PP-2014-19:
Bezhanishvili, Nick and de Jongh, Dick
(2014)
*Stable formulas in intuitionistic logic.*
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## Abstract

NNIL-formulas are propositional formulas that do not allow nesting of

implication to the left. These formulas were introduced in [16], where

it was shown that NNIL-formulas are (up to provable equivalence)

exactly the formulas that are preserved under taking submodels of

Kripke models. In this paper we show that NNIL-formulas are up to

frame equivalence the formulas that are preserved under taking

subframes of (descriptive and Kripke) frames. As a result we obtain

that NNIL-formulas are subframe formulas and that all subframe logics

can be axiomatized by NNIL-formulas.

We also introduce ONNILLI-formulas, only NNIL to the left of

implications, and show that ONNILLI-formulas are (up to frame

equivalence) the formulas that are preserved in monotonic images of

(descriptive and Kripke) frames. As a result, we obtain that

ONNILLI-formulas 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: | PP-2014-19 |

Series Name: | Prepublication (PP) Series |

Year: | 2014 |

Uncontrolled Keywords: | Intuitionistic logic, intermediate logics, monotonic maps, truth-preservation, 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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