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Dunn (and independently investigated by R.D. Epstein) as a variation on a time-honoured logical system by C.I. Lewis\u2019 student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is \u201canalytically contained\u201d in its antecedent. DAI has been investigated both proof-theoretically and model-theoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several different algebraic semantics for DAI, showing their equivalence with the known semantics by Dunn and Epstein. We also show that DAI is algebraisable and we identify its equivalent quasivariety semantics. This class turns out to be a linguistic and axiomatic expansion of <jats:italic>involutive bisemilattices<\/jats:italic>, a subquasivariety of which forms the algebraic counterpart of Paraconsistent Weak Kleene logic (PWK). This fact sheds further light on the relationship between containment logics and logics of nonsense.<\/jats:p>","DOI":"10.1007\/s10992-019-09502-2","type":"journal-article","created":{"date-parts":[[2019,2,13]],"date-time":"2019-02-13T00:58:52Z","timestamp":1550019532000},"page":"957-979","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Algebraic Analysis of Demodalised Analytic Implication"],"prefix":"10.1007","volume":"48","author":[{"given":"Antonio","family":"Ledda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Paoli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michele","family":"Pra Baldi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,2,13]]},"reference":[{"issue":"2","key":"9502_CR1","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/s11225-016-9689-5","volume":"105","author":"S Bonzio","year":"2017","unstructured":"Bonzio, S., Gil F\u00e9rez, J., Paoli, F., Peruzzi, L. 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