Logic Programming with Pseudo-Resolution

Abstract

This paper presents a new proof technique for Automated Reasoning and Logic Programming which based on a generalization of the original Connection Graph paradigm of Kowalski and provides a methodology for Logic Programming in this framework.

We show how execution of a logic program can be executed in the logarithm of the number of steps taken by PROLOG and standard resolution theorem provers, or better.

This paper deals primarily with recursion, both in relation its exploitation and its explication. In dealing with explicit recursion, a modified “compartmentalized” connection graph framework emerges. In dealing with implicit recursion, a filter for the compartmentalized connection graph emerges which forces recursion to be explicitly represented.

The method is demonstrated on standard PROLOG examples.

The work reported here was in the main undertaken while the author was at Macquarie University NSW 2009 AUSTRALIA, and was supported in part by IMPACT Ltd, PETERSHAM NSW 2049 AUSTRALIA, the Australian Telecommunications and Electronics Research Board, and the Australian Research Council (Grant No. A48615954). The author is currently supported under ESPRIT BRA 3012: COMPULOG.