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Formal Characterizations of Active Databases: Part II
, 1997
"... . This paper presents a formal framework for specifying active database systems. Declarative characterization of active databases allows additional flexibility in defining an implementationindependent semantics of the active rules. By making a clear distinction between actual and hypothetical exec ..."
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. This paper presents a formal framework for specifying active database systems. Declarative characterization of active databases allows additional flexibility in defining an implementationindependent semantics of the active rules. By making a clear distinction between actual and hypothetical execution of the actions, one can make claims and about the (possible) effects of an actions' sequence and prove them, without actually executing it. The results that we present extend the active database description language introduced in [5] with additional semantic dimensions. We demonstrate through examples how we can encode the active rules and their operational behavior from different existing systems. 1 Introduction and Motivation The core concept which makes a database system active is the concept of an active rule. The origin of the active rules is the production rule paradigm from the field of Artificial Intelligence with the languages like OPS5 [7], used in expert systems. Typically,...
Hypothetical Reasoning with Intuitionistic Logic
 NonStandard Queries and Answers, Studies on Logic and Computation, chapter 8
, 1994
"... This paper addresses a limitation of most deductive database systems: They cannot reason hypothetically. Although they reason effectively about the world as it is, they are poor at tasks such as planning and design, where one must explore the consequences of hypothetical actions and possibilities. T ..."
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This paper addresses a limitation of most deductive database systems: They cannot reason hypothetically. Although they reason effectively about the world as it is, they are poor at tasks such as planning and design, where one must explore the consequences of hypothetical actions and possibilities. To address this limitation, this paper presents a logicprogramming language in which a user can create hypotheses and draw inferences from them. Two types of hypothetical operations are considered: the insertion of tuples into a database, and the creation of new constant symbols. These two operations are interesting, not only because they extend the capabilities of database systems, but also because they fit neatly into a wellestablished logical framework, namely intuitionistic logic. This paper presents the proof theory for the logic, outlines its intuitionistic model theory, and summarizes results on its complexity and on its ability to express database queries. Our results establish a st...
Intuitionistic Deductive Databases And The Polynomial Time Hierarchy
, 1997
"... this paper, we establish more comprehensive results by exploring the interaction of negationasfailure with a natural syntactic restriction called linearity. The main result is a tight connection between intuitionistic logic, database queries, and the polynomial time hierarchy. A tight connection w ..."
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Cited by 5 (2 self)
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this paper, we establish more comprehensive results by exploring the interaction of negationasfailure with a natural syntactic restriction called linearity. The main result is a tight connection between intuitionistic logic, database queries, and the polynomial time hierarchy. A tight connection with secondorder logic follows as a corollary. First, we show that rulebases in our language fit neatly into a wellestablished logical frameworkintuitionistic logic. Second, we show that linearity reduces their data complexity from PSPACE to NP. Third, we show that negationasfailure increases their complexity from NP to some level in the polynomial time hierarchy (PHIER). Specifically, linear rulebases with k strata are data complete for \Sigma
Implicit Definability and Infinitary Logic in Finite Model Theory (Extended Abstract)
"... Anuj Dawar ?1 , Lauri Hella , Phokion G. Kolaitis ??3 Dept. of Comp. Science, Univ. of Wales, Swansea, Swansea SA2 8PP, U.K. ..."
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Anuj Dawar ?1 , Lauri Hella , Phokion G. Kolaitis ??3 Dept. of Comp. Science, Univ. of Wales, Swansea, Swansea SA2 8PP, U.K.
When do Fixed Point Logics Capture Complexity Classes?
 In Proceedings 10th IEEE Symposium on Logic in Computer Science
, 1995
"... We give examples of classes of rigid structures which are of unbounded rigidity but Least fixed point (Partial fixed point) logic can express all Boolean PTIME (PSPACE) queries on these classes. This shows that definability of linear order in FO+LFP although sufficient for it to capture Boolean PTIM ..."
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We give examples of classes of rigid structures which are of unbounded rigidity but Least fixed point (Partial fixed point) logic can express all Boolean PTIME (PSPACE) queries on these classes. This shows that definability of linear order in FO+LFP although sufficient for it to capture Boolean PTIME queries, is not necessary even on the classes of rigid structures. The situation however appears very different for nonzeroary queries. Next, we turn to the study of fixed point logics on arbitrary classes of structures. We completely characterize the recursively enumerable classes of finite structures on which PFP captures all PSPACE queries of arbitrary arities. We also state in some alternative forms several natural necessary and some sufficient conditions for PFP to capture PSPACE queries on classes of finite structures. The conditions similar to the ones proposed above work for LFP and PTIME also in some special cases but to prove the same necessary conditions in general for LFP to c...
The Descriptive Complexity of Parity Games
, 2008
"... We study the logical definablity of the winning regions of parity games. For games with a bounded number of priorities, it is wellknown that the winning regions are definable in the modal µcalculus. Here we investigate the case of an unbounded number of priorities, both for finite game graphs and ..."
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We study the logical definablity of the winning regions of parity games. For games with a bounded number of priorities, it is wellknown that the winning regions are definable in the modal µcalculus. Here we investigate the case of an unbounded number of priorities, both for finite game graphs and for arbitrary ones. In the general case, winning regions are definable in guarded secondorder logic (GSO), but not in leastfixed point logic (LFP). On finite game graphs, winning regions are LFPdefinable if, and only if, they are computable in polynomial time, and this result extends to any class of finite games that is closed under taking bisimulation quotients.
Computing on Structures
"... this paper various devices operating directly on structures, without encoding. The motivation and benefits for doing this are manyfold. On a fundamental level, encodings of structures seem to be a technical device rather than an intrinsic feature. This point has already been made by several mathemat ..."
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this paper various devices operating directly on structures, without encoding. The motivation and benefits for doing this are manyfold. On a fundamental level, encodings of structures seem to be a technical device rather than an intrinsic feature. This point has already been made by several mathematicians such as Tarski [Tar86], and Harvey Friedman [Fri71] (see Section 5). It has come up more recently in the context of databases, where devices computing on structures model more acurately database computation carried out against an abstract interface hiding the internal representation of data. Thus, the primary benefit of studying devices and languages computing on structures is that they clarify issues which are obscured in classical devices such as Turing machines. For example, they yield new notions of complexity, quite different from classical computational complexity. They reflect more acurately the actual complexity of computation, which, like database computation, cannot take advantage of encodings of structures. An example is provided by the query even on a set
Computational Model Theory: An Overview
 LOGIC JOURNAL OF THE IGPL
, 1998
"... The computational complexity of a problem is the amount of resources, such as time or space, required by a machine that solves the problem. The descriptive complexity of problems is the complexity of describing problems in some logical formalism over finite structures. One of the exciting developmen ..."
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The computational complexity of a problem is the amount of resources, such as time or space, required by a machine that solves the problem. The descriptive complexity of problems is the complexity of describing problems in some logical formalism over finite structures. One of the exciting developments in complexity theory is the discovery of a very intimate connection between computational and descriptive complexity. It is this connection between complexity theory and finitemodel theory that we term computational model theory. In this overview paper we o#er one perspective on computational model theory. Two important observationsunderly our perspective: (1) while computationaldevices work on encodingsof problems, logic is applied directly to the underlying mathematical structures, and this "mismatch" complicates the relationship between logic and complexity significantly, and (2) firstorder logic has severely limited expressive power on finite structures, and one way to increase the...
Finite Models and Finitely Many Variables
 Banach Center Publications
, 1999
"... We consider L  first order logic restricted to k variables, and interpreted in finite structures. The study of classes of finite structures axiomatisable with finitely many variables has assumed importance through connections with computational complexity. In particular, we investigate the relation ..."
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We consider L  first order logic restricted to k variables, and interpreted in finite structures. The study of classes of finite structures axiomatisable with finitely many variables has assumed importance through connections with computational complexity. In particular, we investigate the relationship between the size of a finite structure and the number of distinct types it realizes, with respect to L . Some open questions, formulated as finitary LöwenheimSkolem properties, are presented regarding this relationship. This is also investigated through finitary versions of an EhrenfeuchtMostowski property.
Logical Definability Versus Computational Complexity: Another Equivalence
"... We dene a class of program schemes, NPSB, as the union of an innite hierarchy of classes of program schemes NPSB(1) NPSB(2) : : :, where our program schemes are built around `highlevel' programming constructs such as arrays, whileloops, assignments, and nondeterminism, and take nite structures ..."
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We dene a class of program schemes, NPSB, as the union of an innite hierarchy of classes of program schemes NPSB(1) NPSB(2) : : :, where our program schemes are built around `highlevel' programming constructs such as arrays, whileloops, assignments, and nondeterminism, and take nite structures as their inputs. Every program scheme of NPSB(i) is actually also a program scheme of an existing class of program schemes NPSA(i), with NPSA dened analogously to NPSB. It has previously been shown that the class of problems accepted by the program schemes of NPSA: is contained in PSPACE; can be realized as the class of problems denable by the sentences of a certain vectorized Lindstrom logic; and has a zeroone law. We prove here that the class of problems accepted by the program schemes of NPSB is contained within the complexity class L NP and can also be realized as the class of problems denable by the sentences of a certain vectorized Lindstrom logic; and we exhibit a problem...