Failure of Interpolation in Constant Domain Intuitionistic Logic

Mint︠s︡, Grigori; Olkhovikov, Grigory K.; Urquhart, Alasdair

doi:10.2178/jsl.7803120

Cited by 13 publications

(40 citation statements)

References 11 publications

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“…For many years the status of interpolation for constant domain intuitionistic logic was an open problem. It has recently been established that it does not hold, [17]. It has long been known to hold for intuitionistic logic itself.…”

Section: Resultsmentioning

confidence: 99%

Nested Sequents for Intuitionistic Logics

Fitting¹

2014

Notre Dame J. Formal Logic

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Relatively recently nested sequent systems for modal logics have come to be seen as an attractive deep reasoning extension of familiar sequent calculi. In an earlier paper I showed there was a strong connection between modal nested sequents and modal prefixed tableaux. In this paper I show the connection continues to intuitionistic logic, both standard and constant domain, relating nested intuitionistic sequent calculi to intuitionistic prefixed tableaux. Modal nested sequent machinery generalizes one sided sequent calculi-intuitionistic nested sequents similarly generalize two sided sequents. It is noteworthy that the resulting system for constant domain intuitionistic logic is particularly simple. It amounts to a combination of intuitionistic propositional rules and classical quantifier rules, a combination that is known to be inadequate when conventional intuitionistic sequent systems are used.

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Section: Resultsmentioning

confidence: 99%

Nested Sequents for Intuitionistic Logics

Fitting¹

2014

Notre Dame J. Formal Logic

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“…In the present paper we show that this hypothesis is in fact true. The counterexample we give for Beth's definability property of CD is in close and obvious connection with the counterexample for interpolation given in [1], and we use similar methods to prove that it is in fact a counterexample. However, the models used in the counterexample are somewhat different and more complicated than the ones used to disprove interpolation.…”

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confidence: 80%

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Drawing on the previous work [1] on interpolation failure, we show that Beth's definability theorem does not hold for intuitionistic predicate logic of constant domains without identity.

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mentioning

confidence: 80%

Intuitionistic predicate logic of constant domains does not have Beth property

Olkhovikov

2012

Preprint

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“…Moreover, it admits strong interpolation, as propositional quantifiers are eliminable in propositional quantifier logic. By a result of Mints et al (2013), intuitionistic logic augmented with qs does not interpolate. In contrast to this, other extensive…”

Section: Problem 2 Determine Whether G [01] Admits Interpolationmentioning

confidence: 99%