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However, if we renounce standard completeness, we can study the logic whose semantics is provided by those MTL chains whose monoidal operation is the drastic product. This logic is called ${\\rm S}_{3}{\\rm MTL}$ in [NOG06]. In this note we justify the study of this logic, which we rechristen DP (for drastic product), by mean"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.7166","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-06-27T12:27:48Z","cross_cats_sorted":[],"title_canon_sha256":"d7ca093eb190ce1bfe4a611c34777c4992ec6aaa5031be1c92850ccd8c42da18","abstract_canon_sha256":"ba18472913e0ef8036269cbe5fce9f027ddf138314e7159d6cd10628743c4a88"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:53.939246Z","signature_b64":"6H0ODRJeKNB8SD/Y5WCQKmLSG0g/hhdGC5B8gb+mBlClQsnAcRCburTFz/Bl9YSBWdq48Rvc62fUzw/LC92uBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4b0faf615fa8035c461e1b0befdc9cbe245c92f412e5a7271b4665fc59180ef","last_reissued_at":"2026-05-18T02:48:53.938671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:53.938671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on drastic product logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Diego Valota, Matteo Bianchi, Stefano Aguzzoli","submitted_at":"2014-06-27T12:27:48Z","abstract_excerpt":"The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. 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