{"paper":{"title":"Blending margins: The modal logic K has nullary unification type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Emil Je\\v{r}\\'abek","submitted_at":"2011-08-31T14:28:52Z","abstract_excerpt":"We investigate properties of the formula $p \\to \\Box p$ in the basic modal logic K. We show that K satisfies an infinitary weaker variant of the rule of margins $\\phi \\to \\Box\\phi / \\phi, \\neg\\phi$, and as a consequence, we obtain various negative results about admissibility and unification in K. We describe a complete set of unifiers (i.e., substitutions making the formula provable) of $p \\to \\Box p$, and use it to establish that K has the worst possible unification type: nullary. In well-behaved transitive modal logics, admissibility and unification can be analyzed in terms of projective for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6240","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"}