Datalog and Logic Databases by Sergio Greco

By Sergio Greco

Using common sense in databases all started within the past due Nineteen Sixties. within the early Nineteen Seventies Codd formalized databases when it comes to the relational calculus and the relational algebra. an incredible effect at the use of common sense in databases used to be the advance of the sector of common sense programming. good judgment presents a handy formalism for learning classical database difficulties and has the real estate of being declarative, that's, it Read more...

summary: using common sense in databases all started within the overdue Sixties. within the early Nineteen Seventies Codd formalized databases when it comes to the relational calculus and the relational algebra. a huge impression at the use of good judgment in databases was once the advance of the sector of common sense programming. common sense offers a handy formalism for learning classical database difficulties and has the real estate of being declarative, that's, it permits one to precise what she desires instead of easy methods to get it. for a very long time, relational calculus and algebra have been thought of the relational database languages. in spite of the fact that, there are uncomplicated operations, similar to computing the transitive closure of a graph, which can't be expressed with those languages. Datalog is a declarative question language for relational databases in response to the common sense programming paradigm. one of many peculiarities that distinguishes Datalog from question languages like relational algebra and calculus is recursion, which supplies Datalog the aptitude to specific queries like computing a graph transitive closure. contemporary years have witnessed a revival of curiosity in Datalog in quite a few rising program domain names reminiscent of info integration, info extraction, networking, software research, safety, cloud computing, ontology reasoning, and so on. the purpose of this e-book is to offer the fundamentals of Datalog, a few of its extensions, and up to date purposes to diverse domain names

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T. t. I ; we write I 6ˆ r if r is not satisfied by I . r// D true. PD /. A model M of PD is minimal if no proper subset of M is a model of PD . 20 3. DATALOG It is well known that PD has a unique minimal model, which coincides with the intersection of all models of PD , and thus is the least (under set inclusion) model of PD . e model-theoretic semantics of PD is given by its (unique) least model. us, the model-theoretic semantics for a Datalog program is given by a minimal set of ground atoms satisfying the ground instantiation of the program.

If there exists a unifier of A1 and A2 , then there exists an mgu of A1 and A2 . Indeed, the mgu is unique modulo renaming of variables. , Lloyd [1987] and Apt [1991]). Y; a/ are unifiable, as, for instance, a unifier is D fX=a; Y =a; Z=ag. A most general unifier of A1 and A2 is  D fY =X; Z=ag. Notice that D  ı fX=ag and thus  is more general than . In order to find a proof for B1 ; : : : ; Bm , SLD resolution starts with the goal clause B1 ; : : : ; Bm ; then, it iteratively derives a new goal clause from a previous goal clause (as described in the following) until the empty goal clause is reached—when the empty goal clause is reached the procedure is successful.

1995], Date [2000], Elmasri and Navathe [2000], Garcia-Molina et al. [2009], Maier [1983], Ramakrishnan and Gehrke [2003], Silberschatz et al. [2010], Ullman [1988]. For a more complete treatment of logic programming we refer to Apt [1991], Lloyd [1987], while for a detailed exposition of complexity notions we refer to Johnson [1990] and Papadimitriou [1994]. 17 CHAPTER 3 Datalog Datalog is a declarative query language for relational databases based on the logic programming paradigm. From a syntactical standpoint, an important difference between Datalog and logic programs is that function symbols are not allowed in Datalog.

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