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Top1. Introduction
A causation is a relationship between a sole or multiple causes and a single or multiple effects. 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.
An inference is a cognitive process that deduces a conclusion, particularly a causation, based on evidences and reasoning. Causal inference is one of the central capabilities of human brains that plays a crucial role in thinking, perception, and problem solving (BISC, 2008; Sternberg, 1998; Payne & Wenger, 1998; Zadeh, 1975, 1998, 1999; Smith, 2001; Wang, 2002a, 2007b, 2008b, 2009a; Wang et al., 2006, 2009). The framework of causal inferences can be classified into four categories known as the intuitive, empirical, heuristic, and rational causalities (Wang, 2011a, 2011c, 2012c). Therefore, a causal inference can be conducted based on empirical observations, formal inferences, and/or statistical regulations (Bender, 1996; Wilson and Keil, 2001; Wang, 2007a, 2007b, 2008a, 2011a, 2011c, 2012c).
Formal logic inferences may be classified as deductive, inductive, abductive, and analogical inferences (Schoning, 1989; Sperschneider & Antoniou, 1991; Rose, 1995; Hurley, 1997; van Heijenoort, 1997; Tomassi, 1999; Smith, 2001; Wilson & Keil, 2001; Wang, 2007b; Wang et al., 2006, 2009, 2011xx). Although logic inferences can 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, 1971, 1975, 1983, 2004, 2006, 2008; Wang, 2008a) in the context of denotational mathematics (Wang, 2002b, 2007d, 2008a, 2008c, 2009c, 2011a, 2011c, 2012a, 2012b, 2012c, 2012h; Wang & Chiew, 2011) and cognitive computing (Wang, 2002a, 2003, 2007c, 2007e, 2008d, 2008e, 2009b, 2009d, 2009e, 2010a, 2010b, 2011b, 2011d, 2012d, 2012e, 2012f, 2012g, 2012i, 2012j, 2012k, 2012l, 2013a, 2013b, 2013c; Wang & Wang, 2006; Wang & Fariello, 2012; Wang et al., 2006, 2009, 2010a, 2010b, 2012).