The term non-Aristotelian logic is used for any system of logic which does not divide statements into "true" and "false" statements, as opposed to Aristotle's two-valued system of logic.
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The concept of non-Aristotelian logic was used by A. E. van Vogt as the central theme in his The World of Null-A novels, based on his interest in Alfred Korzybski's General Semantics.
One common interpretation of the theory of Bayesian probability is precisely that probabilities describe degrees of belief in propositions.
See also: Multi-valued logic for another article on this topic.
Compare with: Non-monotonic logic where every statement is true or false, but not immutable.
Some developers of non-Aristotelian logics