Inference Algebra (IA): A Denotational Mathematics for Cognitive Computing and Machine Reasoning (II)

Inference as the basic mechanism of thought is abilities gifted to human beings, which is a cognitive process that creates rational causations between a pair of cause and effect based on empirical arguments, formal reasoning, and/or statistical norms. It's recognized that a coherent theory and mathematical means are needed for dealing with formal causal inferences. Presented is a novel denotational mathematical means for formal inferences known as Inference Algebra (IA) and structured as a set of algebraic operators on a set of formal causations. The taxonomy and framework of formal causal inferences of IA are explored in three categories: a) Logical inferences; b) Analytic inferences; and c) Hybrid inferences. IA introduces the calculus of discrete causal differential and formal models of causations. IA enables artificial intelligence and computational intelligent systems to mimic human inference abilities by cognitive computing. A wide range of applications of IA are identified and demonstrated in cognitive informatics and computational intelligence towards novel theories and technologies for machine-enabled inferences and reasoning. This work is presented in two parts. The inference operators of IA as well as their extensions and applications will be presented in this paper; while the structure of formal inference, the framework of IA, and the mathematical models of formal causations has been published in the first part of the paper in IJCINI 5(4).