{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,27]],"date-time":"2024-10-27T04:13:00Z","timestamp":1730002380523,"version":"3.28.0"},"publisher-location":"California","reference-count":0,"publisher":"International Joint Conferences on Artificial Intelligence Organization","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p>We extend the well-known representation theorem for interlaced bilattices to the broader class of weak interlaced bilattices. Based on this new theorem, we develop a fixpoint theory for non-monotone functions over weak infinitarily interlaced bilattices. Our theory generalizes classical fixpoint constructions introduced by Fitting, as-well-as recent results in the area of approximation fixpoint theory. We argue that the proposed theory has direct practical applications: we develop the semantics of higher-order logic programming with negation under an arbitrary weak infinitarily interlaced bilattice with negation, generalizing in this way recent work on the three-valued semantics of this formalism. We consider a line of research, initiated by Fitting, which investigates the structure of the consistent parts of bilattices in order to obtain natural generalizations of Kleene\u2019s three-valued logic. We demonstrate that the consistent parts of bilattices are closely connected to weak bilattices, generalizing previous results of Fitting and Kondo.<\/jats:p>","DOI":"10.24963\/kr.2024\/23","type":"proceedings-article","created":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T06:30:28Z","timestamp":1729924228000},"page":"243-252","source":"Crossref","is-referenced-by-count":0,"title":["Non-monotone Fixpoint Theory Based on the Structure of Weak Bilattices"],"prefix":"10.24963","author":[{"given":"Angelos","family":"Charalambidis","sequence":"first","affiliation":[{"name":"Harokopio University of Athens"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giannos","family":"Chatziagapis","sequence":"additional","affiliation":[{"name":"National and Kapodistrian University of Athens"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Babis","family":"Kostopoulos","sequence":"additional","affiliation":[{"name":"Harokopio University of Athens"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panos","family":"Rondogiannis","sequence":"additional","affiliation":[{"name":"National and Kapodistrian University of Athens"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"10584","event":{"name":"21st International Conference on Principles of Knowledge Representation and Reasoning {KR-2023}","theme":"Artificial Intelligence","location":"Hanoi, Vietnam","acronym":"KR-2024","number":"21","sponsor":["Artificial Intelligence Journal","Principles of Knowledge Representation and Reasoning Inc.","Academic College of Tel-Aviv","European Association for Artificial Intelligence","National Science Foundation"],"start":{"date-parts":[[2024,11,1]]},"end":{"date-parts":[[2024,11,8]]}},"container-title":["Proceedings of the TwentyFirst International Conference on Principles of Knowledge Representation and Reasoning"],"original-title":[],"deposited":{"date-parts":[[2024,10,26]],"date-time":"2024-10-26T06:30:33Z","timestamp":1729924233000},"score":1,"resource":{"primary":{"URL":"https:\/\/proceedings.kr.org\/2024\/23"}},"subtitle":[],"proceedings-subject":"Artificial Intelligence Research Articles","short-title":[],"issued":{"date-parts":[[2024,11]]},"references-count":0,"URL":"https:\/\/doi.org\/10.24963\/kr.2024\/23","relation":{},"subject":[],"published":{"date-parts":[[2024,11]]}}}