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

Applications of Intuitionistic Logic in Answer Set Programming

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.Comment: 30 pages, Under consideration for publication in Theory and Practice of Logic Programmin

Commonsense axiomatizations for logic programs

AbstractVarious semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas. The semantics of Clark, Fitting, and Kunen are characterized in this framework, and a finite first-order presentation of Kunen's semantics is described. A new axiom to represent “commonsense” reasoning is proposed for logic programs. It is shown that the well-founded semantics and stable models are definable with this axiom. The roles of domain augmentation and domain closure are examined. A “domain foundation” axiom is proposed to replace the domain closure axiom

Using Extended Logic Programs to Formalize Commonsense Reasoning

In this dissertation, we investigate how commonsense reasoning can be formalized by using extended logic programs. In this investigation, we first use extended logic programs to formalize inheritance hierarchies with exceptions by adopting McCarthy's simple abnormality formalism to express uncertain knowledge. In our representation, not only credulous reasoning can be performed but also the ambiguity-blocking inheritance and the ambiguity-propagating inheritance in skeptical reasoning are simulated. In response to the anomalous extension problem, we explore and discover that the intuition underlying commonsense reasoning is a kind of forward reasoning. The unidirectional nature of this reasoning is applied by many reformulations of the Yale shooting problem to exclude the undesired conclusion. We then identify defeasible conclusions in our representation based on the syntax of extended logic programs. A similar idea is also applied to other formalizations of commonsense reasoning to achieve such a purpose

Dmodel and Dalgebra : a data model and algebra for office documents

This dissertation presents a data model (called D_model) and an algebra (called D_ algebra) for office documents. The data model adopts a very natural view of modeling office documents. Documents are grouped into classes; each class is characterized by a frame template , which describes the properties (or attributes) for the class of documents. A frame template is instantiated by providing it with values to form a frame instance which becomes the synopsis of the document of the class associated with the frame template. Different frame instances can be grouped into a folder. Therefore, a folder is a set of frame instances which need not be over the same frame template. The D_model is a dual model which describes documents using two hierarchies: a document type hierarchy which depicts the structural organization of the documents and a folder organization, which represents the user\u27s real-world document filing system. The document type hierarchy exploits structural commonalities between frame templates. Such a hierarchy helps classify various documents. The folder organization mimics the user\u27s real-world document filing system and provides the user with an intuitively clear view of the filing system. This facilitates document retrieval activities. The D_algebra includes a family of operators which together comprise the fundamental query language for the D_model. The algebra provides operators that can be applied to folders which contain frame instances of different types. It has more expressive power than the relational algebra. It extends the classical relational algebra by associating attributes with types, and supporting attribute inheritance. Aggregate operators which can be applied to different frame instances in a folder are also provided. The proposed algebra is used as a sound basis to express the semantics of a high level query language for a document processing system, called TEXPROS. In the model, frame instances can represent incomplete information. Null values of the form value at present unknown are used to denote missing information in some fields of the incomplete frame instances. This dissertation provides a proof-theoretic characterization of the data model and defines the semantics of the null values within the proof-theoretic paradigm

Disjunctively incomplete information in relational databases: modeling and related issues

In this dissertation, the issues related to the information incompleteness in relational databases are explored. In general, this dissertation can be divided into two parts. The first part extends the relational natural join operator and the update operations of insertion and deletion to I-tables, an extended relational model representing inclusively indefinite and maybe information, in a semantically correct manner. Rudimentary or naive algorithms for computing natural joins on I-tables require an exponential number of pair-up operations and block accesses proportional to the size of I-tables due to the combinatorial nature of natural joins on I-tables. Thus, the problem becomes intractable for large I-tables. An algorithm for computing natural joins under the extended model which reduces the number of pair-up operations to a linear order of complexity in general and in the worst case to a polynomial order of complexity with respect to the size of I-tables is proposed in this dissertation. In addition, this algorithm also reduces the number of block accesses to a linear order of complexity with respect to the size of I-tables;The second part is related to the modeling aspect of incomplete databases. An extended relational model, called E-table, is proposed. E-table is capable of representing exclusively disjunctive information. That is, disjunctions of the form P[subscript]1\mid P[subscript]2\mid·s\mid P[subscript]n, where ǁ denotes a generalized logical exclusive or indicating that exactly one of the P[subscript]i\u27s can be true. The information content of an E-table is precisely defined and relational operators of selection, projection, difference, union, intersection, and cartisian product are extended to E-tables in a semantically correct manner. Conditions under which redundancies could arise due to the presence of exclusively disjunctive information are characterized and the procedure for resolving redundancies is presented;Finally, this dissertation is concluded with discussions on the directions for further research in the area of incomplete information modeling. In particular, a sketch of a relational model, IE-table (Inclusive and Exclusive table), for representing both inclusively and exclusively disjunctive information is provided

Studies related to the process of program development

The submitted work consists of a collection of publications arising from research carried out at Rhodes University (1970-1980) and at Heriot-Watt University (1980-1992). The theme of this research is the process of program development, i.e. the process of creating a computer program to solve some particular problem. The papers presented cover a number of different topics which relate to this process, viz. (a) Programming methodology programming. (b) Properties of programming languages. aspects of structured. (c) Formal specification of programming languages. (d) Compiler techniques. (e) Declarative programming languages. (f) Program development aids. (g) Automatic program generation. (h) Databases. (i) Algorithms and applications

Computing Protected Circumscription

: This paper deals with computing circumscription in the case of Horn data with addi ional protection (indefinite data), an intermediate investigation between Reiter's result on predicate a c completion and Lifschitz's efforts to make general (formula) circumscription more efficient as omputational tool. Reiter has shown a close tie between McCarthy's circumscription and Clark's - t predicate completion. Here we investigate a similar tie between an extended version of circumscrip ion involving protected data, and an extended version of predicate completion. When we have a e u fully ground atomic protected theory, we show that an extension to the relational algebra can b sed to obtain all (and only) correct answers. When general Horn axioms are added to the protected e c theory, we show that Horn axioms also can be used to compute sound answers; however, som orrect answers will not be found. 1. Introduction During the past several years, a number of notions have been developed surroundi..