. This paper presents a formal framework for specifying active database systems. Declarative characterization of active databases allows additional flexibility in defining an implementation--independent 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,...

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 logic-programming 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 well-established 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...

this paper, we establish more comprehensive results by exploring the interaction of negation-as-failure 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 second-order logic follows as a corollary. First, we show that rulebases in our language fit neatly into a well-established logical framework---intuitionistic logic. Second, we show that linearity reduces their data complexity from PSPACE to NP. Third, we show that negation-as-failure 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

Anuj Dawar ?1 , Lauri Hella , Phokion G. Kolaitis ??3 Dept. of Comp. Science, Univ. of Wales, Swansea, Swansea SA2 8PP, U.K.

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 nonzero-ary 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...

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

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 µ-calculus. 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 second-order logic (GSO), but not in least-fixed point logic (LFP). On finite game graphs, winning regions are LFP-definable 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.

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 Löwenheim-Skolem properties, are presented regarding this relationship. This is also investigated through finitary versions of an Ehrenfeucht-Mostowski property.

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 `high-level' programming constructs such as arrays, while-loops, assignments, and non-determinism, 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 zero-one 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...

We consider an alternative semantics for partial fixed-point logic (PFP). To define the fixed point of a formula in this semantics, the sequence of stages induced by the formula is considered. As soon as this sequence becomes cyclic, the set of elements contained in every stage of the cycle is taken as the fixed point. It is shown that on finite structures, this fixed-point semantics and the standard semantics for PFP as considered infinite model theory are equivalent, although arguably the formalisation of properties might even become simpler and more intuitive.