摘要：Inference as the basic mechanism of thought is one of the fundamental gifted abilities of human beings. Inference can be described as a cognitive process that creates rational causations between a pair of cause and effect based on empirical arguments, formal reasoning, and/or statistical regulations. Although there are various inference schemes and methods developed in a wide range of disciplines and applications, the framework of formal inferences can be described in five categories known as the relational, rule-based, logical, fuzzy logical, and causal inferences. With an extended expressive power, causal inferences are a set of advanced inference methodologies building upon other fundamental layers. The coherent framework of formal inferences reveals how human reasoning may be formalized and how machines may rigorously mimic the human inference mechanisms. This talk presents a theory of formal inferences and a framework of causal inferences based on the denotational mathematical structure known as Inference Algebra (IA). The taxonomy and framework of formal causal inferences are explored in three categories: a) Logical inferences on Boolean and fuzzy causations; b) Analytic inferences on general functional, correlative, linear regressive, and nonlinear regressive causations; and c) Hybrid inferences on qualitative and quantitative causations. As that of Boolean algebra for explicit logical reasoning and fuzzy logic for approximate and uncertainty reasoning, IA is created as a denotational mathematical structure with a set of algebraic operators on a set of formal causations or logical, analytic, and hybrid inferences. In IA, the general forms of causations are rigorously modeled as the Boolean, fuzzy, functional, correlative, linear-regression, nonlinear-regression, qualitative, and quantitative causations. Eight algebraic inference operators (K) of IA are modeled for manipulating the formal causations. IA elicits and formalizes the common and empirical reasoning processes of humans in a rigorous form, which enable AI and computational intelligent systems to mimic and implement similar inference abilities of the brain 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. |