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This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.

Artificial intelligence --- Mathematical theory of computation --- Computer programming / software development --- Software Engineering --- Artificial Intelligence --- Mathematical Logic and Formal Languages --- Logics and Meanings of Programs --- Formal Languages and Automata Theory --- Computer Science Logic and Foundations of Programming --- automata theory --- boolean functions --- computer programming --- first order logic --- formal languages --- formal logic --- logic programming --- model checking --- program verification --- semantics --- software architecture --- software design --- software quality --- software verification --- theorem provers --- theorem proving --- Computer programming / software engineering --- Computer architecture & logic design

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This volume containsthe full papers presentedat the 12th InternationalConf- ence on Logic for Programming, Arti?cial Intelligence, and Reasoning (LPAR), held 2-6 December 2006,in MontegoBay,Jamaica.The callfor papersattracted 108 full paper submissions, each of which were reviewed by at least three - viewers. The Program Committee accepted the 46 papers that appear in these proceedings. The conference program also included 4 invited talks, by Tom Ball of Microsoft Research, Doug Lenat of Cycorp, Roberto Nieuwenhuis of the U- versidad Polit´ ecnica de Cataluna ˜ , and Allen Van Gelder of the University of California at Santa Cruz. Papers or abstracts for the invited talks are in these proceedings. In addition to the main program, the conference o?ered a short paper track, which attracted 13 submissions, of which 12 were accepted, and the Workshop on Emperically Successful Higher Order Logic (ESHOL). Thanks go to: the authors (of both accepted and rejected papers); the P- gramCommitteeandtheirreviewers;theinvitedspeakers;ChristophBenzmuller ¨ , John Harrison, and Carsten Schur ¨ mann for organizing ESHOL; Celia Alleyne- Ebanks for administering the conference in Jamaica; the Honorable Minister Phillip Paulwell of the Ministry of Commerce, Science and Technology for op- ing the conference (and Daphne Simmonds for introducing us to the minister); the Mona Institute of Applied Sciences at the University of the West Indies for their support; Microsoft Research for sponsorship of student regsitrations; the Kurt Godel ¨ Society for taking registrations; and EasyChair for hosting the review process.

Mathematical logic --- Computer science --- Programming --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- programmeren (informatica) --- wiskunde --- software engineering --- logica --- robots

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Software engineering. --- Artificial intelligence. --- Computer programming. --- Computer logic. --- Mathematical logic. --- Software Engineering/Programming and Operating Systems. --- Artificial Intelligence. --- Programming Techniques. --- Software Engineering. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- Logic programming --- Automatic theorem proving --- Artificial intelligence

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Software engineering. --- Artificial intelligence. --- Computer programming. --- Computer logic. --- Mathematical logic. --- Software Engineering/Programming and Operating Systems. --- Artificial Intelligence. --- Programming Techniques. --- Software Engineering. --- Logics and Meanings of Programs. --- Mathematical Logic and Formal Languages. --- Logic programming --- Automatic theorem proving --- Artificial intelligence