Formal Inferences

ion is a gifted capability of human beings. Abstraction is a basic cognitive process of the brain at the meta cognitive layer according to the Layered Reference Model of the Brain (LRMB) (Wang, 2003a, 2007c; Wang, Liu, & Wang, 2003, 2006). Only by abstraction can important theorems and laws about the objects under study be elicited and discovered from a great variety of phenomena and empirical observations in an area of inquiry. Definition 2: Inferences are a formal cognitive process that reasons a possible causality from given premises based on known causal relations between a pair of cause and effect proven true by empirical arguments, theoretical inferences, or statistical regulations. Mathematical logic, such as propositional and predicate logic, provide a powerful means for logical reasoning and inference on truth and falsity (Hurley, 1997; Schoning, 1989; Sperschneider & Antoniou, 1991; Van Heije� noort, 1997). Definition 3. An argument  is an assertion that yields () a proposition Q called the conclusion from a given finite set of propositions known as the premises P1, P2, ..., Pn, that is: BL  (P1BL ∧ P2BL ∧ ... ∧ PnBL  QBL)BL (1) where the argument and all propositions are in type Boolean (BL). Hence, BL = T called a valid argument, otherwise it is a fallacy, that is, BL = F. Equation 1 can also be denoted in the fol� lowing inference structure:  1 2 ... n Premises P P P Conclusion Q  BL BL BL BL BL BL BL (2) Example 1 The following expressions are concrete argu� ments: a. A concrete deductive argument 1 2 Information processing is an intelligent behavior ( ). Computer is able to process information ( ). Computer is an itelligent machine ( ). 1 P P