CHARACTERIZING THE 'PRINCIPLES' OF NON CONTRADICTION AND EXCLUDED MIDDLE IN [0,1]
Under an interpretation of the principles of non-contradiction and excluded-middle based on the concept of self-contradiction, this paper mainly deals with the principles' verification in the case of the unit interval of the real line. Such verification is done in the three following cases: (1) The unit interval is totally ordered by the restriction to it of the usual order of the real line, (2) the unit interval is partially ordered by the sharpened order, and (3) the unit interval is under a new particular preorder. The first case is immediately extended to characterize the case of fuzzy sets.
excluded middle non-contradiction unit interval fuzzy sets self-contradiction