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

Inference as the basic mechanism of thought is one of the gifted abilities of human beings. It is recognized that a coherent theory and mathematical means are needed for dealing with formal causal inferences. This paper presents a novel denotational mathematical means for formal inferences known as Inference Algebra (IA). IA is 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 on Boolean, fuzzy, and general logic causations; (b) Analytic inferences on general functional, correlative, linear regression, and nonlinear regression causations; and (c) Hybrid inferences on qualification and quantification causations. IA introduces a calculus of discrete causal differential and formal models of causations; based on them nine algebraic inference operators of IA are created for manipulating the formal causations. IA is one of the basic studies towards the next generation of intelligent computers known as cognitive computers. 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.