Similarity Logic And Translations

A similarity-based fuzzy logic was proposed by M.S.Ying in [10] and successively investigated in [2]. The basic idea is that we can make ”approximate” reasoning by allowing an inference rule to work also in the case the antecedent clauses match only approximately previously proven formulas. Some tentative to applying such an idea to logic programming was proposed in [1], [6] and [7]. In this note we investigate the possibility of applying the notion of ”translation” which is on the basis of several abstract treatment of logic (see, for example, [4], [3], [5], [8]) to the similarity-based logic. This since any similarity relation enables us to define a family of translations. We refer to classical first order logic as defined, as an example, by E. Mendelson in [4]. In particular, we define the class of well-formed formulae (wff ) by assuming that if α and β are wff then (¬α), (α ∧ β), (α ∨ β), and (∀xiα) are wff too. As usual, sometimes we reduce the number of unnecessary parethesis.