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A model is a procedure for making inferences. An inference may be “correct” or “incorrect”; ideally, a model makes only correct inferences. To ensure that this happens, the builder of a model needs principles that discriminate correct from incorrect inferences. Logic postulates the existence of these principles.
The principles that discriminate are called “the principles of reasoning.” Logic is the science of these principles.
In the branch of logic called the “deductive” logic, it is axiomatic that every proposition has a variable which is called its “truth-value”; the value of the truth-value is true or it is false. In reality, though, one observes that a proposition may be neither true nor false but rather may be true in a proportion of instances in which it is asserted lying between 0% and 100%; thid proportion is called the “probability” of the proposition. The deductive logic may be generalized to conform to this reality by replacement of the axiom that every proposition has a true-value by the axiom that every proposition has a probability; this generalization produces the so-called “probabilistic” logic. Strong evidence supports the contention that logic and the probabilistic logic are equivalent.