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Reading
Reading

... that AE is κ-satisfiable. AE is unsatisfiable otherwise. SAT = the set of satisfiable abstraction principles. DEFINITION 3.2: An abstraction principle AE is Field conservative iff, for any theory T and formula Φ in L\@E, if T~(∃Y)(x = @(Y)) ∪ {AE} ⇒ Φ~(∃Y)(x = @(Y)) then T ⇒ Φ. AE is Field-nonconser ...
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Abstraction (computer science)

In computer science, abstraction is a technique for managing complexity of computer systems. It works by establishing a level of complexity on which a person interacts with the system, suppressing the more complex details below the current level. The programmer works with an idealized interface (usually well defined) and can add additional levels of functionality that would otherwise be too complex to handle. For example, a programmer writing code that involves numerical operations may not be interested in the way numbers are represented in the underlying hardware (e.g. whether they're 16 bit or 32 bit integers), and where those details have been suppressed it can be said that they were abstracted away, leaving simply numbers with which the programmer can work.In addition, a task of sending an email message across continents would be extremely complex if you start with a piece of optic cable and basic hardware components. By using layers of complexity that have been created to abstract away the physical cables, network layout and presenting the programmer with a virtual data channel, this task is manageable.Abstraction can apply to control or to data: Control abstraction is the abstraction of actions while data abstraction is that of data structures. Control abstraction involves the use of subprograms and related concepts control flows Data abstraction allows handling data bits in meaningful ways. For example, it is the basic motivation behind datatype.One can view the notion of an object as a way to combine abstractions of data and code.The same abstract definition can be used as a common interface for a family of objects with different implementations and behaviors but which share the same meaning. The inheritance mechanism in object-oriented programming can be used to define an abstract class as the common interface.The recommendation that programmers use abstractions whenever suitable in order to avoid duplication (usually of code) is known as the abstraction principle. The requirement that a programming language provide suitable abstractions is also called the abstraction principle.
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