Paraconsistent Constructive Modal Logic

doi:10.1007/978-3-031-99536-1_5

Paraconsistent Constructive Modal Logic

2026-01-01

1

PRE

AI

H

Han Gao *

D

Daniil Kozhemiachenko

N

Nicola Olivetti

DOI：10.1007/978-3-031-99536-1_5

Original

Original request for help

Save

Abstract

En 中文

We present a family of paraconsistent counterparts of the constructive modal logic CK. These logics aim to formalise reasoning about contradictory but non-trivial propositional attitudes like beliefs or obligations. We define their Kripke-style semantics based on intuitionistic frames with two valuations which provide independent support for truth and falsity; they are connected by strong negation as defined in Nelson's logic. A family of systems is obtained depending on whether both modal operators are defined using the same or by different accessibility relations for their positive and negative support. We propose Hilbert-style axiomatisations for all logics determined by this semantic framework. We also propose a family of modular cut-free sequent calculi that we use to establish decidability.

Keywords:

constructive modal logic

paraconsistent logic

Nelson logic

sequent calculi

decidability

Paraconsistent Constructive Modal Logic

Abstract

Journal

Organization