Perspectives in deductive databases

AbstractI discuss my experiences, some of the work that I have done, and related work that influenced me, concerning deductive databases, over the last 30 years. I divide this time period into three roughly equal parts: 1957–1968, 1969–1978, 1979–present. For the first I describe how my interest started in deductive databases in 1957, at a time when the field of databases did not even exist. I describe work in the beginning years, leading to the start of deductive databases about 1968 with the work of Cordell Green and Bertram Raphael. The second period saw a great deal of work in theorem providing as well as the introduction of logic programming. The existence and importance of deductive databases as a formal and viable discipline received its impetus at a workshop held in Toulouse, France, in 1977, which culminated in the book Logic and Data Bases. The relationship of deductive databases and logic programming was recognized at that time. During the third period we have seen formal theories of databases come about as an outgrowth of that work, and the recognition that artificial intelligence and deductive databases are closely related, at least through the so-called expert database systems. I expect that the relationships between techniques from formal logic, databases, logic programming, and artificial intelligence will continue to be explored and the field of deductive databases will become a more prominent area of computer science in coming years

Cooperative answers in database systems

A major concern of researchers who seek to improve human-computer communication involves how to move beyond literal interpretations of queries to a level of responsiveness that takes the user's misconceptions, expectations, desires, and interests into consideration. At Maryland, we are investigating how to better meet a user's needs within the framework of the cooperative answering system of Gal and Minker. We have been exploring how to use semantic information about the database to formulate coherent and informative answers. The work has two main thrusts: (1) the construction of a logic formula which embodies the content of a cooperative answer; and (2) the presentation of the logic formula to the user in a natural language form. The information that is available in a deductive database system for building cooperative answers includes integrity constraints, user constraints, the search tree for answers to the query, and false presuppositions that are present in the query. The basic cooperative answering theory of Gal and Minker forms the foundation of a cooperative answering system that integrates the new construction and presentation methods. This paper provides an overview of the cooperative answering strategies used in the CARMIN cooperative answering system, an ongoing research effort at Maryland. Section 2 gives some useful background definitions. Section 3 describes techniques for collecting cooperative logical formulae. Section 4 discusses which natural language generation techniques are useful for presenting the logic formula in natural language text. Section 5 presents a diagram of the system

Semantics of Horn and disjunctive logic programs

AbstractVan Emden and Kowalski proposed a fixpoint semantics based on model-theory and an operational semantics based on proof-theory for Horn logic programs. They prove the equivalence of these semantics using fixpoint techniques. The main goal of this paper is to present a unified theory for the semantics of Horn and disjunctive logic programs. For this, we extend the fixpoint semantics and the operational or procedural semantics to the class of disjunctive logic programs and prove their equivalence using techniques similar to the ones used for Horn programs

Computing Stable and Partial Stable Models of Extended Disjunctive Logic Programs

In [Prz91], Przymusinski introduced the partial (or 3-valued) stable model semantics which extends the (2-valued) stable model semantics defined originally by Gelfond and Lifschitz [GL88]. In this paper we describe a procedure to compute the collection of all partial stable models of an extended disjunctive logic program. This procedure consists in transforming an extended disjunctive logic program into a constrained disjunctive program free of negation-by-default whose set of 2-valued minimal models corresponds to the set of partial stable models of the original program. (Also cross-referenced as UMIACS-TR-95-49

Semantic Query Optimization for Bottom-Up Evaluation

Semantic query optimization uses semantic knowledge in databases (represented in the form of integrity constraints) to rewrite queries and logic programs for the purpose of more efficient query evaluation. Much work has been done to develop various techniques for optimization. Most of it, however, is only applicable to top-down query evaluation strategies. Moreover, little attention has been paid to the cost of the optimization itself. In this paper, we address the issue of semantic query optimization for bottom-up query evaluation strategies with an emphasis on overall efficiency. We restrict our attention to a single optimization technique, join elimination. We discuss various factors that influence the cost of semantic optimization, and present two abstract algorithms for different optimization approaches. The first one pre-processes a query statically before it is evaluated; the second approach combines query evaluation with semantic optimization using heuristics to achieve the largest possible savings. (Also cross-referenced as UMIACS-TR-95-109

Updating Disjunctive Datbases via Model Trees

In this paper we study the problem of updating disjunctive databases, which contain indefinite data given as positive injunctive closes. We give correct algorithms for the insertion of a clause into and the deletion of a clause from such databases. Although the algorithms presented here are oriented towards model trees, they apply to any representation of minimal models. (Also cross-referenced as UMIACS-TR-95-11

Model Generation and State Generation for Disjunctive Logic Programs

This paper investigates two fixpoint approaches for minimal model reasoning with disjunctive logic programs DB. The first one, called model generation [4], is based on an operator TI defined on sets of Herbrand interpretations, whose least fixpoint is logically equivalent to the set of minimal Herbrand models of the program. The second approach, called state generation [12], uses a fixpoint operator TS based on hyperresolution. It operates on disjunctive Herbrand states and its least fixpoint is the set of logical consequences of DB, the so--called minimal model state of the program. We establish a useful relationship between hyperresolution by TS and model generation by TI. Then we investigate the problem of continuity of the two operators TS and TI. It is known that the operator TS is continuous [12], and so it reaches its least fixpoint in at most omega steps. On the other hand, the question of whether TI is continuous has been open. We show by a counterexample that TI is not continuous. Nevertheless, we prove that it converges towards its least fixpoint in at most omega steps too, as follows from the relationship that we show exists between hyperresolution and model generation. We define an iterative version of TI that computes the perfect model semantics of stratified disjunctive logic programs. On each stratum of the program, this operator converges in at most omega steps. Model generations for the stable semantics and the partial stable (and so the well--founded semantics) are respectively achieved by using this iterative operator together with the evidential transformation [3] and the 3-S transformation [16]. (Also cross-referenced as UMIACS-TR-95-99

Logic and Databases: a 20 Year Retrospective

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1..

SOME APPLICATIONS OF ORTHOGONAL SYSTEMS OF FUNCTIONS TO INTERPOLATION ANDANALYTIC CONTINUATION

Abstract not availabl