{"paper":{"title":"Valuations in G\\\"{o}del Logic, and the Euler Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.LO"],"primary_cat":"cs.LO","authors_text":"Ottavio M. D'Antona, Pietro Codara, Vincenzo Marra","submitted_at":"2014-01-21T10:27:26Z","abstract_excerpt":"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 G\\\"{o}del 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 $\\varphi$, and prove that they indeed provide information about the logical status of $\\varphi$ in G\\\"{o}del logic. Specifi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5254","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}