# A preference-based non-normal semantics for CTD

## Authors

Erica Calardo, Guido Governatori and Antonino Rotolo

University of Bologna

NICTA

Queensland University of Technology

## Abstract

In \cite{ajl:ctd} the authors developed a logical system based on the definition of a new non-classical connective $\otimes$ capturing the notion of reparative obligation. The system proved to be appropriate for handling well-known contrary-to-duty paradoxes but no model-theoretic semantics was presented. In this paper we fill the gap and define a suitable possible-world semantics for the system for which we can prove soundness and completeness. The semantics is a preference-based non-normal one extending and generalizing semantics for classical modal logics.

## BibTeX Entry

  @inproceedings{Calardo_GR_14,
publisher        = {Springer},
doi              = {http://dx.doi.org/10.1007/978-3-319-08615-6_5},
author           = {Calardo, Erica and Governatori, Guido and Rotolo, Antonino},
month            = jul,
editor           = {{Fabrizio Cariani, Davide Grossi, Joke Meheus, Xavier Parent}},
year             = {2014},
keywords         = {deontic logic, contrary to duty, possible world semantics},
title            = {A Preference-based Non-normal Semantics for {CTD}},
booktitle        = {Deontic Logic in Computer Science},
pages            = {65-80},
}