Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c ("backtracks") as soon as it determines that c cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight queens on a standard chessboard so that no queen attacks any other.
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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.
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Model theory
In mathematics, model theory is the study of (classes of) mathematical structures using tools from mathematical logic. It has close ties to abstract algebra, particularly universal algebra. Objects of study in model theory are models for formal languages which are structures that give meaning to the sentences of these formal languages.
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Operational semantics
In computer science, operational semantics is a way to give meaning to computer programs in a mathematically rigorous way. Operational semantics are classified into two categories: structural operational semantics (or small-step semantics) formally describe how the individual steps of a computation take place in a computer-based system. By opposition natural semantics (or big-step semantics) describe how the overall results of the executions are obtained.
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Infinity
Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics. Having a recognizable history in these disciplines reaching back into the time of ancient Greek civilization, the term in the English language derives from Latin infinitas, which is translated as "unboundedness". In mathematics, "infinity" is often treated as if it were a number but it is not the same sort of number as the real numbers.
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