A note on the interpretability logic of finitely axiomatized theories
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In  Albert Visser shows that ILP completely axiomatizes all schemata about provability and relative interpretability that are provable in finitely axiomatized theories. In this paper we introduce a system called ILPω that completely axiomatizes the arithmetically valid principles of provability in and interpretability over such theories. To prove the arithmetical completeness of ILPω we use a suitable kind of tail models; as a byproduct we obtain a somewhat modified proof of Visser's completeness result.
KeywordsMathematical Logic Computational Linguistic Completeness Result Valid Principle Tail Model
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