Symbolic logic, propositions

Even thongh the general linguistic structure of the propositions remains the same their symbolic counterparts provide shorter expressions. For example, antecedent part of a proposition can be symbolized as A and consequent part as B, and hence, a simple proposition in symbolic logic can be expressed as,... 

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... 

The algebra of sets, or set theory, includes such fundamental mathematical concepts as set cardinality and subsets, which are a part of the study of various levels of mathematics from arithmetic to calculus and beyond. The algebra of propositions (logic or propositional calculus) was developed to fecilitate the reasoning process by providing a way to symbolically represent statements and to perform calculations based on defined operations, properties, and truth tables. Logic is studied in philosophy, as well... 

Computer Circuits. Shannon showed how logic could be used to design and simplify electric circuits. For example, consider a circuit with switches p and q that can be open or closed, corresponding to the Boolean binary elements, 0 and 1. A series circuit corresponds to a conjunction because both switches must be closed for electric current to flow. A circuit where electricity flows whenever at least one of the switches is closed is a parallel circuit this corresponds to a disjunction. Because the complement for a given switch is a switch in the opposite position, this corresponds to a negation table. When a circuit is represented in symbolic notation, its simplification may use the laws of logic, such as De Morgan s laws. The simplification may also use tables in the same way as the analysis of the equivalence of propositions. 

Propositions have also formal logic as objects of a formal language. The form of a proposition depends on the type of logic. The elements of such language are either variables (cause-reason-input or effect-result-output), predictive relationships, mathematical symbols and operators, functions, quantifiers and constants. One can propose his/her view of point about an event and then s/he must defend it against the critical debates of others. 

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