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

by   Simone Martini, et al.

We extend to natural deduction the approach of Linear Nested Sequents and 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction—only one introduction and one elimination rule per connective, no additional (structural) rule, no explicit reference to the accessibility relation of the intended Kripke models. We give systems for the normal modal logics from K to S4. For the intuitionistic versions of the systems, we define proof reduction, and prove proof normalisation, thus obtaining a syntactical proof of consistency. For logics K and K4 we use existence predicates (following Scott) for formulating sound deduction rules.


page 1

page 2

page 3

page 4


Nested Sequents for Intuitionistic Grammar Logics via Structural Refinement

Intuitionistic grammar logics fuse constructive and multi-modal reasonin...

Nested Sequents for Intuitionistic Modal Logics via Structural Refinement

We employ a recently developed methodology – called "structural refineme...

Proof systems: from nestings to sequents and back

In this work, we explore proof theoretical connections between sequent, ...

Separability and harmony in ecumenical systems

The quest of smoothly combining logics so that connectives from classica...

Hypersequent calculi for non-normal modal and deontic logics: Countermodels and optimal complexity

We present some hypersequent calculi for all systems of the classical cu...

A journey in modal proof theory: From minimal normal modal logic to discrete linear temporal logic

Extending and generalizing the approach of 2-sequents (Masini, 1992), we...

Ecumenical modal logic

The discussion about how to put together Gentzen's systems for classical...

Please sign up or login with your details

Forgot password? Click here to reset