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Plain Semi-Post algebras as a poset-based generalization of post algebras and their representability

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Abstract

Semi-Post algebras of any type T being a poset have been introduced and investigated in [CR87a], [CR87b]. Plain Semi-Post algebras are in this paper singled out among semi-Post algebras because of their simplicity, greatest similarity with Post algebras as well as their importance in logics for approximation reasoning ([Ra87a], [Ra87b], [RaEp87]). They are pseudo-Boolean algebras generated in a sense by corresponding Boolean algebras and a poset T. Every element has a unique descending representation by means of elements in a corresponding Boolean algebra and primitive Post constants which form a poset T. An axiomatization and another characterization, subalgebras, homomorphisms, congruences determined by special filters and a representability theory of these algebras, connected with that for Boolean algebras, are the subject of this paper.

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Authors and Affiliations

  1. Institute of Computer Sciences and Cybernetics, National Institute of Sciences of Vietnam, Hanoi, Vietnam

    Nguyen Cat Ho & Helena Rasiowa

  2. Institute of Mathematics, University of Warsaw, PKiN, 00-901, Warszawa, Poland

    Nguyen Cat Ho & Helena Rasiowa

Authors
  1. Nguyen Cat Ho
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  2. Helena Rasiowa
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To the memory of Jerzy Słupecki

Research reported here has been supported by Polish Government Grant CPBP 01.01

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Ho, N.C., Rasiowa, H. Plain Semi-Post algebras as a poset-based generalization of post algebras and their representability. Studia Logica 48, 509–530 (1989). https://doi.org/10.1007/BF00370204

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