The Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler characteristic on NM algebras, the algebraic counterpart of Nilpotent Minimum logic. Then, we introduce a new valuation, a modified version of the Euler characteristic we call idempotent Euler characteristic. We show that the new valuation encodes information about the formulas in NM propositional logic.
Valuations in Nilpotent Minimum Logic / P. Codara, D. Valota - In: International Symposium on Multiple-Valued Logic (ISMVL)Piscataway (NJ., USA) : Institute of Electrical and Electronics Engineers (IEEE), 2015. - ISBN 9781479917778. - pp. 90-95 (( Intervento presentato al 45. convegno International Symposium on Multiple-Valued Logic (ISMVL) tenutosi a Waterloo, ON, Canada nel 2015 [10.1109/ISMVL.2015.19].
Valuations in Nilpotent Minimum Logic
P. CodaraPrimo
;D. Valota
2015
Abstract
The Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler characteristic on NM algebras, the algebraic counterpart of Nilpotent Minimum logic. Then, we introduce a new valuation, a modified version of the Euler characteristic we call idempotent Euler characteristic. We show that the new valuation encodes information about the formulas in NM propositional logic.
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