Separability and harmony in ecumenical systems

04/05/2022
by   Sonia Marin, et al.
0

The quest of smoothly combining logics so that connectives from classical and intuitionistic logics can co-exist in peace has been a fascinating topic of research for decades now. In 2015, Dag Prawitz proposed a natural deduction system for an ecumenical first-order logic. We start this work by proposing a pure sequent calculus version for it, in the sense that connectives are introduced without the use of other connectives. For doing this, we extend sequents with an extra context, the stoup, and define the ecumenical notion of polarities. Finally, we smoothly extend these ideas for handling modalities, presenting pure labeled and nested systems for ecumenical modal logics.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

05/28/2020

Ecumenical modal logic

The discussion about how to put together Gentzen's systems for classical...
07/23/2020

From 2-sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics

We extend to natural deduction the approach of Linear Nested Sequents an...
03/13/2015

Non-normal modalities in variants of Linear Logic

This article presents modal versions of resource-conscious logics. We co...
08/20/2018

A continuum of incomplete intermediate logics

This paper generalizes the 1977 paper of V.B. Shehtman, which constructe...
01/28/2019

Intuitionistic Non-Normal Modal Logics: A general framework

We define a family of intuitionistic non-normal modal logics; they can b...
05/30/2017

Strength Factors: An Uncertainty System for a Quantified Modal Logic

We present a new system S for handling uncertainty in a quantified modal...
10/05/2012

Relative Expressiveness of Defeasible Logics

We address the relative expressiveness of defeasible logics in the frame...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.