Formal Solution to Systems of Interval Linear or Non-Linear Equations

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This is the first of two papers which present the Modal Interval Analysis as a framework where the search and interpretation of formal solutions for a set of simultaneous interval linear or non-linear equations is started on, together with the interval estimations for sets of solutions of real-valued systems in which coefficients and right-hand sides belong to certain intervals. The main purpose of this first paper is to show that the modal intervals are a suitable tool to approach problems where logical reference appear. Thus, it is possible to give a logical meaning to general solutions of the system of equations, obtained, in the linear case, by means of an algorithm whose convergence conditions are studied.

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