“Setting” n-Opposition

Logica Universalis 2 (2):235-263 (2008)
Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory, exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced by any given modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal geometrisation of this logic
Keywords Opposition theory  classical modal logic  Blanché’s logical hexagon  Aristotle’s square  logical bisimplexes  logical cube   β-structure  tetraicosahedron   n-opposition   n-partition of the true  strong n-opposition  weak n-opposition  Moretti’fs modal graph  set translation of modal graphs
Categories (categorize this paper)
DOI 10.1007/s11787-008-0038-y
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 29,861
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
The Geometry of Standard Deontic Logic.Alessio Moretti - 2009 - Logica Universalis 3 (1):19-57.
The Power of the Hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Was Lewis Carroll an Amazing Oppositional Geometer?Alessio Moretti - 2014 - History and Philosophy of Logic 35 (4):383-409.

Add more citations

Similar books and articles
Added to PP index

Total downloads
56 ( #101,852 of 2,210,666 )

Recent downloads (6 months)
6 ( #82,527 of 2,210,666 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature