A model of computation on multi-dimensional words, based on the overlapping operation, induces a categorical structure, to which a new type of logic corresponds, whose formulae express properties of computations in a language containing all first order formulae. While the resulting deductive system is strictly less powerful than (intuitionistic) first order logic, it is more powerful than coherent logic. The approach is illustrated through an example of an online game of map-colouring.
More-than-coherent logic for operations on images / P. Bottoni, A. Labella, S. Kasangian - In: Proceedings of the VLL 2009 workshop on Visual Languages and Logic / [a cura di] P. Cox, A. Fish, J. Howse. - Corvallis, Oregon, USA : IEEE, 2009 Sep 20. - pp. 2-17 (( Intervento presentato al 5. convegno Visual Languages and Logic (VLL) tenutosi a Corvallis nel 2009.
More-than-coherent logic for operations on images
S. KasangianUltimo
2009
Abstract
A model of computation on multi-dimensional words, based on the overlapping operation, induces a categorical structure, to which a new type of logic corresponds, whose formulae express properties of computations in a language containing all first order formulae. While the resulting deductive system is strictly less powerful than (intuitionistic) first order logic, it is more powerful than coherent logic. The approach is illustrated through an example of an online game of map-colouring.
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