We investigate the relationship between programming with constraints and database query languages. We show that efficient, declarative database programming can be combined with efficient constraint solving. The key intuition is that the generalization of a ground fact, or tuple, is a conjunction of constraints over a small number of variables. We describe the basic Constraint Query Language design principles and illustrate them with four classes of constraints: real polynomial inequalities, dense linear order inequalities, equalities over an infinite domain, and boolean equalities. For the analysis, we use quantifier elimination techniques from logic and the concept of data complexity from database theory. This framework is applicable to managing spatial data and can be combined with existing multidimensional searching algorithms and data structures.

We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the model-checking problem.

We define formal notions of temporal domain and temporal database, and use them to survey a wide spectrum of temporal query languages. We distinguish between an abstract temporal database and its concrete representations, and accordingly between abstract and concrete temporal query languages. We also address the issue of incomplete temporal information. 1 Introduction A temporal database is a repository of temporal information. A temporal query language is any query language for temporal databases. In this paper we propose a formal notion of temporal database and use this notion in surveying a wide spectrum of temporal query languages. The need to store temporal information arises in many computer applications. Consider, for example, records of various kinds: financial [37], personnel, medical [98], or judicial. Also, monitoring data, e.g., in telecommunications network management [4] or process control, has often a temporal dimension. There has been a lot of research in temporal dat...

Constraints are a natural mechanism for the specification of similarity queries on time-series data. However, to realize the expressive power of constraint programming in this context, one must provide the matching implementation technology for efficient indexing of very large data sets. In this paper, we formalize the intuitive notions of exact and approximate similarity between time-series patterns and data. Our definition of similarity extends the distance metric used in [2, 7] with invariance under a group of transformations. Our main observation is that the resulting, more expressive, set of constraint queries can be supported by a new indexing technique, which preserves all the desirable properties of the indexing scheme proposed in [2, 7].

Symbolic approaches attack the state explosion problem by introducing implicit representations that allow the simultaneous manipulation of large sets of states. The most commonly used representation in this context is the Binary Decision Diagram (BDD). This paper takes the point of view that other structures than BDD's can be useful for representing sets of values, and that combining implicit and explicit representations can be fruitful. It introduces a representation of complex periodic sets of integer values, shows how this representation can be manipulated, and describes its application to the state-space exploration of protocols. Preliminary experimental results indicate that the method can dramatically reduce the resources required for state-space exploration.

. The declarative programming paradigms used in constraint languages can lead to powerful extensions of Codd's relational data model. The development of constraint database query languages from logical database query languages has many similarities with the development of constraint logic programming from logic programming, but with the additional requirements of data efficient, set-at-a-time, and bottomup evaluation. In this overview of constraint query languages (CQLs) we first present the framework of [41]. The principal idea is that: "the k-tuple (or record) data type can be generalized by a conjunction of quantifier-free constraints over k variables". The generalization must preserve various language properties of the relational data model, e.g., the calculus/algebra equivalence, and have time complexity polynomial in the size of the data. We next present an algebra for dense order constraints that is simpler to evaluate than the calculus described in [41], and we sharpen some of...

We survey a number of approaches to the problem of finite representation of infinite temporal extensions. Two of them, Datalog 1S and Templog, are syntactical extensions of Datalog; the third is based on repetition and arithmetic constraints. We provide precise characterizations of the expressiveness and the computational complexity of these languages. We also describe query evaluation methods.

Temporal logic is obtained by adding temporal connectives to a logic language. Explicit references to time are hidden inside the temporal connectives. Different variants of temporal logic use different sets of such connectives. In this chapter, we survey the fundamental varieties of temporal logic and describe their applications in information systems. Several features of temporal logic make it especially attractive as a query and integrity constraint language for temporal databases. First, because the references to time are hidden, queries and integrity constraints are formulated in an abstract, representationindependent way. Second, temporal logic is amenable to efficient implementation. Temporal logic queries can be translated to an algebraic language. Temporal logic constraints can be efficiently enforced using auxiliary stored information. More general languages, with explicit references to time, do not share these properties. Recent research has proposed various implementation t...

This paper introduces a finite-automata based representation of Presburger arithmetic definable sets of integer vectors. The representation consists of concurrent automata operating on the binary encodings of the elements of the represented sets. This representation has several advantages. First, being automata-based it is operational in nature and hence leads directly to algorithms, for instance all usual operations on sets of integer vectors translate naturally to operations on automata. Second, the use of concurrent automata makes it compact. Third, it is insensitive to the representation size of integers. Our representation can be used whenever arithmetic constraints are needed. To il...

Time is unbounded by nature. A temporal predicate (one that varies with time) will thus often have an infinite extension. To store such a predicate in a database, one can either artificially restrict its extension to a finite set or, more desirably, use a formalism that allows the finite representation of at least some infinite temporal extensions. Several such formalisms have been proposed in the past few years. The formalism that extends traditional relational databases most directly is the generalized databases described in [KSW90]. There, database tuples are extended with an arbitrary number of additional columns carrying linear repeating points. These represent periodic sets of time points possibly constrained by linear inequalities. The query language proposed in [KSW90] is a multi-sorted first-order logic in which predicates have...