M. Arenas, L. Bertossi, and M. Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In International Conference on Computational Logic, pp. 926--941. Springer-Verlag, LNCS 1861, 2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....have been considered in this context: 2.1. Repairs are answer sets of a logic program [4,6,15] The compact representation is the program, and to obtain consistent answers, one runs the program. 2.2. Repairs are some distinguished minimal models of a theory written in annotated predicate logic [8,14]. 2.3. Repairs are maximal independent sets in a hypergraph whose nodes are database tuples and edges consist of sets of tuples participating in a violation of a denial constraint. This approach has been applied in [28] to quantifier free first order queries and in [5,7] to aggregation queries. ....

....would lead to an inconsistent theory and the trivialization of reasoning. In consequence, if we want a first order theory, we have to depart from classical logic, moving to non classical logic, where reasoning in the presence of classical inconsistencies does not necessarily collapse. Following [8], we show here how to generate a consistent first order theory with a non classical semantics. We use Annotated Predicate Calculus (APC) 67] In APC, database atoms are annotated with truth values taken from a truth value lattice. The most common annotations are: true (t) false (f ) ....

[Article contains additional citation context not shown here]

M. Arenas, L. Bertossi, and M. Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In International Conference on Computational Logic, pages 926--941. Springer-Verlag, LNCS 1861, 2000.

....is proven, as well as its completeness for particular ICs (binary ICs) Termination of computing T is also guaranteed under proper conditions. A variant of the T operator is described in [9] which is proven to be sound, terminating and complete for some classes of ICs extending those in [2] In [3] the Annotated Predicate Calculus (APC) is adopted, a logic where inconsistent information does not unravel logical inference and where causes of inconsistencies can be reasoned about. The inconsistent database is embedded in APC which is then used to define database repairs and query answers. ....

M. Arenas, L. Bertossi, and M. Kifer. Applications of annotated predicate calculus to querying inconsistent databases. In J. Lloyd et al. (editors), Proc. CL'2000/DOOD'2000, pp. 926--941, LNCS 1861. Springer, 2000.

....proven, as well as its completeness for particular ICs (binary ICs) Termination of computing T is also guaranteed under proper conditions. A variant of the T operator is described in [9] which is proven to be sound, terminating and complete for some classes of ICs extending those in [2] In [3] the Annotated Predicate Calculus (APC) is adopted, a logic where inconsistent information does not unravel logical inference and where causes of inconsistencies can be reasoned about The inconsistent database is embedded in APC which is then used to define database repairs and query answers. This ....

M. Arenas, L. Bertossi, and M. Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In Proc. DOOD'2000, London, UK, July 2000.

....been considered in this context: 2.1. Repairs are answer sets of a logic program [4,6,14,15] The compact representation is the program, and to obtain consistent answers, one runs the program. 2.2. Repairs are some distinguished minimal models of a theory written in annotated predicate logic [8,14]. 2.3. Repairs are maximal independent sets in a hypergraph whose nodes are database tuples and whose edges are sets of tuples participating in a violation of a denial constraint. This approach has been applied in [29] to quantifier free first order queries and in [5,7] to aggregation queries. ....

....would lead to an inconsistent theory and the trivialization of reasoning. In consequence, if we want a first order theory, we have to depart from classical logic, moving to nonclassical logic, where reasoning in the presence of classical inconsistencies does not necessarily collapse. Following [8], we show here how to generate a consistent first order theory with a nonclassical semantics. We use Annotated Predicate Calculus (APC) 68] In APC, database atoms are annotated with truth values taken from a truth value lattice. The most common annotations are: true (t) false (f) ....

[Article contains additional citation context not shown here]

M. Arenas, L. Bertossi, and M. Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In International Conference on Computational Logic, pp. 926--941. Springer-Verlag, LNCS 1861, 2000.

....pieces of information may be mutually inconsistent, we need a logic that does not collapse in the presence of contradictions. A non classical logic, like AnnotatedPredicate Calculus (APC) 27] for which a classically inconsistent set of premises can still have a model, is a natural candidate. In [3], a new declarative semantic framework was presented for studying the problem of query answering in databases that are inconsistent with respect to universal integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in ....

....problem of query answering in databases that are inconsistent with respect to universal integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in APC, with an appropriate, non classical truth values lattice Latt . In [3] it was shown that there is a one to one correspondence between some minimal models of the annotated theory and the repairs of the inconsistent database for universal ICs. In this way, a non monotonic logical speci cation of the database repairs was achieved. The annotated theory was used to ....

[Article contains additional citation context not shown here]

Arenas, M., Bertossi, L. and Kifer, M. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In ############## ##### # ####### ####### ### ############# ########## ## ##### ### ####### ## ######### ###########. Springer Lecture Notes in Arti cial Intelligence 1861, 2000, pp. 926-941.

....classical disjunctive normal programs with a stable model semantics. The database predicates in these programs contain annotations as extra arguments. In their turn, the annotations are inspired by the theories written in annotated predicate logic that specify database repairs as presented in [3, 8]. Nevertheless, the programs are classical, as opposed to annotated or paraconsistent logic programs [11, 25] The coherent stable models of the program turn out to correspond to the database repairs. The logic programs introduced in [4, 23] to specify database repairs may contain an exponential ....

....order to answer a query, the better. We have experimented with DLV , an implementation of the disjunctive stable model semantics [19] The methodology presented here works for arbitrary rst order queries and arbitrary universal ICs, what considerable extends the cases that could be han dled in [2, 4, 3]. We also show how to apply the methodology in the presence of referential integrity constraints [1] 2 Preliminaries 2.1 Database repairs and consistent answers We consider a xed relational database schema = D; P; B) consisting of a xed, possibly in nite, database domain D = fc 1 ; c 2 ; ....

[Article contains additional citation context not shown here]

Arenas, M.; Bertossi, L. and Kifer, M. \Applications of Annotated Predicate Calculus to Querying Inconsistent Databases". In `Computational Logic - CL

....pieces of information may be mutually inconsistent, we need a logic that does not collapse in the presence of contradictions. A non classical logic, like Annotated Predicate Calculus (APC) 27] for which a classically inconsistent set of premises can still have a model, is a natural candidate. In [3], a new declarative semantic framework was presented for studying the problem of query answering in databases that are inconsistent with respect to universal integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in ....

....problem of query answering in databases that are inconsistent with respect to universal integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in APC, with an appropriate, non classical truth values lattice Latt . In [3] it was shown that there is a one to one correspondence between some minimal models of the annotated theory and the repairs of the inconsistent database for universal ICs. In this way, a non monotonic logical speci cation of the database repairs was achieved. The annotated theory was used to ....

[Article contains additional citation context not shown here]

Arenas, M., Bertossi, L. and Kifer, M. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In `Computational Logic - CL

....order to answer a query, the better. We have experimented with )V, an implementation of the disjunctive stable model semantics [20] The methodology presented here works for arbitrary first order queries and arbitrary universal ICs, what considerable extends the cases that could be han dled in [2, 4, 3]. We also show how to apply the methodology in the presence of referential integrity constraints [1] 2 Preliminaries 2.1 Database repairs and consistent answers We consider a fixed relational database schema = D, P, B) consisting of a fixed, possibly infinite, database domain D = Cl, c2, ....

....Calculus was introduced in [25] It constitutes a non classical logic where classical inconsistencies may be accommodated without trivializing reasoning. Its syntax is similar to that of classical logic, except for the fact that atoms are annotated with values drawn from a truth values lattice. In [3], in order to embed the database and the ICs into a single consistent theory, a particular lattice was introduced. It contains the truth values: t, f (classical true and false) T (inconsistent) 2 (unknown) to, td, fd, fc, ta and fa. The values t, f are used to annotate what is needed for ....

[Article contains additional citation context not shown here]

Arenas, M.; Bertossi, L. and Kifer, M. "Applications of Annotated Predicate Calculus to Querying Inconsistent Databases". In 'Computational Logic - CL

....the information contained in the ICs. Since these two pieces of information are mutually inconsistent, we need a logic that does not collapse in the presence of contradictions. A paraconsistent logic , for which an inconsistent set of premises could still have a model, is a natural candidate. In [3], a new declarative semantic framework was presented for studying the problem of query answering in databases that are inconsistent with integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in Annotated Predicate ....

....answering in databases that are inconsistent with integrity constraints. This was done by embedding both the database instance and the integrity constraints into a single theory written in Annotated Predicate Calculus (APC ) 10] with an appropriate non classical truth values lattice Latt . In [3] it was shown that there is a one to one correspondence between some minimal models of the annotated theory and the repairs of the inconsistent database for universal ICs. In this way, a logical speci cation of the database repairs was achieved. The annotated theory was used to obtain some ....

[Article contains additional citation context not shown here]

Arenas, M.; Bertossi, L. and Kifer, M. \Applications of Annotated Predicate Calculus to Querying Inconsistent Databases". In `Computational Logic - CL2000.

....the database repairs by means of simple classical disjunctive normal programs with a stable model semantics. These programs contain the annotations as extra arguments of the database predicates. They are inspired by the theories written in annotated predicate logic that specify database repairs [3, 7]. Nevertheless, the programs are classical, as opposed to annotated and paraconsistent logic programs [9, 19] The coherent stable models of the program turn out to correspond to the database repairs. With this approach we reach to goals. The rst goal consists in obtaining a computable speci ....

....is true of every stable model. For this purpose, an implementation of the disjunctive stable model semantics, like DLV [13] can be used. The methodology presented here works for arbitrary rst order queries and arbitrary universal ICs, what considerable extends the cases that could be handled in [2, 4, 3]. We also show how to apply the methodology in the presence of referential integrity constraints [1] 2 Preliminaries 2.1 Database repairs and consistent answers In the context of relational databases, we will consider a xed relational schema = D; P [ B) that determines a rst order ....

[Article contains additional citation context not shown here]

Arenas, M.; Bertossi, L. and Kifer, M. \Applications of Annotated Predicate Calculus to Querying Inconsistent Databases". In `Computational Logic - CL2000' Stream: 6th International Conference on Rules and Objects in Databases (DOOD'2000). Springer Lecture Notes in Arti cial Intelligence 1861, 2000, pp. 926-941.

....have been considered: 2.1. Repairs are stable models of a logic program [4, 6, 13] The compact representation is the program, and to obtain consistent answers, one runs the program. 2.2. Repairs are some distinguished minimal models of a theory written in annotated predicate logic [8, 13]. 2.3. Repairs are maximal independent sets in a hypergraph whose nodes are database tuples and edges consists of tuples participating in a violation of a denial constraint. This approach has been applied in [24] to quantifierfree first order queries and in [5, 7] to aggregation queries. 2.4. ....

....would lead to an inconsistent theory and the trivialization of reasoning. In consequence, if we want a first order theory, we have to depart from classical logic, moving to non classical logic, where reasoning in the presence of classical inconsistencies does not necessarily collapse. Following [8], we show here how to generate a consistent first order theory with a non classical semantics. We use Annotated Predicate Calculus (APC) 50] In APC, database atoms are annotated with truth values taken from a truthvalue lattice. The most common annotations are: true (t) false (f ) ....

[Article contains additional citation context not shown here]

Arenas, M.; Bertossi, L. and Kifer, M. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In `Computational Logic - CL 2000.

....disjunctive table (with rows that are disjunctions of atoms with the same relation symbol) This is not as obvious as it seems, as the repairs require an exclusive representation of disjunctions, which is forced through the minimal model semantics of disjunctive formulas. This idea is implicit in [3]. The relationship in the other direction does not hold. e.g. the set of minimal models of the formula p(a 1 ; b 1 ) p(a 2 ; b 2 ) cannot be represented as a set of repairs of any set of FDs. We also conjecture that if F is a set of two FDs and R is a BCNF schema over F , then for every ....

M. Arenas, L. Bertossi, and M. Kifer. Applications of Annotated Predicate Calculus to Querying Inconsistent Databases. In Proc. 6th International Conference on Rules and Objects in Databases (DOOD'2000). To appear in Springer LNCS, 2000.

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