{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T12:06:03Z","timestamp":1753877163175,"version":"3.41.2"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T00:00:00Z","timestamp":1708905600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,6,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Filter pairs are a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with certain properties ensuring that the resulting logic is substitution invariant. Every substitution invariant logic arises from a filter pair. Particular classes of logics can be characterized as arising from special classes of filter pairs. We consider so-called congruence filter pairs, i.e. filter pairs for which the domain of the lattice homomorphism is a lattice of congruences for some quasivariety. We show that the class of logics admitting a presentation by such a filter pair is exactly the class of logics having an algebraic semantics. We study the properties of a certain Galois connection coming with such filter pairs. We give criteria for a congruence filter pair to present a logic in some classes of the Leibniz hierarchy by means of this Galois connection, and its interplay with the Leibniz operator.<\/jats:p>","DOI":"10.1093\/logcom\/exae002","type":"journal-article","created":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T19:35:11Z","timestamp":1708976111000},"source":"Crossref","is-referenced-by-count":0,"title":["Congruence filter pairs, equational filter pairs and adjoints"],"prefix":"10.1093","volume":"35","author":[{"given":"Peter","family":"Arndt","sequence":"first","affiliation":[{"name":"WE Informatik, University of D\u00fcsseldorf , Universit\u00e4tsstr. 1, D\u00fcsseldorf, 40225, Germany"}]},{"given":"Hugo","family":"Luiz Mariano","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of S\u00e3o Paulo , Rua do Mat\u00e3o, 1010, S\u00e3o Paulo, 05508-090, S\u00e3o Paulo, Brazil"}]},{"given":"Darllan Concei\u00e7\u00e3o","family":"Pinto","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Federal University of Bahia , Av. 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