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Top1. Introduction
Causal inference is one of the central capabilities of human brains that play a crucial role in thinking, perception, reasoning, and problem solving (Zadeh, 1975; Payne & Wenger, 1998; Smith, 2001; Sternberg, 1998; Wang, 2003, 2007b, 2009b; Wang et al., 2009). Inferences are a cognitive process that reasons a possible causality from given premises between a pair of cause and effect. A causal inference can be conducted based on empirical observations, formal inferences, and/or statistical norms (Bender, 1996; Wang, 2007a, 2007b, 2008; Wilson & Keil, 2001).
A causation is usually a pair of (cause, effect). The causal relations may be 1-1, 1-n, n-1, and n-m, where n and m are integers greater than 1 that represent multiple relations. The cause in a causation is a premise state such as an event, phenomenon, action, behavior, or existence; while the effect is a consequent or conclusive state such as an event, phenomenon, action, behavior, or existence.
Formal logic inferences may be classified as deductive, inductive, abductive, and analogical inferences (Hurley, 1997; Ross, 1995; Schoning, 1989; Smith, 2001; Sternberg, 1998; Tomassi, 1999; van Heijenoort, 1997; Wang, 2007b, 2007c; Wang et al., 2009; Wilson & Keil, 2001). Deduction is a cognitive process by which a specific conclusion necessarily follows from a set of general premises. Induction is a cognitive process by which a general conclusion is drawn from a set of specific premises based on a set of samples in reasoning or experimental evidences. Abduction is a cognitive process by which an inference to the best explanation or most likely reason of an observation or event. Analogy is a cognitive process by which an inference about the similarity of the same relations holds between different domains or systems, and/or examines that if two things agree in certain respects then they probably agree in others.
Although logic inferences may be carried out on the basis of abstraction and symbolic reasoning with crisp sets and Boolean logic, more human inference mechanisms and rules such as those of intuitive, empirical, heuristic, and perceptive inferences, are fuzzy and uncertain, which are yet to be studied by fuzzy inferences on the basis of fuzzy sets and fuzzy logic (Zadeh, 1965, 1975, 2006; Wang, 2008).
This paper presents a theory of causation network toward machine-enabled inference and reasoning in cognitive informatics and computational intelligence. In the remainder of this paper, the taxonomy and mathematic models of causations are explored in Section 2 based on the causation network. The framework and properties of causal inferences are described in Section 3. Methodologies for uncertain causal inferences are elaborated in Section 4, followed by the analysis of humor and jokes as false causality.