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A preference-based non-normal semantics for CTD


Erica Calardo, Guido Governatori and Antonino Rotolo

University of Bologna


Queensland University of Technology


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

    publisher        = {Springer},
    doi              = {},
    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},
    address          = {Ghent, Belgium}


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