-
Expand entry
-
Added by: Sophie NaglerAbstract:
Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK, where exactly one logical operator figures in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK. We prove that nEK is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions.
2021, Pimentel, E. et al. (2021) An ecumenical notion of entailment. Synthese (Dordrecht). [Online] 198 (Suppl 22), 5391–5413.-
Expand entry
-
Added by: Sophie Nagler, Contributed by: Sophie NaglerAbstract:
Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason that sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems.
Comment: A relatively light-touch and philosophically focussed introduction to ecumenical proof systems, i.e. sequent calculi that combine aspects of different logics. Suitable for discussion in a class on philosophy of logic class or on proof theory if more philosophically focussed. Also potentially usable for a class on logical pluralism.
Can’t find it?Contribute the texts you think should be here and we’ll add them soon!
-
Marin, Sonia, et al.. A Pure View of Ecumenical Modalities
2021, In Logic, Language, Information, and Computation. [Online]. Switzerland: Springer International Publishing AG. pp. 388–407
Comment: Suitable for a specialist class on logical pluralism (if focussed on ecumenical systems) or alethic modalities