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A Discrete Representation of Lattice Frames

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Logic, Rationality, and Interaction (LORI 2019)

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Abstract

We characterize those doubly ordered frames that are embeddable into the canonical frames of their complex algebras defined by Alasdair Urquhart in his representation theorem for bounded general lattices [31]. Our result together with the topology-free version of Urquhart’s representation leads to a discrete (i.e. topology free) duality for bounded general lattices. We also show that doubly ordered frames are definable neither in a logic endowed with only a possibility operator nor a logic with only a sufficiency operator, but in a logic based on mixed algebras with both a possibility and a sufficiency operator.

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Acknowledgements

We are grateful to Alasdair Urquhart for stimulating discussions. We also thank the anonymous referees for careful reviewing and helpful suggestions. I. Düntsch gratefully acknowledges support by the National Natural Science Foundation of China, Grant No. 61976053.

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Author notes

  1. Ivo Düntsch

    Present address: Department of Computer Science, Brock University, St. Catharines, ON, Canada

Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian, China

    Ivo Düntsch

  2. National Institute of Telecommunications, Szachowa 1, 04–894, Warsaw, Poland

    Ewa Orłowska

Authors
  1. Ivo Düntsch
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  2. Ewa Orłowska
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Correspondence to Ivo Düntsch .

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Editors and Affiliations

  1. Roskilde University, Roskilde, Denmark

    Patrick Blackburn

  2. Université Paul Sabatier, IRIT-CNRS, Toulouse, France

    Emiliano Lorini

  3. Southwest University, Chongqing, China

    Meiyun Guo

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Düntsch, I., Orłowska, E. (2019). A Discrete Representation of Lattice Frames. In: Blackburn, P., Lorini, E., Guo, M. (eds) Logic, Rationality, and Interaction. LORI 2019. Lecture Notes in Computer Science(), vol 11813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-60292-8_7

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  • DOI: https://doi.org/10.1007/978-3-662-60292-8_7

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