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Preferential modalities revisited

2016

  • Authors:
    Arina Britz , Varzinczak, I.

    Publication date:
    2016

    Institution:
    Stellenbosch University

    Output type:
    Workshop paper

    Abstract:

    We venture beyond the customary semantic approach in NMR, namely that of placing orderings on worlds (or valuations). In a modal-logic setting, we motivate and investigate the idea of ordering elements of the accessibility relations in Kripke frames, i.e, world pairs (w,w') (or arrows). The underlying intuition is that some world pairs may be seen as more normal (or typical, or expected) than others. We show this delivers an elegant and intuitive semantic construction, which gives a new perspective on present notions of defeasible necessity. From a modeler's perspective, the new framework we propose is more intuitively appealing. Technically, though, the revisited logic happens to not substantively increase the expressive power of the previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Lest this be seen as a negative result, it essentially means that reasoners based on the previous semantics (which have been shown to preserve the computational complexity of the underlying classical modal language) suffice for reasoning over the new semantics. Finally, we show that the kind of construction we here propose has many fruitful applications, notably in a description-logic context, where it provides the foundations on which to ground useful notions of defeasibility in ontologies yet to be explored.

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