PP201419: Bezhanishvili, Nick and de Jongh, Dick (2014) Stable formulas in intuitionistic logic. [Report]

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Abstract
NNILformulas are propositional formulas that do not allow nesting of implication to the left. These formulas were introduced in [16], where it was shown that NNILformulas are (up to provable equivalence) exactly the formulas that are preserved under taking submodels of Kripke models. In this paper we show that NNILformulas are up to frame equivalence the formulas that are preserved under taking subframes of (descriptive and Kripke) frames. As a result we obtain that NNILformulas are subframe formulas and that all subframe logics can be axiomatized by NNILformulas. We also introduce ONNILLIformulas, only NNIL to the left of implications, and show that ONNILLIformulas are (up to frame equivalence) the formulas that are preserved in monotonic images of (descriptive and Kripke) frames. As a result, we obtain that ONNILLIformulas are stable formulas as introduced in [1] and that ONNILLI is a syntactically defined set of formulas that axiomatize all stable logics. This resolves an open problem of [1].
Item Type:  Report 

Report Nr:  PP201419 
Series Name:  Prepublication (PP) Series 
Year:  2014 
Uncontrolled Keywords:  Intuitionistic logic, intermediate logics, monotonic maps, truthpreservation, axiomatization 
Subjects:  Logic 
Date Deposited:  12 Oct 2016 14:37 
Last Modified:  12 Oct 2016 14:37 
URI:  https://eprints.illc.uva.nl/id/eprint/507 
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