Neumann: Failure as an Independent Logical Entity

„To permit failure as an independent logical entity means that one does not state the axioms in a rigorous manner. The axioms are not of the form: if A and B happen, C will follow. The axioms are always of this variety: if A and B happen, Cwill follow with a certain specified probability, D will follow with another specified probability, and so on. In other words, in every situation several alternatives are permitted with various probabilities. Mathematically it is simplest to say that anything can follow upon anything in accordance with a probability matrix. You may put your question in this manner: If A and B have happened, what is the probability that C will follow? This probability pattern gives you a probabilistic system of logics. Both artificial and natural automata should be discussed in this system as soon as there is any degree of involvement.“ (p. 58) #Neumann #failure #probability #automata

Neumann, John von, Theory of Self-Reproducing Automata; herausgegeben von Arthur W. Burks. Urbana/London: University of Illinois Press 1966.