Concepts inConjunctive queries determinacy and rewriting
Determinacy
In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.
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Conjunctive query
In database theory, a conjunctive query is a restricted form of first-order queries. A large part of queries issued on relational databases can be written as conjunctive queries, and large parts of other first-order queries can be written as conjunctive queries. Conjunctive queries also have a number of desirable theoretical properties that larger classes of queries (e.g. , the relational algebra queries) do not share.
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Rewriting
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. What is considered are rewriting systems (also known as rewrite systems or reduction systems). In their most basic form, they consist of a set of objects, plus relations on how to transform those objects. Rewriting can be non-deterministic.
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Total order
In set theory, a total order, linear order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ¿) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain. If X is totally ordered under ¿, then the following statements hold for all a, b and c in X: If a ¿ b and b ¿ a then a = b; If a ¿ b and b ¿ c then a ¿ c; a ¿ b or b ¿ a .
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Bounded set
"Bounded" and "boundary" are distinct concepts; for the latter see boundary (topology). A circle in isolation is a boundaryless bounded set, while the half plane is unbounded yet has a boundary. In mathematical analysis and related areas of mathematics, a set is called bounded, if it is, in a certain sense, of finite size. Conversely, a set which is not bounded is called unbounded. The word bounded makes no sense in a general topological space, without a metric.
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Decidability (logic)
In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a Boolean true or false value (instead of looping indefinitely). Logical systems such as propositional logic are decidable if membership in their set of logically valid formulas (or theorems) can be effectively determined.
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If and only if
¿ ¿ ¿ Logical symbolsrepresenting iff In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements. In that it is biconditional, the connective can be likened to the standard material conditional ("only if," equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other, i.e.
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