Valuations in Gödel Logic, and the Euler Characteristic
Pietro Codara,
Ottavio M. D'Antona,
Vincenzo Marra
Abstract:Using the lattice-theoretic version of the Euler characteristic introduced by V. Klee and G.-C. Rota in the Sixties, we define the Euler characteristic of a formula in Gödel logic (over finitely or infinitely many truth-values). We then prove that the information encoded by the Euler characteristic is classical, i.e. coincides with the analogous notion defined over Boolean logic. Building on this, we define many-valued versions of the Euler characteristic of a formula ϕ, and prove that they indeed provide info… Show more
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