PP-2005-15: The many faces of interpretability

PP-2005-15: Goris, Evan and Joosten, Joost J. (2005) The many faces of interpretability. [Report]

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Abstract

In this paper we discus work in progress on interpretability logics. We show how semantical considerations have allowed us to formulate non-trivial principles about formalized interpretability. In particular we falsify the conjecture about the nature of the interpretability logic of all reasonable arithmetical theories. We consider this an interesting example of how purely semantical considerations give new non-trivial facts about syntactical and arithmetical notions. In addition we give some apparatus that allows us to push 'global' semantical properties into more 'local' syntactical ones. With this apparatus, the rather wild behavior of the different interpretability logics are nicely formulated in a single notion that expresses their differences in a uniform way.

Item Type: Report
Report Nr: PP-2005-15
Series Name: Prepublication (PP) Series
Year: 2005
Uncontrolled Keywords: provability logic, interpretabilty logic, modal semantics, modal completeness proofs
Subjects: Logic
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/160

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