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166
Complexity and Expressive Power of Logic Programming
, 1997
"... This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results ..."
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Cited by 366 (57 self)
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This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.
A general Datalogbased framework for tractable query answering over ontologies
 In Proc. PODS2009. ACM
, 2009
"... Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DLLite family of tractable description logics (DLs) [11, 19]. ..."
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Cited by 135 (24 self)
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Ontologies play a key role in the Semantic Web [4], data modeling, and information integration [16]. Recent trends in ontological reasoning have shifted from decidability issues to tractability ones, as e.g. reflected by the work on the DLLite family of tractable description logics (DLs) [11, 19]. An important result of these works is that the main
ILOG: Declarative Creation and Manipulation of Object Identifiers
, 1991
"... yosikawaQkyotosu.ac.jp Abstract: This paper introduces ILOG ( a declarative language in the style of (stratified) datalog ( which can be used for querying, schema translation, and schema augmentation in the context of objectbased data models. The semantics of ILOG is based on the use of Skolem fun ..."
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Cited by 106 (1 self)
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yosikawaQkyotosu.ac.jp Abstract: This paper introduces ILOG ( a declarative language in the style of (stratified) datalog ( which can be used for querying, schema translation, and schema augmentation in the context of objectbased data models. The semantics of ILOG is based on the use of Skolem functors, and is closely related to semantics for objectbased data manipulation languages which provide mechanisms for explicit creation of object identifiers (OIDs). A normal form is presented for ILOG ’ programs not involving recursion through OID creation, which identifies a precise correspondence between OIDs created in the target, and values and OIDs in the source. The expressive power of various sublanguages of ILOG ’ is shown to range from a natural generalization of the conjunctive queries to the objectbased context, to a language which can specify all computable database translat.ions (up to duplicate copies). The issue of testing vuliilityof ILOG programs translat.ing one semantic schema to another is studied: cases are presented for which severalvalidity issues (e.g., functional and/or subset relationships in the
Constraint Programming and Database Query Languages
 In Proc. 2nd Conference on Theoretical Aspects of Computer Software (TACS
, 1994
"... . The declarative programming paradigms used in constraint languages can lead to powerful extensions of Codd's relational data model. The development of constraint database query languages from logical database query languages has many similarities with the development of constraint logic progr ..."
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Cited by 62 (3 self)
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. The declarative programming paradigms used in constraint languages can lead to powerful extensions of Codd's relational data model. The development of constraint database query languages from logical database query languages has many similarities with the development of constraint logic programming from logic programming, but with the additional requirements of data efficient, setatatime, and bottomup evaluation. In this overview of constraint query languages (CQLs) we first present the framework of [41]. The principal idea is that: "the ktuple (or record) data type can be generalized by a conjunction of quantifierfree constraints over k variables". The generalization must preserve various language properties of the relational data model, e.g., the calculus/algebra equivalence, and have time complexity polynomial in the size of the data. We next present an algebra for dense order constraints that is simpler to evaluate than the calculus described in [41], and we sharpen some of...
Infinitary Logic and Inductive Definability over Finite Structures
 Information and Computation
, 1995
"... The extensions of firstorder logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [Abi ..."
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Cited by 58 (7 self)
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The extensions of firstorder logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [Abiteboul and Vianu, 1991b] investigated the relationship of these two logics in the absence of an ordering, using a machine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables, L ! 1! (see, for instance, [Kolaitis and Vardi, 1990]). We investigate this logic of finite structures and provide a normal form for it. We also present a treatment of the results in [Abiteboul and Vianu, 1991b] from this point of view. In particular, we show that we can write a formula of FO + LFP that defines ...
Finitely Representable Databases
, 1995
"... : We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove ..."
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Cited by 57 (8 self)
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: We study classes of infinite but finitely representable databases based on constraints, motivated by new database applications such as geographical databases. We formally define these notions and introduce the concept of query which generalizes queries over classical relational databases. We prove that in this context the basic properties of queries (satisfiability, containment, equivalence, etc.) are nonrecursive. We investigate the theory of finitely representable models and prove that it differs strongly from both classical model theory and finite model theory. In particular, we show that most of the well known theorems of either one fail (compactness, completeness, locality, 0/1 laws, etc.). An immediate consequence is the lack of tools to consider the definability of queries in the relational calculus over finitely representable databases. We illustrate this very challenging problem through some classical examples. We then mainly concentrate on dense order databases, and exhibit...
Computing With FirstOrder Logic
, 1995
"... We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtaine ..."
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Cited by 55 (13 self)
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We study two important extensions of firstorder logic (FO) with iteration, the fixpoint and while queries. The main result of the paper concerns the open problem of the relationship between fixpoint and while: they are the same iff ptime = pspace. These and other expressibility results are obtained using a powerful normal form for while which shows that each while computation over an unordered domain can be reduced to a while computation over an ordered domain via a fixpoint query. The fixpoint query computes an equivalence relation on tuples which is a congruence with respect to the rest of the computation. The same technique is used to show that equivalence of tuples and structures with respect to FO formulas with bounded number of variables is definable in fixpoint. Generalizing fixpoint and while, we consider more powerful languages which model arbitrary computation interacting with a database using a finite set of FO queries. Such computation is modeled by a relational machine...
A Unified Semantics for Active and Deductive Databases
, 1994
"... These two ruleoriented paradigms of databases have been the focus of extensive research and are now coming of age in the commercial DBMS world. However, the systems developed so far support well only one of the two paradigmsthus limiting the effectiveness of such systems in many applications tha ..."
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Cited by 45 (11 self)
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These two ruleoriented paradigms of databases have been the focus of extensive research and are now coming of age in the commercial DBMS world. However, the systems developed so far support well only one of the two paradigmsthus limiting the effectiveness of such systems in many applications that require complete integration of both kinds of rules. In this paper, we discuss the technical problems that make such an integration difficult, and trace their roots to a lack of a unified underlying semantics. Then, we review recent advances in the semantics of nonmonotonic logic and show that they can be used to unify the foundations of active databases and deductive databases. Finally, we outline the design a new rule language for databases that integrates a deductive system with a triggerbased DBMS. 1 Introduction Rules provide the main paradigm for expressing computation in active databases and deductive databases. The unification of the two paradigms represents a research problem o...
A Logic For Programming Database Transactions
, 1998
"... : We propose an extension of classical predicate calculus, called Transaction Logic, which provides a logical foundation for the phenomenon of state changes in logic programs and databases. Transaction Logic comes with a natural model theory and a sound and complete proof theory. The proof theory n ..."
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Cited by 44 (21 self)
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: We propose an extension of classical predicate calculus, called Transaction Logic, which provides a logical foundation for the phenomenon of state changes in logic programs and databases. Transaction Logic comes with a natural model theory and a sound and complete proof theory. The proof theory not only verifies programs, but also executes them, which makes this logic an ideal tool for declarative programming of database transactions and statemodifying logic programs. The semantics of Transaction Logic leads naturally to features whose amalgamation in a single logic has proved elusive in the past. These features include hypothetical and committed updates, dynamic constraints on transaction execution, nondeterminism, and bulk updates. Finally, Transaction Logic holds promise as a logical model of hitherto nonlogical phenomena, including socalled procedural knowledge in AI, and the behavior of objectoriented databases, especially methods with side effects. This paper presents the...
Language Constructs for Programming Active Databases
 IN PROC. OF INTL. CONF. ON VERY LARGE DATA BASES
, 1991
"... ... constructs that can be used to realize a variety of different semantics for rule application in active database systems. The primary novel feature introduced is the "delayed update", or delta, which is a firstclass value representing a set of proposed modifications to the underly ..."
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Cited by 42 (13 self)
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... constructs that can be used to realize a variety of different semantics for rule application in active database systems. The primary novel feature introduced is the "delayed update", or delta, which is a firstclass value representing a set of proposed modifications to the underlying persistent store. Deltas can be created, inspected, and combined without committing to the given modifications. The utility of these concepts for expressing the semantics of active databases is demonstrated through a series of examples, including the presentation of the essential features of rule application in the AP5 system of USC/Information Sciences Institute and the Starburst Rule System being developed at IBM Almaden. Technical results concerning the simulatability of certain fundamental constructs by other fundamental constructs are also presented. The