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42
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 281 (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.
Fixpoint Logics, Relational Machines, and Computational Complexity
 In Structure and Complexity
, 1993
"... We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1storder operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have t ..."
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Cited by 36 (5 self)
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We establish a general connection between fixpoint logic and complexity. On one side, we have fixpoint logic, parameterized by the choices of 1storder operators (inflationary or noninflationary) and iteration constructs (deterministic, nondeterministic, or alternating). On the other side, we have the complexity classes between P and EXPTIME. Our parameterized fixpoint logics capture the complexity classes P, NP, PSPACE, and EXPTIME, but equality is achieved only over ordered structures. There is, however, an inherent mismatch between complexity and logic  while computational devices work on encodings of problems, logic is applied directly to the underlying mathematical structures. To overcome this mismatch, we develop a theory of relational complexity, which bridges tha gap between standard complexity and fixpoint logic. On one hand, we show that questions about containments among standard complexity classes can be translated to questions about containments among relational complex...
Logics with Aggregate Operators
 Journal of the ACM
"... We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, a ..."
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Cited by 24 (12 self)
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We study adding aggregate operators, such as summing up elements of a column of a relation, to logics with counting mechanisms. The primary motivation comes from database applications, where aggregate operators are present in all real life query languages. Unlike other features of query languages, aggregates are not adequately captured by the existing logical formalisms. Consequently, all previous approaches to analyzing the expressive power of aggregation were only capable of producing partial results, depending on the allowed class of aggregate and arithmetic operations. We consider a powerful counting logic, and extend it with the set of all aggregate operators. We show that the resulting logic satis es analogs of Hanf's and Gaifman's theorems, meaning that it can only express local properties. We consider a database query language that expresses all the standard aggregates found in commercial query languages, and show how it can be translated into the aggregate logic, thereby pro...
Semantics and Expressiveness Issues in Active Databases
 J. OF COMPUTER AND SYSTEM SCIENCES
, 1995
"... A formal framework is introduced for studying the semantics and expressiveness of active databases. The power of various abstract trigger languages is characterized, and related to several major active database prototypes such as ARDL, HiPAC, Postgres, Starburst, and Sybase. This allows to forma ..."
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Cited by 23 (1 self)
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A formal framework is introduced for studying the semantics and expressiveness of active databases. The power of various abstract trigger languages is characterized, and related to several major active database prototypes such as ARDL, HiPAC, Postgres, Starburst, and Sybase. This allows to formally compare the expressiveness of the prototypes. The results provide insight into the programming paradigm of active databases, the interplay of various features, and their impact on expressiveness and complexity.
Decidability and Undecidability Results for the Termination Problem of Active Database Rules
 In Proceedings of the 17th ACM SIGMODSIGACTSIGART Symposium on Principles of Database Systems
, 1998
"... Active database systems enhance the functionality of traditional databases through the use of active rules or `triggers'. One of the principal questions for such systems is that of termination  is it possible for the rules to recursively activate one another indefinitely, given an initial triggerin ..."
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Cited by 19 (8 self)
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Active database systems enhance the functionality of traditional databases through the use of active rules or `triggers'. One of the principal questions for such systems is that of termination  is it possible for the rules to recursively activate one another indefinitely, given an initial triggering event. In this paper, we study the decidability of the termination problem, our aim being to delimit the boundary between the decidable and the undecidable. We present two families of rule languages, the one literal languages where each update is permitted to have just one atom in its body, and the unary languages where only unary relations may be updated, but higher arity relations may be accessed through views. Within each of these, we identify members close to the boundary of (un)decidability. Our context is similar to the while query language and the dynamics gives an interesting contrast to Datalog with negation; our results shed insights on the power of triggers as well as comparison of the termination problem to boundedness and query containment.
On the Forms of Locality over Finite Models
 In Proc. 12th IEEE Symp. on Logic in Computer Science
, 1997
"... Most proofs showing limitations of expressive power of firstorder logic rely on EhrenfeuchtFraisse games. Playing the game often involves a nontrivial combinatorial argument, so it was proposed to find easier tools for proving expressivity bounds. Most of those known for firstorder logic are base ..."
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Cited by 18 (10 self)
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Most proofs showing limitations of expressive power of firstorder logic rely on EhrenfeuchtFraisse games. Playing the game often involves a nontrivial combinatorial argument, so it was proposed to find easier tools for proving expressivity bounds. Most of those known for firstorder logic are based on its "locality", that is defined in different ways. In this paper we characterize the relationship between those notions of locality. We note that Gaifman's locality theorem gives rise to two notions: one deals with sentences and one with open formulae. We prove that the former implies Hanf's notion of locality, which in turn implies Gaifman's locality for open formulae. Each of these implies the bounded degree property, which is one of the easiest tools for proving expressivity bounds. These results apply beyond the firstorder case. We use them to derive expressivity bounds for firstorder logic with unary quantifiers and counting. Finally, we apply these results to relational database...
Local Normal Forms for FirstOrder Logic with Applications to Games and Automata
 DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1998
"... ..."
Querying Spatial Databases via Topological Invariants
 In PODS'98
, 1998
"... The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered ..."
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Cited by 17 (2 self)
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The paper investigates the use of topological annotations (called topological invariants) to answer topological queries in spatial databases. The focus is on the translation of topological queries against the spatial database into queries against the topological invariant. The languages considered are firstorder on the spatial database side, and fixpoint + counting, fixpoint, and firstorder on the topological invariant side. In particular, it is shown that fixpoint + counting expresses precisely all the ptime queries on topological invariants; if the regions are connected, fixpoint expresses all ptime queries on topological invariants. 1 Introduction Spatial data is an increasingly important part of database systems. It is present in a wide range of applications: geographic information systems, video databases, medical imaging, CADCAM, VLSI, robotics, etc. Different applications pose different requirements on query languages and therefore on the kind of spatial information th...
First Order Logic, Fixed Point Logic and Linear Order
, 1995
"... The Ordered conjecture of Kolaitis and Vardi asks whether fixedpoint logic differs from firstorder logic on every infinite class of finite ordered structures. In this paper, we develop the tool of bounded variable element types, and illustrate its application to this and the original conjectures o ..."
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Cited by 16 (0 self)
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The Ordered conjecture of Kolaitis and Vardi asks whether fixedpoint logic differs from firstorder logic on every infinite class of finite ordered structures. In this paper, we develop the tool of bounded variable element types, and illustrate its application to this and the original conjectures of McColm, which arose from the study of inductive definability and infinitary logic on proficient classes of finite structures (those admitting an unbounded induction). In particular, for a class of finite structures, we introduce a compactness notion which yields a new proof of a ramified version of McColm's second conjecture. Furthermore, we show a connection between a modeltheoretic preservation property and the Ordered Conjecture, allowing us to prove it for classes of strings (colored orderings). We also elaborate on complexitytheoretic implications of this line of research.
On Counting Logics and Local Properties
, 1998
"... The expressive power of firstorder logic over finite structures is limited in two ways: it lacks a recursion mechanism, and it cannot count. Overcoming the first limitation has been a subject of extensive study. A number of fixpoint logics have been introduced, and shown to be subsumed by an infini ..."
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Cited by 16 (10 self)
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The expressive power of firstorder logic over finite structures is limited in two ways: it lacks a recursion mechanism, and it cannot count. Overcoming the first limitation has been a subject of extensive study. A number of fixpoint logics have been introduced, and shown to be subsumed by an infinitary logic L ! 1! . This logic is easier to analyze than fixpoint logics, and it still lacks counting power, as it has a 01 law. On the counting side, there is no analog of L ! 1! . There are a number of logics with counting power, usually introduced via generalized quantifiers. Most known expressivity bounds are based on the fact that counting extensions of firstorder logic preserve the locality properties. This paper has three main goals. First, we introduce a new logic L 1! (C) that plays the same role for counting as L ! 1! does for recursion  it subsumes a number of extensions of firstorder logic with counting, and has nice properties that make it easy to study. Second, we ...