A Linear Deduction System with Integrated Semantic Guidance

Guidance systems are central to the success of automated deduction systems. Semantic guidance systems are guidance systems that exploit semantic information when guiding the search of a deduction system. The general objective of this research has been to investigate how semantic guidance can be used to improve the performance of automated deduction systems. More specifically, this research has investigated how semantic guidance can be used to improve the performance of linear deduction systems. As semantic guidance has, until now, been considered unsuitable for use in linear deduction systems, the results presented in this thesis are noteworthy in automated deduction research. A new chain format linear deduction system, called Guided Linear Deduction (GLD), has been developed as part of this work. GLD improves upon existing linear deduction systems in several aspects. In the context of this research, an important feature in GLD is the provision of an explicit entry point for the incorporation of guidance systems. This entry point has been used to incorporate a semantic guidance system into GLD, to form the Semantically Guided Linear Deduction (SGLD) system. SGLD's semantic guidance system builds upon four separate developments, as follows. (i) Linear-input subset analysis, which is a method of determining some of the structure in GLD deductions. (ii) A truth value semantic deletion system for (chain format) linear deduction systems. This system uses linear-input subset analysis to determine when it can be applied. (iii) A sort value semantic deletion system that has the same format as the truth value deletion system. (iv) A heuristic function that uses semantic information to evaluate the quality of clauses in a deduction. The combination of the latter three of these developments forms the semantic guidance system used in SGLD. For any semantic guidance system to operate, an interpretive structure is required to store the semantic information used. It is desirable that the interpretive structure be representationally powerful, space efficient, effective in supplying semantic information and also user friendly. A new form of interpretive structure which fulfils these criteria has been developed. The new structures are called designations. SGLD has been implemented in Prolog. Each component of SGLD is of individual interest and their combination is unique in the field of automated deduction. The performance of SGLD has been investigated.