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THE HOMEPAGE OF "NOT"
(N-Opposition Theory),
a.k.a. "Oppositional Geometry"
Stemming from works on the geometry of logical negation, “N-opposition
theory” (“NOT”, for short) is the name of a new branch of mathematics,
similar to, but different from graph theory and knot
theory. Also known as “the geometry of (logical) oppositions”, NOT gives
the general framework explaining what are things
like the “square of opposition” or "logical
square" (200 a.D.), the “logical
hexagon” (1951), the "logical cube"
(2004) and so on. One of the backbones of NOT, the theory of the “logical
poly-simplexes (of dimension m)”, is itself generated by an “ask-answer”
game-theoretical device, the “Aristotelian pQ-semantics” and its
“Aristotelian pQ-lattices”. NOT gives to mathematicians, logicians,
philosophers, linguists, ontologists, computer scientists and many others a
general framework for modelling and handling, formally but practically, any
“opposition phenomena”. The concept of “opposition” being a very fundamental
and pervasive one (recall that, for instance, “negation” – a highly important
concept – is just one particular kind of opposition), NOT has already found
applications in linguistics, modal logic,
many-valued logic, formal ontology, artificial intelligence and in the humanities.
And the field is growing. The NOT-workshops aim
at promoting the exchange, possibly interdisciplinary, between scholars concerned in various ways with opposition
phenomena and opposition structures.
Webmaster : homepage - e-mail. Website created the 16th March 2009
Last update: 04th/05/2012. The figure is taken from: Moretti, A.,
The Geometry of Logical Opposition, ch. 8 (2009)