{"paper":{"title":"On the (Intuitionistic) Logic of Next-Token Prediction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Paul Tarau (University of North Texas)","submitted_at":"2026-08-08T14:08:14Z","abstract_excerpt":"We model in intuitionistic implicational logic the key enabler of today's GenerativeAI: the next-token prediction in autoregressive causal neural networks.\n  In our framework, next-token prediction corresponds to modus ponens, and sequence processing becomes constructive proof extension under the Curry-Howard correspondence. Our Prolog-based specialized theorem provers validate fundamental properties of the neural models, among which relations between commutative vs. non-commutative sequencing  and single-token vs. multi-token prediction choices.\n  We derive a neural architecture equivalent to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08145","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.08145/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}