Decomposability and Its Role in Parallel Logic-Program Evaluation

This paper is concerned with the issue of parallel evaluation of logic programs. We define the concept of program decomposability, which means that the load of evaluation can be partitioned among a number of processors, without a need for communication among them. This in turn results in a very significant speed-up of the evaluation process. Some programs are decomposable, whereas others are not. We completely syntactically characterize three classes of single rule programs with respect to decomposability: nonrecursive, simple linear, and simple chain programs. We also establish two sufficient conditions for decomposability

Massively parallel reasoning in transitive relationship hierarchies

This research focuses on building a parallel knowledge representation and reasoning system for the purpose of making progress in realizing human-like intelligence. To achieve human-like intelligence, it is necessary to model human reasoning processes by programs. Knowledge in the real world is huge in size, complex in structure, and is also constantly changing even in limited domains. Unfortunately, reasoning algorithms are very often intractable, which means that they are too slow for any practical applications. One technique to deal with this problem is to design special-purpose reasoners. Many past Al systems have worked rather nicely for limited problem sizes, but attempts to extend them to realistic subsets of world knowledge have led to difficulties. Even special purpose reasoners are not immune to this impasse. In this work, to overcome this problem, we are combining special purpose reasoners with massive We have developed and implemented a massively parallel transitive closure reasoner, called Hydra, that can dynamically assimilate any transitive, binary relation and efficiently answer queries using the transitive closure of all those relations. Within certain limitations, we achieve constant-time responses for transitive closure queries. Hydra can dynamically insert new concepts or new links into a. knowledge base for realistic problem sizes. To get near human-like reasoning capabilities requires the possibility of dynamic updates of the transitive relation hierarchies. Our incremental, massively parallel, update algorithms can achieve almost constant time updates of large knowledge bases. Hydra expands the boundaries of Knowledge Representation and Reasoning in a number of different directions: (1) Hydra improves the representational power of current systems. We have developed a set-based representation for class hierarchies that makes it easy to represent class hierarchies on arrays of processors. Furthermore, we have developed and implemented two methods for mapping this set-based representation onto the processor space of a Connection Machine. These two representations, the Grid Representation and the Double Strand Representation successively improve transitive closure reasoning in terms of speed and processor utilization. (2) Hydra allows fast rerieval and dynamic update of a large knowledge base. New fast update algorithms are formulated to dynamically insert new concepts or new relations into a knowledge base of thousands of nodes. (3) Hydra provides reasoning based on mixed hierarchical representations. We have designed representational tools and massively parallel reasoning algorithms to model reasoning in combined IS-A, Part-of, and Contained-in hierarchies. (4) Hydra\u27s reasoning facilities have been successfully applied to the Medical Entities Dictionary, a large medical vocabulary of Columbia Presbyterian Medical Center. As a result of (1) - (3), Hydra is more general than many current special-purpose reasoners, faster than currently existing general-purpose reasoners, and its knowledge base can be updated dynamically