By Zoran Majkić

This ebook offers a unique method of database ideas, describing a express common sense for database schema mapping in response to perspectives, inside a framework for database integration/exchange and peer-to-peer. Database mappings, database programming languages, and denotational and operational semantics are mentioned extensive. An research strategy can also be built that mixes concepts from moment order good judgment, information modeling, co-algebras and functorial categorial semantics. positive factors: offers an creation to logics, co-algebras, databases, schema mappings and classification idea; describes the middle innovations of huge info integration concept, with examples; examines the houses of the DB type; defines the categorial RDB computer; offers complete operational semantics for database mappings; discusses matching and merging operators for databases, common algebra issues and algebraic lattices of the databases; explores the connection of the database susceptible monoidal topos w.r.t. intuitionistic logic.

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**Extra resources for Big Data Integration Theory: Theory and Methods of Database Mappings, Programming Languages, and Semantics**

**Example text**

While qB (x) is a conjunctive query with relational symbols in SB . An instance of M is an instance pair (A, B) (where A is an instance of A and B is an instance of B) that satisfies every tgds in M, denoted by (A, B) |= MAB . We write Inst(M) to denote all instances (A, B) of M. Notice that the formula with built-in predicates, in the left side of implication of a tgd, can be expressed by only two logical connectives, conjunction and negation, from the fact that implication and disjunction can be reduced to equivalent formulae with these two logical connectives.

For a given category C, its “arrow category” is denoted by C ↓ C. Objects of this arrow category are the triples A, B, f where f : A → B is a morphism in C, and each morphism in this arrow category is a couple of two morphisms (k1 ; k2 ) : A, B, f → C, D, g such that k2 ◦ f = g ◦ k1 : A → D. Let us introduce, for a category C and its arrow category C ↓ C, an encapsulation operator J : MorC −→ ObC↓C and its inverse ψ , such that for any arrow f : A −→ B, J (f ) = A, B, f is its corresponding object in C ↓ C and ψ( A, B, f ) = f .

Atrr (n) where all ai = atrr (m) ∈ att, 1 ≤ m ≤ n, must be distinct: if we use two equal domains for different attributes then we denote them by ai (1), . . , ai (k) (ai equals to ai (0)). Each index (“column”) i, 1 ≤ i ≤ ar(r), has a distinct column name nrr (i) ∈ SN where SN is the set of names with nr(r) = nrr (1), . . , nrr (n) . A relation r ∈ R can be used as an atom r(x) of FOL with variables in x assigned to its columns, so that ΣA denotes a set of sentences (FOL formulae without free variables) called integrity constraints of the sorted FOL with sorts in att.