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    Why the Logical Hexagon?Alessio Moretti - 2012 - Logica Universalis 6 (1-2):69-107.
    The logical hexagon (or hexagon of opposition) is a strange, yet beautiful, highly symmetrical mathematical figure, mysteriously intertwining fundamental logical and geometrical features. It was discovered more or less at the same time (i.e. around 1950), independently, by a few scholars. It is the successor of an equally strange (but mathematically less impressive) structure, the “logical square” (or “square of opposition”), of which it is a much more general and powerful “relative”. The discovery of the former did not raise interest, (...)
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  2. The geometry of standard deontic logic.Alessio Moretti - 2009 - Logica Universalis 3 (1):19-57.
    Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic (both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”, “permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s “logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a (...)
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  3.  58
    Was Lewis Carroll an Amazing Oppositional Geometer?Alessio Moretti - 2014 - History and Philosophy of Logic 35 (4):383-409.
    Some Carrollian posthumous manuscripts reveal, in addition to his famous ‘logical diagrams’, two mysterious ‘logical charts’. The first chart, a strange network making out of fourteen logical sentences a large 2D ‘triangle’ containing three smaller ones, has been shown equivalent—modulo the rediscovery of a fourth smaller triangle implicit in Carroll's global picture—to a 3D tetrahedron, the four triangular faces of which are the 3+1 Carrollian complex triangles. As it happens, such an until now very mysterious 3D logical shape—slightly deformed—has been (...)
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  4. Let’s be Logical (Studies in the Philosophy and History of Logic).Amirouche Moktefi, Alessio Moretti & Fabien Schang (eds.) - 2016 - London: College Publications.
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  5.  30
    The critics of paraconsistency and of many-valuedness and the geometry of oppositions.Alessio Moretti - 2010 - Logic and Logical Philosophy 19 (1-2):63-94.
    In 1995 Slater argued both against Priest’s paraconsistent system LP (1979) and against paraconsistency in general, invoking the fundamental opposition relations ruling the classical logical square. Around 2002 Béziau constructed a double defence of paraconsistency (logical and philosophical), relying, in its philosophical part, on Sesmat’s (1951) and Blanche’s (1953) “logical hexagon”, a geometrical, conservative extension of the logical square, and proposing a new (tridimensional) “solid of opposition”, meant to shed new light on the point raised by Slater. By using n-opposition (...)
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