Toward the logical formalization of approximate reasoning

The present work proposes an alternative approach to represent approximate reasoning inferences, called approximate rules of inference, where a mechanism is introduced in order to define the syntactic expression for the approximate inferred conclusions. The evaluation of the approximate validity of the inference is done through: 1) the numerical weights attached to the logical formulae; 2) the explicit inclusion of the notion of semantic approximation/equivalence between fuzzy propositions in the process of inference; and 3) considering the set of generative axioms be complemented by a rule of detachment (Modus Ponens). It is possible to see from the approximate rules of inference´s logical aspects and interpretations some potentialities of the present methodology to formalize and also to bridge the gap between the distinct approaches for existing approximate reasoning inferences