{"paper":{"title":"Expanding Belnap: dualities for a new class of default bilattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Andrew Craig, Brian A. Davey, Miroslav Haviar","submitted_at":"2018-08-29T04:50:44Z","abstract_excerpt":"Bilattices provide an algebraic tool with which to model simultaneously knowledge and truth. They were introduced by Belnap in 1977 in a paper entitled \\emph{How a computer should think}. Belnap argued that instead of using a logic with two values, for `true' ($t$) and `false' ($f$), a computer should use a logic with two further values, for `contradiction' ($\\top$) and `no information' ($\\bot$). The resulting structure is equipped with two lattice orders, a \\emph{knowledge order} and a \\emph{truth order}, and hence is called a \\emph{bilattice}.\n  Prioritised default bilattices include not onl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09636","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"}