HILOG: A High-Order Logic Programming Language for Non-1NF Deductive Databases

A formal framework of a strongly typed logic programming language with high-order terms (HILOG) is developed which extends Logic Programming (LP) from First-Order Logic (FOL) and which generalizes deductive databases to handle non-normalized relations. To remedy the limitations of current approaches by treating complex objects as function terms of the FOL, we reformulate the key Logic Programming (LP) notions through the introduction of appropriate mathematical concepts such as partial containment, packing and unpacking. In this paper, we have developed the extended notion of the satisfaction, the existence of a minimal model closure, the uniqueness of a standard (packed) minimal model for a HILOG program, the model p-intersection theorem, and the extended least fixpoint characteristics of the HILOG minimal model. Therefore, HILOG provides a canonical framework for high-order LP in which semantics covers the key points of LP. HILOG Language has the capabilities of representing structured knowledge and type hierarchies which are important for integrating the LP notions to other programming systems for handling complex objects and for developing non-1NF deductive databases. An example is given to demonstrate the use of HILOG in representing structured knowledge and in deductive retrieval of complex objects.