PP-2014-19: Stable formulas in intuitionistic logic

PP-2014-19: Bezhanishvili, Nick and de Jongh, Dick (2014) Stable formulas in intuitionistic logic. [Report]

Preview	Text (Full Text) PP-2014-19.text.pdf Download (336kB) | Preview
	Text (Abstract) PP-2014-19.abstract.txt Download (1kB)

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

Actions (login required)

View Item