Higher-Order Logic Programming Languages with Constraints: A Semantics

Data mining discovers knowledge and useful information from large amounts of data stored in databases. With the increasing popularity of object-oriented database system in advanced database applications, it is significantly important to study the data mining methods for object-oriented database. This paper proposes that higher-order logic programming languages and techniques is very suitable for object-oriented data mining, and presents a framework for object-oriented data mining based on higher-order logic programming. Such a framework is inductive logic programming which adopts higher-order logic programming language Escher as knowledge representation formalism. In addition, Escher is a generalization of the attribute-value representation, thus many higher-order logic learners under this framework can be upgraded directly from corresponding propositional learners.

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Higher-Order Logic Programming

Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 5: Logic Programming ◽

10.1093/oso/9780198537922.003.0011 ◽

1998 ◽

Author(s):

Gopalan Nadathur ◽

Dale Miller

Keyword(s):

Logic Programming ◽

Programming Languages ◽

Functional Programming ◽

Ad Hoc ◽

Order Type ◽

Higher Order ◽

Order Logic ◽

Higher Order Logic ◽

Functional Programming Languages ◽

Logical Basis

Modern programming languages such as Lisp, Scheme and ML permit procedures to be encapsulated within data in such a way that they can subsequently be retrieved and used to guide computations. The languages that provide this kind of an ability are usually based on the functional programming paradigm, and the procedures that can be encapsulated in them correspond to functions. The objects that are encapsulated are, therefore, of higher-order type and so also are the functions that manipulate them. For this reason, these languages are said to allow for higher-order programming. This form of programming is popular among the users of these languages and its theory is well developed. The success of this style of encapsulation in functional programming makes is natural to ask if similar ideas can be supported within the logic programming setting. Noting that procedures are implemented by predicates in logic programming, higher-order programming in this setting would correspond to mechanisms for encapsulating predicate expressions within terms and for later retrieving and invoking such stored predicates. At least some devices supporting such an ability have been seen to be useful in practice. Attempts have therefore been made to integrate such features into Prolog (see, for example, [Warren, 1982]), and many existing implementations of Prolog provide for some aspects of higher-order programming. These attempts, however, are unsatisfactory in two respects. First, they have relied on the use of ad hoc mechanisms that are at variance with the declarative foundations of logic programming. Second, they have largely imported the notion of higher-order programming as it is understood within functional programming and have not examined a notion that is intrinsic to logic programming. In this chapter, we develop the idea of higher-order logic programming by utilizing a higher-order logic as the basis for computing. There are, of course, many choices for the higher-order logic that might be used in such a study. If the desire is only to emulate the higher-order features found in functional programming languages, it is possible to adopt a “minimalist” approach, i.e., to consider extending the logic of first-order Horn clauses— the logical basis of Prolog—in as small a way as possible to realize the additional functionality.

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