{"paper":{"title":"Belief as Willingness to Bet","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LO","authors_text":"Bryan Renne, Jan van Eijck","submitted_at":"2014-12-16T17:34:25Z","abstract_excerpt":"We investigate modal logics of high probability having two unary modal operators: an operator $K$ expressing probabilistic certainty and an operator $B$ expressing probability exceeding a fixed rational threshold $c\\geq\\frac 12$. Identifying knowledge with the former and belief with the latter, we may think of $c$ as the agent's betting threshold, which leads to the motto \"belief is willingness to bet.\" The logic $\\mathsf{KB.5}$ for $c=\\frac 12$ has an $\\mathsf{S5}$ $K$ modality along with a sub-normal $B$ modality that extends the minimal modal logic $\\mathsf{EMND45}$ by way of four schemes r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5090","kind":"arxiv","version":2},"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"}