Classical and Symbolic Logic

In everyday life human beings make many predictions especially on the basis of qualitative data and past experiences. Additionally, expert opinions help to shape and to refine such predictions besides the mutual discussion and confidence. In predictions there are similarities, which are the input information about the phenomenon concerned, output clues and the logical connectivity between these two sources of information. On the basis of certain clues, it is possible to make judgments about output information. The default of these judgments is the commonly available scientific thinking and its sublime version of logic (classical or fuzzy) leading to rational results. This provides ability for any individual to develop actuarial models for various real-life prediction problems. 

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Both classical and symbolic logic systans do not care for uncertainty, and their inferences are all certain, which gives the impression to engineers that they are also correct and valid universally. However, since four decades Loth Asker Zadeh [12] proposed a logic with uncertainty ingredients that is the fuzzy logic, which is bound to be used more frequently in future. 

CPNs model the system structure and its dynamic behavior in the same model. The dynamic behavior is modelled thanks to token evolution. After each transition firing, some tokens are consumed and some other are produced. This notion of production/consumption cannot he expressed in classical logic, that is why the mill was preferred. On the other hand, unlike Ordinary Petri Nets, token in CPN isofacertain type (color)and belongs to a set of this type (color set) and is transformed by arc expressions. So the translation from CPN to mill must respect these properties. That is why, the FirstOrder mill (MILL I) is used for the translation. CPN Places are expressed in mill i by imary relation symbols (Propositional variables) which allow... 

Boole s seminal contribution to information processing is widely appreciated. Following his analysis of language in terms of the truth or falsehood of elementary statements, the representation of truth or falsehood with the symbols 0 and 1 allowed algebraic manipulation and analysis so that Aristotle s classical logic could be greatly extended. Subsequently, these ideas evolved into Boolean logic where... 

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