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The WellFounded Semantics for General Logic Programs
 Journal of the ACM
, 1991
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The expressive powers of logic programming semantics
 Abstract in Proc. PODS 90
, 1995
"... We study the expressive powers of two semantics for deductive databases and logic programming: the wellfounded semantics and the stable semantics. We compare them especially to two older semantics, the twovalued and threevalued program completion semantics. We identify the expressive power of the ..."
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Cited by 85 (5 self)
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We study the expressive powers of two semantics for deductive databases and logic programming: the wellfounded semantics and the stable semantics. We compare them especially to two older semantics, the twovalued and threevalued program completion semantics. We identify the expressive power of the stable semantics, and in fairly general circumstances that of the wellfounded semantics. In particular, over infinite Herbrand universes, the four semantics all have the same expressive power. We discuss a feature of certain logic programming semantics, which we call the Principle of Stratification, a feature allowing a program to be built easily in modules. The threevalued program completion and wellfounded semantics satisfy this principle. Over infinite Herbrand models, we consider a notion of translatability between the threevalued program completion and wellfounded semantics which is in a sense uniform in the strata. In this sense of uniform translatability we show the wellfounded semantics to be more expressive than the threevalued program completion. The proof is a corollary of our result that over nonHerbrand infinite models, the wellfounded semantics is more expressive than the threevalued program completion semantics. 1
Database Query Languages Embedded in the Typed Lambda Calculus
, 1993
"... We investigate the expressive power of the typed calculus when expressing computations over finite structures, i.e., databases. We show that the simply typed calculus can express various database query languages such as the relational algebra, fixpoint logic, and the complex object algebra. In ..."
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Cited by 26 (6 self)
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We investigate the expressive power of the typed calculus when expressing computations over finite structures, i.e., databases. We show that the simply typed calculus can express various database query languages such as the relational algebra, fixpoint logic, and the complex object algebra. In our embeddings, inputs and outputs are terms encoding databases, and a program expressing a query is a term which types when applied to an input and reduces to an output.
Tractable Query Languages for Complex Object Databases
, 1995
"... The expressiveness and complexity of several calculusbased query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objec ..."
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Cited by 24 (4 self)
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The expressiveness and complexity of several calculusbased query languages for complex objects is considered. Unlike previous investigations, we are concerned with the complexity of queries on databases of complex objects, rather than flat databases. This raises new issues specific to complex objects. For instance, it is shown that the way the database makes use of its higherorder types has direct impact on query complexity. The use of fixpoint operators is shown to yield languages wellbehaved with respect to complexity and expressiveness. In particular, an extension of the fixpoint queries to complex objects is shown to express precisely the PTIME queries, under the assumption that the database makes "full" use of all its types. Similar results involve rangerestricted queries. 1 Introduction Complex objects are increasingly part of advanced database systems. They provide the structural core of objectoriented databases. Several query languages for complex objects have been propo...
Asymptotic probabilities of languages with generalized quantifiers
 Proc. 8th IEEE Symp. on Logic in Computer Science
, 1993
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On the Expressive Power of Counting
, 1994
"... We investigate the expressive power of various extensions of firstorder, inductive, and infinitary logic with counting quantifiers. We consider in particular a LOGSPACE extension of firstorder logic, and a PTIME extension of fixpoint logic with counters. Counting is a fundamental tool of algorith ..."
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Cited by 7 (1 self)
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We investigate the expressive power of various extensions of firstorder, inductive, and infinitary logic with counting quantifiers. We consider in particular a LOGSPACE extension of firstorder logic, and a PTIME extension of fixpoint logic with counters. Counting is a fundamental tool of algorithms. It is essential in the case of unordered structures. Our aim is to understand the expressive power gained with a limited counting ability. We consider two problems: (i) unnested counters, and (ii) counters with no free variables. We prove a hierarchy result based on the arity of the counters under the first restriction. The proof is based on a game technique that is introduced in the paper. We also establish results on the asymptotic probabilities of sentences with counters under the second restriction. In particular, we show that firstorder logic with equality of the cardinalities of relations has a 0/1 law.
On NonDeterminism in Machines and Languages
"... this paper, we compare various means to define nondeterministic constructs, both in computing devices and in logical languages. Our goal is to establish correspondences between different formalisms, and to better understand the expressive power of the constructs. A deterministic query is a mapping ..."
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Cited by 2 (0 self)
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this paper, we compare various means to define nondeterministic constructs, both in computing devices and in logical languages. Our goal is to establish correspondences between different formalisms, and to better understand the expressive power of the constructs. A deterministic query is a mapping from databases to relations. A nondeterministic query is a relation which associates possibly several distinct relations to each database. We define the class NQ of all computable nondeterministic queries. Our purpose is to characterize subclasses of NQ with query languages on one side and classes of queries computable on machines of various complexity classes on the other side. Nondeterministic queries correspond to multivalued functions in complexity theory [Sel94]. Classes of deterministic queries computable on Turing machines with bounded resources are defined with respect to the recognition problem as usual [Kan90]. In the case of nondeterministic queries, we followed the definition of [ASV90], and considered the computation problem, which is more appropriate in the later case. We consider classical complexity classes in the polynomial range, PTIME, NP, and their complement and intersections, NP"coNP, etc. We also consider less usual classes, such as in particular the class UP of unambiguous computations [Val76], the class DP, of problems whose computation requires in parallel a branch in NP and a branch in coNP [PY82], and the class P
CommonSense Axiomatizations for Logic Programs
"... Abstract Various semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite firstorder presentation of ..."
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Abstract Various semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite firstorder presentation of Kunen's semantics is described. A new axiom to represent &quot;common sense &quot; reasoning is proposed for logic programs. It is shown that the wellfounded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A &quot;domain foundation &quot; axiom is proposed to replace the domain closure axiom. 1 Introduction Although the semantics of Horn logic programs is standard, as given in the seminal work of van Emden and Kowalski [47], there is presently no universally accepted semantics for logic programs with negation. The first purpose of this paper is to describe various existing proposals using a common framework of classical (twovalued) logic, thereby to delineate their differences more clearly. A second purpose is to explore the effects of various constraints on the universe (or domain) of interpretation on the logical consequences of the program. Our approach is to identify the program's &quot;declarative semantics &quot; with the logical consequences of the rules in the program, together with various additional axioms. Various sets of additional axioms give rise to various semantics. We avoid the use of procedural definitions and nonstandard logics; in some cases we use second order formulas, since they can be very useful in distinguishing concepts.
Verification of ConjunctiveQUery Based . . .
, 2011
"... We introduce semantic artifacts, which are a mechanism that provides both a semantically rich representation of the information on the domain of interest in terms of an ontology, including the underlying data, and a set of actions to change such information over time. In this paper, the ontology is ..."
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We introduce semantic artifacts, which are a mechanism that provides both a semantically rich representation of the information on the domain of interest in terms of an ontology, including the underlying data, and a set of actions to change such information over time. In this paper, the ontology is specified as a DLLite TBox together with an ABox that may contain both (known) constants and unknown individuals (labeled nulls, represented as Skolem terms). Actions are specified as sets of conditional effects, where conditions are based on conjunctive queries over the ontology (TBox and ABox), and effects are expressed in terms of new ABoxes. In this setting, which is obviously not finite state, we address the verification of temporal/dynamic properties expressed in µcalculus. Notably, we show decidability of verification, under a suitable restriction inspired by the notion of acyclicity in data exchange.
The Alternating Fixpoint of Logic Programs with Negation \Lambda
, 1995
"... The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the wellfounded partial model, and (2) that alternating fixpoint logic is at least as expressive as fixpoint logic on all structures. Also, on finite structures, fixpoint logic is as express ..."
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The principal contributions of this work are (1) that the alternating fixpoint partial model is identical to the wellfounded partial model, and (2) that alternating fixpoint logic is at least as expressive as fixpoint logic on all structures. Also, on finite structures, fixpoint logic is as expressive as alternating fixpoint logic.