12-06-2012, 12:30 PM
Seminar on Relational Calculus
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Comes in two flavours: Tuple relational calculus (TRC) and Domain relational calculus (DRC).
Calculus has variables, constants, comparison ops, logical connectives and quantifiers.
TRC: Variables range over (i.e., get bound to) tuples.
DRC: Variables range over domain elements (= field values).
Both TRC and DRC are simple subsets of first-order logic.
Expressions in the calculus are called formulas. An answer tuple is essentially an assignment of constants to variables that make the formula evaluate to true.
First-Order Predicate Logic
Predicate: is a feature of language which you can use to make a statement about something, e.g., to attribute a property to that thing.
Peter is tall. We predicated tallness of peter or attributed tallness to peter.
A predicate may be thought of as a kind of function which applies to individuals and yields a proposition.
Proposition logic is concerned only with sentential connectives such as and, or, not.
Predicate Logic, where a logic is concerned not only with the sentential connectives but also with the internal structure of atomic propositions.
Summary
Relational calculus is non-operational, and users define queries in terms of what they want, not in terms of how to compute it. (Declarativeness.)
Algebra and safe calculus have same expressive power, leading to the notion of relational completeness.
[attachment=928]
Comes in two flavours: Tuple relational calculus (TRC) and Domain relational calculus (DRC).
Calculus has variables, constants, comparison ops, logical connectives and quantifiers.
TRC: Variables range over (i.e., get bound to) tuples.
DRC: Variables range over domain elements (= field values).
Both TRC and DRC are simple subsets of first-order logic.
Expressions in the calculus are called formulas. An answer tuple is essentially an assignment of constants to variables that make the formula evaluate to true.
First-Order Predicate Logic
Predicate: is a feature of language which you can use to make a statement about something, e.g., to attribute a property to that thing.
Peter is tall. We predicated tallness of peter or attributed tallness to peter.
A predicate may be thought of as a kind of function which applies to individuals and yields a proposition.
Proposition logic is concerned only with sentential connectives such as and, or, not.
Predicate Logic, where a logic is concerned not only with the sentential connectives but also with the internal structure of atomic propositions.
Summary
Relational calculus is non-operational, and users define queries in terms of what they want, not in terms of how to compute it. (Declarativeness.)
Algebra and safe calculus have same expressive power, leading to the notion of relational completeness.