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Generalized ortho negation. (English) Zbl 0979.03027
Wansing, Heinrich (ed.), Negation. A notion in focus. Proceedings volume of an interdisciplinary workshop held during the conference Analyomen 2 of the Gesellschaft für Analytische Philosophie (GAP), Leipzig, Germany, September 7-10, 1994. Berlin: De Gruyter. Perspekt. Anal. Philos. 7, 3-26 (1996).
Summary: There are various more or less familiar ways of defining negation in nonclassical logics, e.g., the Kripke definition of negation for intuitonistic logic, and Goldblatt’s definition of ortho negation (in a weak version of quantum logic). This last uses an orthogonality (“perp”) relation. In earlier papers I have already examined some relationships of these to each other and to some other definitions. In this paper I partly survey this earlier work and extend and systematize it, concentrating on the perp-style definition of negation. Things are made complicated by the fact that there can be various underlying order-structures (poset, semilattice, lattice, distributive lattice). For simplicity we shall stress the first and last of these.
For the entire collection see [Zbl 0964.00034].

MSC:
03B60 Other nonclassical logic
03G10 Logical aspects of lattices and related structures
03G12 Quantum logic
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