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Completeness and Correspondence in Chellas–Segerberg Semantics

Abstract

We investigate a lattice of conditional logics described by a Kripke type semantics, which was suggested by Chellas and Segerberg – Chellas–Segerberg (CS) semantics – plus 30 further principles. We (i) present a non-trivial frame-based completeness result, (ii) a translation procedure which gives one corresponding trivial frame conditions for arbitrary formula schemata, and (iii) non-trivial frame conditions in CS semantics which correspond to the 30 principles.

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Correspondence to Matthias Unterhuber.

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Unterhuber, M., Schurz, G. Completeness and Correspondence in Chellas–Segerberg Semantics. Stud Logica 102, 891–911 (2014). https://doi.org/10.1007/s11225-013-9504-5

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Keywords

  • Chellas–Segerberg Semantics
  • Standard Segerberg Frame Completeness
  • Correspondence
  • Non-trivial Frame Condition
  • Conditional Logic