{"paper":{"title":"A Linear Temporal Logic of Frequencies on Series of Events","license":"http://creativecommons.org/licenses/by/4.0/","headline":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system.","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Alessandro Giuseppe Buda, Giuseppe Primiero, Leonardo Ceragioli, Melissa Antonelli","submitted_at":"2026-04-12T14:52:24Z","abstract_excerpt":"This paper introduces LTLF, a temporal logic designed to express the frequency properties of event series in a natural but rigorous manner. By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers. The core novelty lies in the introduction of original modal quantifiers associated with a standard Kripke-style semantics. These quantifiers enable the explicit formalization of event series properties an"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the proposed Kripke-style semantics with added modal quantifiers can be defined consistently to capture both actual observed frequencies and ideal distributions without internal contradictions or loss of useful logical properties.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"LTLF adds measure-sensitive modal quantifiers to temporal logic for formalizing frequencies in event series and relating observed to ideal distributions.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5154656f5cd9b59879abacfd14b86dcf3adedcdfed8b41cf3cba7be750093d9b"},"source":{"id":"2604.10669","kind":"arxiv","version":2},"verdict":{"id":"d3bcff64-88a2-4654-b37b-0d0273a8eb3c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T15:50:06.604723Z","strongest_claim":"By introducing novel, measure-sensitive operators, LTLF allows for the evaluation of frequencies and the prediction of future occurrences, thus providing a formal framework to monitor and control quantitative systems, such as machine learning classifiers.","one_line_summary":"LTLF adds measure-sensitive modal quantifiers to temporal logic for formalizing frequencies in event series and relating observed to ideal distributions.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the proposed Kripke-style semantics with added modal quantifiers can be defined consistently to capture both actual observed frequencies and ideal distributions without internal contradictions or loss of useful logical properties.","pith_extraction_headline":"LTLF adds modal quantifiers to linear temporal logic so frequencies of events in sequences can be expressed and compared to ideal distributions inside one formal system."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.10669/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"}