the familiar kind of geometry on the plane or in three dimensions. Mathematicians sometimes use the term to encompass higher dimensional geometries with similar properties. Euclidean geometry someti is an abstract structure, but the theory of continental drift is not, because it depends on the geology of the Earth.A formal language is an abstract structure, but a natural language is not, because its rules of grammar and syntax are open to debate and interpretation.
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