Concepts inA compositional query algebra for second-order logic and uncertain databases

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. Second-order logic is in turn extended by higher-order logic and type theory. First-order logic uses only variables that range over individuals (elements of the domain of discourse); second-order logic has these variables as well as additional variables that range over sets of individuals.
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Database

A database is an organized collection of data, today typically in digital form. The data are typically organized to model relevant aspects of reality (for example, the availability of rooms in hotels), in a way that supports processes requiring this information (for example, finding a hotel with vacancies). The term database is correctly applied to the data and their supporting data structures, and not to the database management system (DBMS).
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Polynomial hierarchy

In computational complexity theory, the polynomial hierarchy is a hierarchy of complexity classes that generalize the classes P, NP and co-NP to oracle machines. It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic.
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SO (complexity)

Second-order logic is an extension of first-order with second orders quantifiers, hence the reader should first read FO (complexity) to be able to understand this article. In descriptive complexity we can see that the languages recognised by SO formulae is exactly equal to the language decided by a Turing machine in the polynomial hierarchy. Extensions of SO with some operators also give us the same expressivity than some well known complexity class.
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Null (SQL)

Null is a special marker used in Structured Query Language (SQL) to indicate that a data value does not exist in the database. Introduced by the creator of the relational database model, E. F. Codd, SQL Null serves to fulfill the requirement that all true relational database management systems (RDBMS) support a representation of "missing information and inapplicable information". Codd also introduced the use of the lowercase Greek omega (¿) symbol to represent Null in database theory.
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A set has closure under an operation if performance of that operation on members of the set always produces a member of the same set. For example, the real numbers are closed under subtraction, but the natural numbers are not: 3 and 8 are both natural numbers, but the result of 3 ¿ 8 is not a natural number. Another example is the set containing only the number zero, which is a closed set under multiplication.
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Query language

Query languages are computer languages used to make queries into databases and information systems. Broadly, query languages can be classified according to whether they are database query languages or information retrieval query languages. The difference is that a database query language attempts to give factual answers to factual questions, while an information retrieval query language attempts to find documents containing information that is relevant to an area of inquiry. Examples include: .
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