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Logic and Databases Past, Present, and Future

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Logic and Databases Past, Present, and Future AI Magazine Volume 18 Number 3 (1997) (© AAAI) Articles Logic and Databases Past, Present, and Future Jack Minker ■ At a workshop held in Toulouse, France, in 1977, a number of other individuals also had the idea Gallaire, Minker, and Nicolas stated that logic and of using logic as a mechanism to handle data- databases was a field in its own right. This was the bases and deduction, and they were invited to first time that this designation was made. The participate in the workshop. The book Logic impetus for it started approximately 20 years ago and Data Bases (1978), edited by Gallaire and in 1976 when I visited Gallaire and Nicolas in Minker, was highly influential in the develop- Toulouse, France. In this article, I provide an ment of the field, as were the two volumes of assessment about what has been achieved in the 20 years since the field started as a distinct disci- Advances in Database Theory (Gallaire, Minker, pline. I review developments in the field, assess and Nocholas 1984a, 1981) that were the result contributions, consider the status of implementa- of two subsequent workshops held in Tou- tions of deductive databases, and discuss future louse. Another influential development was work needed in deductive databases. the article by Gallaire, Minker, and Nicolas (1984b), which surveyed work in the field to he use of logic and deduction in databas- that point. es, as noted in Minker (1988b), started in The use of logic in databases was received by Tthe late 1960s. Prominent among devel- the database community with a great deal of opments was work by Levien and Maron (1965) skepticism: Was deductive databases (DDBs) a and Kuhns (1967), and by Green and Raphael field? Did DDBs contribute to database theory (1968a), who were the first to realize the impor- or practice (Harel 1980)? The accomplishments tance of the Robinson (1965) resolution princi- I cite in this article are testaments to the fact ple for databases. For early uses of logic in data- that logic has contributed significantly both to bases, see Minker (1988b), and for detailed the theory and the practice of databases. It is descriptions of many accomplishments made clear that logic has everything to do with the in the 1960s, see Minker and Sable (1970). theory of databases, and many of those who A major influence on the use of logic in data- were then critical of the field have changed bases was the development of the field of logic their position. In the remainder of this article, programming: Kowalski (1974) promulgated I describe what I believe to be the major intel- the concept of logic as a programming lan- lectual developments in the field, the status of guage, and Colmerauer and his students devel- commercial implementations, and future oped the first Prolog interpreter (Colmerauer et trends. As we see, the field of logic and data- al. 1973). I refer to logic programs that are bases has been prolific. function free as deductive databases (DDBs), or as datalog. I do so because databases are finite Intellectual Contributions of structures. Most of the results discussed can be extended to include logic programming. Deductive Databases The impetus for the use of logic in databases In 1970, Codd (1970) formalized databases in came about through meetings in 1976 in terms of the relational calculus and the rela- Toulouse, France, when I visited Herve Gallaire tional algebra. He provided a logic language and Jean-Marie Nicolas while on sabbatical. and the relational calculus and described how The idea of a workshop on logic and databases to compute answers to questions in the rela- was also conceived at this time. It is clear that tional algebra and the relational calculus. Both Copyright © 1997, American Association for Artificial Intelligence. All rights reserved. 0738-4602-1997 / $2.00 FALL 1997 21 Articles the relational calculus and the relational alge- between logic-based systems and knowledge- bra provide declarative formalisms to specify based systems; (10) a formalization of how to queries. This was a significant advance over handle incomplete information in knowledge network and hierarchic systems (Ullman 1989, bases; and (11) a correspondence that relates 1988), which only provided procedural lan- alternative formalisms of nonmonotonic rea- guages for databases. The relational algebra and soning to databases and knowledge bases. the relational calculus permitted individuals I address the area of implementations of who were not computer specialists to write DDBs in Implementation Status of Deductive declarative queries and have the computer Databases, where commercial developments answer the queries. The development of syn- have not progressed as rapidly as intellectual tactic optimization techniques (Ullman 1989, developments. I then discuss some trends and 1988) permitted relational database systems to future directions in Emerging Areas and Trends. retrieve answers to queries efficiently and com- Formalizing pete with network and hierarchic implementa- Formalizing Database Theory tions. Relational systems have been enhanced Reiter (1984) was the first to formalize databas- databases to include views. A view, as used in relational es in terms of logic and noted that underlying through logic databases, is essentially a nonrecursive proce- relational databases were a number of assump- dure. There are numerous commercial imple- tions that were not made explicit. One has played a mentations of relational database systems for assumption deals with negation, that facts not significant large database manipulation and for personal known to be true in a relational database are computers. Relational databases are a forerun- assumed to be false. This assumption is the role in our ner of logic in databases. well-known closed-world assumption (CWA), understanding Although relational databases used the lan- expounded earlier by Reiter (1978). The of what guage of logic in the relational calculus, it was unique-name assumption states that any item in not formalized in terms of logic. The formal- a database has a unique name and that indi- constitutes ization of relational databases in terms of logic viduals with different names are different. The a database, and the extensions that have been developed domain-closure assumption states that there are are the focus of this article. Indeed, formaliz- no other individuals than those in the data- what is ing databases through logic has played a signif- base. Reiter then formalized relational databas- meant by icant role in our understanding of what consti- es as a set of ground assertions over a language tutes a database, what is meant by a query, L together with a set of axioms. The language a query, what is meant by an answer to a query, and L does not contain function symbols. These what is how databases can be generalized for knowl- assertions and axioms are as follows: … edge bases. It has also provided tools and Assertions: R(a1, , an), where R is an n-ary meant by an … answers to problems that would have been relational symbol in L, and a1 , an are constant answer to extremely difficult without the use of logic. symbols in L. … a query, In the remainder of the article, I focus on Unique-name axiom: If a1, , ap are all the some of the more significant aspects con- constant symbols of L, then and how tributed by logic in databases: (1) a formaliza- ≠ … ≠ ≠ … (a1 a2), , (a1 ap), (a2 a3), , tion of what constitutes a database, a query, ≠ databases (ap–1 ap) . and an answer to a query; (2) a realization that Domain-closure axiom: If a , …, a are all can be logic programming extends relational data- 1 p the constant symbols of L, then generalized bases; (3) a clear understanding of the seman- ; … for knowledge tics of large classes of databases that include X((X = a1) ~ ~ (X = ap)) . alternative forms of negation as well as dis- Completion Axioms: For each relational bases. junction; (4) an understanding of relationships 1 … 1 … m … m symbol R, if R(a1, an), , R(a 1, , a n) denote between model theory, fixpoint theory, and all facts under R, the completion axiom for R proof procedures; (5) an understanding of the is properties that alternative semantics can have … … → ;X1 ; Xn (R(X1, , Xn) and their complexity; (6) an understanding of 1 … 1 … (X1 = a1 ` ` Xn = an) ~ ~ (X1 = what is meant by integrity constraints and m … m = a ` ` Xn = a )) . how they can be used to perform updates, 1 n semantic query optimization (SQO), coopera- Equality Axioms: tive answering, and database merging; (7) a ;X(X = X) formalization and solutions to the update and ;X ;Y ((X = Y) → (Y = X)) view-update problems; (8) an understanding of ;X ;Y ;Z ((X = Y) ` (Y = Z) → (X = Z)) … … bounded recursion and recursion and how ;X1 ;Xn (P(X1, , Xn) ` … they can be implemented in a practical man- (X1 = Y1) ` ` (Xn = Yn) → … ner; (9) an understanding of the relationship P(Y1, Yn )) . 22 AI MAGAZINE Articles Example 1 illustrates the translation of a small database to logic. It is clear that handling such databases through conventional tech- Consider the family database to consist of the Father rela- niques will lead to a faster implementation. tion with schema Father(father, child) and the Mother rela- However, it serves to formalize previously tion with schema Mother(mother, child). Let the database be unformalized databases. The completion axiom was proposed by Clark FATHER father child (1978) as the basis for his negation-as-failure rule: It states that the only tuples that a relation j m can have are those that are specified in the rela- j s tional table. This statement is implicit in every relational database. The completion axiom MOTHER mother child makes this explicit. Another contribution of logic programs and databases is that the formal- r m ization of relational databases in terms of logic r s permits the definition of a query and an answer to a query to be defined precisely.
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