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  2. Tuple relational calculus - Wikipedia

    en.wikipedia.org/wiki/Tuple_relational_calculus

    Since the calculus is a query language for relational databases we first have to define a relational database. The basic relational building block is the domain (somewhat similar, but not equal to, a data type). A tuple is a finite sequence of attributes, which are ordered pairs of domains and values. A relation is a set of (compatible) tuples ...

  3. Domain relational calculus - Wikipedia

    en.wikipedia.org/wiki/Domain_relational_calculus

    This language uses the same operators as tuple calculus, the logical connectives ∧ (and), ∨ (or) and ¬ (not). The existential quantifier (∃) and the universal quantifier (∀) can be used to bind the variables. Its computational expressiveness is equivalent to that of relational algebra. [2]

  4. Relational calculus - Wikipedia

    en.wikipedia.org/wiki/Relational_calculus

    The relational calculus is similar to the relational algebra, which is also part of the relational model: While the relational calculus is meant as a declarative language that prescribes no execution order on the subexpressions of a relational calculus expression, the relational algebra is meant as an imperative language: the sub-expressions of ...

  5. Quantifier (logic) - Wikipedia

    en.wikipedia.org/wiki/Quantifier_(logic)

    The most commonly used quantifiers are and . These quantifiers are standardly defined as duals ; in classical logic , they are interdefinable using negation . They can also be used to define more complex quantifiers, as in the formula ¬ ∃ x P ( x ) {\displaystyle \neg \exists xP(x)} which expresses that nothing has the property P ...

  6. Conjunctive query - Wikipedia

    en.wikipedia.org/wiki/Conjunctive_Query

    Conjunctive queries without distinguished variables are called boolean conjunctive queries.Conjunctive queries where all variables are distinguished (and no variables are bound) are called equi-join queries, [1] because they are the equivalent, in the relational calculus, of the equi-join queries in the relational algebra (when selecting all columns of the result).

  7. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.

  8. Finitary relation - Wikipedia

    en.wikipedia.org/wiki/Finitary_relation

    Aside from the set-theoretic extension of a relational concept or term, the term "relation" can also be used to refer to the corresponding logical entity, either the logical comprehension, which is the totality of intensions or abstract properties shared by all elements in the relation, or else the symbols denoting these elements and intensions ...

  9. Second-order logic - Wikipedia

    en.wikipedia.org/wiki/Second-order_logic

    In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. [a] Second-order logic is in turn extended by higher-order logic and type theory.