Nested sequent calculi are a useful generalization of ordinary sequent calculi, where sequents are allowed to occur within sequents. Nested sequent calculi have been profitably employed in the area of (multi)-modal logic to obtain analytic and modular proof systems for these logics. In this work, we extend the realm of nested sequents by providing nested sequent calculi for the basic conditional logic CK and some of its significant extensions. The calculi are internal (a sequent can be directly translated into a formula), cut-free and analytic. Moreover, they can be used to design (sometimes optimal) decision procedures for the respective logics, and to obtain complexity upper bounds. Our calculi are an argument in favour of nested sequent calculi for modal logics and alike, showing their versatility and power.

Nested Sequent Calculi for Conditional Logics

POZZATO, GIAN LUCA
2012-01-01

Abstract

Nested sequent calculi are a useful generalization of ordinary sequent calculi, where sequents are allowed to occur within sequents. Nested sequent calculi have been profitably employed in the area of (multi)-modal logic to obtain analytic and modular proof systems for these logics. In this work, we extend the realm of nested sequents by providing nested sequent calculi for the basic conditional logic CK and some of its significant extensions. The calculi are internal (a sequent can be directly translated into a formula), cut-free and analytic. Moreover, they can be used to design (sometimes optimal) decision procedures for the respective logics, and to obtain complexity upper bounds. Our calculi are an argument in favour of nested sequent calculi for modal logics and alike, showing their versatility and power.
2012
Logics in Artificial Intelligence - 13th European Conference, JELIA 2012
Toulouse, France
24-26 Settembre 2012
Logics in Artificial Intelligence - 13th European Conference, JELIA 2012
springer
7519
14
27
9783642333521
http://link.springer.com/book/10.1007/978-3-642-33353-8/page/1
Sequent Calculi; Conditional Logics; modal and multimodal logic; Nonmonotonic Reasoning
R. Alenda; N. Olivetti; G.L. Pozzato
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/120456
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