Studia Logica

, Volume 71, Issue 1, pp 1–30 | Cite as

Completeness of Certain Bimodal Logics for Subset Spaces

  • M. Angela Weiss
  • Rohit Parikh


Subset Spaces were introduced by L. Moss and R. Parikh in [8]. These spaces model the reasoning about knowledge of changing states.

In [2] a kind of subset space called intersection space was considered and the question about the existence of a set of axioms that is complete for the logic of intersection spaces was addressed. In [9] the first author introduced the class of directed spaces and proved that any set of axioms for directed frames also characterizes intersection spaces.

We give here a complete axiomatization for directed spaces. We also show that it is not possible to reduce this set of axioms to a finite set.

Multi-modal logics logic of knowledge topological reasoning 


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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • M. Angela Weiss
    • 1
  • Rohit Parikh
    • 2
  1. 1.Instituto de Matemática e Estatística USPSão PauloBrazil
  2. 2.Brooklyn College and CUNY — Graduate CenterUSA

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