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318
On the Relative Expressiveness of Description Logics and Predicate Logics
 ARTIFICIAL INTELLIGENCE JOURNAL
, 1996
"... It is natural to view concept and role definitions in Description Logics as expressing monadic and dyadic predicates in Predicate Calculus. We show that the descriptions built using the constructors usually considered in the DL literature are characterized exactly as the predicates definable by form ..."
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Cited by 174 (3 self)
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It is natural to view concept and role definitions in Description Logics as expressing monadic and dyadic predicates in Predicate Calculus. We show that the descriptions built using the constructors usually considered in the DL literature are characterized exactly as the predicates definable by formulas in ¨L³, the subset of First Order Predicate Calculus with monadic and dyadic predicates which allows only three variable symbols. In order to handle “number bounds”, we allow numeric quantifiers, and for transitive closure of roles we use infinitary disjunction. Using previous results in the literature concerning languages with limited numbers of variables, we get as corollaries the existence of formulae of FOPC which cannot be expressed as descriptions. We also show that by omitting role composition, descriptions express exactly the formulae in ¨L², which is known to be decidable.
On optimal lower bound on the number of variables for graph identification
 Combinatorica
, 1992
"... ..."
Logic and the Challenge of Computer Science
, 1988
"... Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objec ..."
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Cited by 165 (16 self)
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Nowadays computer science is surpassing mathematics as the primary field of logic applications, but logic is not tuned properly to the new role. In particular, classical logic is preoccupied mostly with infinite static structures whereas many objects of interest in computer science are dynamic objects with bounded resources. This chapter consists of two independent parts. The first part is devoted to finite model theory; it is mostly a survey of logics tailored for computational complexity. The second part is devoted to dynamic structures with bounded resources. In particular, we use dynamic structures with bounded resources to model Pascal.
On Uniformity within NC¹
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1990
"... In order to study circuit complexity classes within NC¹ in a uniform setting, we need a uniformity condition which is more restrictive than those in common use. Two such conditions, stricter than NC¹ uniformity [Ru81,Co85], have appeared in recent research: Immerman's families of circuits defin ..."
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Cited by 127 (19 self)
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In order to study circuit complexity classes within NC¹ in a uniform setting, we need a uniformity condition which is more restrictive than those in common use. Two such conditions, stricter than NC¹ uniformity [Ru81,Co85], have appeared in recent research: Immerman's families of circuits defined by firstorder formulas [Im87a,Im87b] and a uniformity corresponding to Buss' deterministic logtime reductions [Bu87]. We show that these two notions are equivalent, leading to a natural notion of uniformity for lowlevel circuit complexity classes. We show that recent results on the structure of NC¹ [Ba89] still hold true in this very uniform setting. Finally, we investigate a parallel notion of uniformity, still more restrictive, based on the regular languages. Here we give characterizations of subclasses of the regular languages based on their logical expressibility, extending recent work of Straubing, Th'erien, and Thomas [STT88]. A preliminary version of this work appeared as [BIS88].
Fixedpoint extensions of firstorder logic
 in “Proceedings, 26th Annu. IEEE Symposium on Foundations of Computer Science
, 1985
"... Communicated byA. Nerode ..."
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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 89 (6 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
Toward Logic Tailored for Computational Complexity
 COMPUTATION AND PROOF THEORY
, 1984
"... Whereas firstorder logic was developed to confront the infinite it is often used in computer science in such a way that infinite models are meaningless. We discuss the firstorder theory of finite structures and alternatives to firstorder logic, especially polynomial time logic. ..."
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Cited by 87 (7 self)
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Whereas firstorder logic was developed to confront the infinite it is often used in computer science in such a way that infinite models are meaningless. We discuss the firstorder theory of finite structures and alternatives to firstorder logic, especially polynomial time logic.
Bounded Linear Logic: A Modular Approach to Polynomial Time Computability (Extended Abstract), in: 141
"... A typed, modular paradigm for polynomial time computation is proposed. ..."
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Cited by 86 (6 self)
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A typed, modular paradigm for polynomial time computation is proposed.