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01790416 Mundici, Daniele Reasoning on imprecisely defined functions. Nov\'ak, Vil\'em (ed.) et al., Discovering the world with fuzzy logic. Heidelberg: Physica-Verlag. Stud. Fuzziness Soft Comput. 57, 331-366 (2000). 2000 Heidelberg: Physica-Verlag EN MV-algebras infinite-valued {\L}ukasiewicz logic inverse of an imprecisely specified function Standard functions assign to input elements single output elements. Formally, they can be described by cases (for finite range), i.e., by means of a standard partition of the input space $X$ induced from the range of the discussed function. The problem of finding an ``inverse function'' $(y \mapsto x)$ can be transformed into a deduction theorem of classical propositional logic. The reviewed book chapter generalizes the above problem to the case of imprecisely defined functions linked to MV-algebras and to infinite-valued {\L}ukasiewicz logic. The chapter starts with a motivating prologue including an example (recognition of hand-written letters), showing the need to compute the inverse of an imprecisely specified function $F$, but also showing its links to the infinite-valued calculus of {\L}ukasiewicz. Later it is shown that the infinite-valued consequence relation provides a universal algorithm for analyzing imprecisely defined functions. For example, the existence of a Turing machine is shown that is able to decide in a finite number of steps the satisfiability of the block-recognition problem (observe that the author works with finite MV-partitions). The results of this chapter promise interesting applications in computer-aided deduction and decision in several domains where imprecisely defined functions occur. Radko Mesiar (Bratislava)