Formulas as Programs

We provide here a computational interpretation of first-order logic based on a constructive interpretation of satisfiability w.r.t. a fixed but arbitrary interpretation. In this approach the formulas themselves are programs. This contrasts with the so-called formulas as types approach in which the proofs of the formulas are typed terms that can be taken as programs. This view of computing is inspired by logic programming and constraint logic programming but differs from them in a number of crucial aspects. Formulas as programs is argued to yield a realistic approach to programming that has been realized in the implemented programming language ALMA-0 (Apt et al.) that combines the advantages of imperative and logic programming. The work here reported can also be used to reason about the correctness of non-recursive ALMA-0 programs that do not include destructive assignment.Comment: 34 pages, appears in: The Logic Programming Paradigm: a 25 Years Perspective, K.R. Apt, V. Marek, M. Truszczynski and D.S. Warren (eds), Springer-Verlag, Artificial Intelligence Serie

Negation as failure. II

AbstractThe use of the negation as failure rule in logic programming is often considered to be tantamount to reasoning from Clark's “completed data base” [2]. Continuing the investigations of Clark and Shepherdson [2,7], we show that this is not fully equivalent to negation as failure either using classical logic or the more appropriate intuitionistic logic. We doubt whether there is any simple and useful logical meaning of negation as failure in the general case, and study in detail some special kinds of data base where the relationship of the completed data base to negation as failure is closer, e.g. where the data base is definite Horn or hierarchic

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

Intensional Query Processing in Deductive Database Systems.

This dissertation addresses the problem of deriving a set of non-ground first-order logic formulas (intensional answers), as an answer set to a given query, rather than a set of facts (extensional answers), in deductive database (DDB) systems based on non-recursive Horn clauses. A strategy in previous work in this area is to use resolution to derive intensional answers. It leaves however, several important problems. Some of them are: no specific resolution strategy is given; no specific methodologies to formalize the meaningful intensional answers are given; no solution is given to handle large facts in extensional databases (EDB); and no strategy is given to avoid deriving meaningless intensional answers. As a solution, a three-stage formalization process (pre-resolution, resolution, and post-resolution) for the derivation of meaningful intensional answers is proposed which can solve all of the problems mentioned above. A specific resolution strategy called SLD-RC resolution is proposed, which can derive a set of meaningful intensional answers. The notions of relevant literals and relevant clauses are introduced to avoid deriving meaningless intensional answers. The soundness and the completeness of SLD-RC resolution for intensional query processing are proved. An algorithm for the three-stage formalization process is presented and the correctness of the algorithm is proved. Furthermore, it is shown that there are two relationships between intensional answers and extensional answers. In a syntactic relationship, intensional answers are sufficient conditions to derive extensional answers. In a semantic relationship, intensional answers are sufficient and necessary conditions to derive extensional answers. Based on these relationships, the notions of the global and local completeness of an intensional database (IDB) are defined. It is proved that all incomplete IDBs can be transformed into globally complete IDBs, in which all extensional answers can be generated by evaluating intensional answers against an EDB. We claim that the intensional query processing provide a new methodology for query processing in DDBs and thus, extending the categories of queries, will greatly increase our insight into the nature of DDBs

Incorporating Stratified Negation into Query-Subquery Nets for Evaluating Queries to Stratified Deductive Databases

Most of the previously known evaluation methods for deductive databases are either breadth-first or depth-first (and recursive). There are cases when these strategies are not the best ones. It is desirable to have an evaluation framework for stratified DatalogN that is goal-driven, set-at-a-time (as opposed to tuple-at-a-time) and adjustable w.r.t. flow-of-control strategies. These properties are important for efficient query evaluation on large and complex deductive databases. In this paper, by incorporating stratified negation into so-called query-subquery nets, we develop an evaluation framework, called QSQNSTR, with such properties for evaluating queries to stratified DatalogN databases. A variety of flow-of-control strategies can be used for QSQNSTR. The generic evaluation method QSQNSTR for stratified DatalogN is sound, complete and has a PTIME data complexity