Inference engine based on closure and join operators over Truth Table Binary Relations

• We propose a Conceptual Reasoning (CR) method for an inference engine.
• We map each rule to its corresponding Truth Table Binary Relation (TTBR).
• By combining TTBRs and applying Galois connection we derive new deductions.
• We propose a modular and cooperative CR to reduce the system complexity.

We propose a conceptual reasoning method for an inference engine. Starting from a knowledge base made of decision rules, we first map each rule to its corresponding Truth Table Binary Relation (TTBR), considered as a formal context. Objects in the domain of TTBR correspond to all possible rule interpretations (in terms of their truth value assignments), and elements in the range of TTBR correspond to the attributes. By using the ‘natural join’ operator in the ‘ContextCombine’ Algorithm, we combine all truth tables into a global relation which has the advantage of containing the complete knowledge of all deducible rules. By conceptual reasoning using closure operators, from the initial rules we obtain all possible conclusions with respect to the global relation. We may then check if expected goals are among these possible conclusions. We also provide an approximate solution for the exponential growth of the global relation, by proposing modular and cooperative conceptual reasoning. We finally present experimental results for two case studies and discuss the effectiveness of our approach.