Randomization of Lukasiewicz 3-ValuedPpropositional Logic System

In quantitative logic, every atomic formula has the same truth degree. To overcome the shortcomings of truth degree, this paper gives randomized truth degree by introducing randomized mapping in Lukasiewicz three-valued propositional logic. Randomized truth degree is a generalization of truth degree, and the role of the different atomic formula is reflected in it. Based on randomized truth degree, randomized logic pseudo-metric is obtained and it is proved that randomized logic pseudo-metric is also an extension of metric space in quantified logic. Randomized truth degree is a combination of quantitative logic and probability logic and is also a generalization of probabilities of formulas in classical propositional logic.