The sense of approximate reasoning within fuzzy logic has given rise to speculation as to whether precise reasoning within classical logic can even be considered a feasible way of handling most of the world’s problems. Now, another question can be raised; can fuzzy logic, by itself, justify/handle the sort of uncertainty found in problems that belong to the class of open world problems? This family of problems corresponds to the case of ambiguous mathematical theories mainly due to the fact that there is just imperfect/incomplete information about them. Recently, Zadeh introduced an extension of fuzzy logic, claimed to bridge the gaps in conventional approaches to the open world problems. In this paper, we present a basic background of extended fuzzy logic (FLe). We address several main concepts such as f-transformation and f-validity, enhance the definition of generalized constraints, and propose that FLe’s rules have two layers: one based on the implication model and another based on the conjunction model. In addition, we explore how FLe can handle those conditions described in antonym pairs as well as those occurred without considering rationality in the framework. Both cases challenge most decision-making theories. We also suggest FLe and second-order probability are f-complementary rather than fcompetitive. The paper asserts that FLe is highly capable of constructing mathematical solutions to problems (including computational problems) that are stated in natural language.

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