{"paper":{"title":"From Coalgebraic Determinization to Belief Construction for Partial Observability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The semantics of a partially observable system coincides with that of its belief coalgebra, and under further conditions matches its fully observable counterpart.","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Kazuki Watanabe, Mayuko Kori","submitted_at":"2026-04-28T08:16:30Z","abstract_excerpt":"The belief construction is a fundamental technique for transforming partially observable systems to fully observable ones while preserving the relevant semantics. It plays a central role in the analysis of partially observable systems, in particular partially observable Markov decision processes (POMDPs), which is a central model in artificial intelligence and formal verification. In this paper, we develop a coalgebraic framework for the belief construction. To handle observations categorically, we lift a monad to slice categories and introduce a belief decomposition that reorganizes states ac"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The semantics of a partially observable system coincides with that of the corresponding belief coalgebra; under further conditions the latter agrees with the semantics of its fully observable counterpart, recovering the standard equivalence between POMDPs and belief MDPs and obtaining a new equivalence for weighted transition systems with the multiset monad.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The monad can be lifted to the slice category in a way that preserves the relevant coalgebraic semantics, and the belief decomposition correctly reorganizes states by observations without altering the underlying behavior.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A coalgebraic generalization of the belief construction shows semantics of partially observable systems coincide with belief coalgebras, recovering POMDP equivalences and yielding a new equivalence for weighted transition systems with the multiset monad.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The semantics of a partially observable system coincides with that of its belief coalgebra, and under further conditions matches its fully observable counterpart.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"2920de623e01c9e61babe2da56ab0dfbf96f001ffc819f2f10ee3c696e231ba4"},"source":{"id":"2604.25355","kind":"arxiv","version":2},"verdict":{"id":"f8f86613-940c-4a60-a06e-5e1dcc24e8f2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T15:14:59.314513Z","strongest_claim":"The semantics of a partially observable system coincides with that of the corresponding belief coalgebra; under further conditions the latter agrees with the semantics of its fully observable counterpart, recovering the standard equivalence between POMDPs and belief MDPs and obtaining a new equivalence for weighted transition systems with the multiset monad.","one_line_summary":"A coalgebraic generalization of the belief construction shows semantics of partially observable systems coincide with belief coalgebras, recovering POMDP equivalences and yielding a new equivalence for weighted transition systems with the multiset monad.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The monad can be lifted to the slice category in a way that preserves the relevant coalgebraic semantics, and the belief decomposition correctly reorganizes states by observations without altering the underlying behavior.","pith_extraction_headline":"The semantics of a partially observable system coincides with that of its belief coalgebra, and under further conditions matches its fully observable counterpart."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.25355/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_compliance","ran_at":"2026-05-19T21:13:03.607943Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"d8fb0284ec58b280ebbd5a4e96fd1366e202c16ed945c03356a0e22b52ffcc31"},"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"}