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On theory multiple contraction
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Abstract(s)
The one which is considered the standard model of theory change was presented in
[AGM85] and is known as the AGM model. In particular, that paper introduced
the class of partial meet contractions. In subsequent works several alternative constructive models for that same class of functions were presented, e.g.: safe/kernel
contractions ([AM85, Han94]), system of spheres-based contractions ([Gro88]) and
epistemic entrenchment-based contractions ([G ar88, GM88]).
Besides, several generalizations of such model were investigated. In that regard
we emphasise the presentation of models which accounted for contractions by sets of
sentences rather than only by a single sentence, i.e. multiple contractions. However, until now, only two of the above mentioned models have been generalized in the
sense of addressing the case of contractions by sets of sentences: The partial meet
multiple contractions were presented in [Han89, FH94], while the kernel multiple
contractions were introduced in [FSS03].
In this thesis we propose two new constructive models of multiple contraction
functions, namely the system of spheres-based and the epistemic entrenchment-based
multiple contractions which generalize the models of system of spheres-based and of
epistemic entrenchment-based contractions, respectively, to the case of contractions
(of theories) by sets of sentences. Furthermore, analogously to what is the case
in what concerns the corresponding classes of contraction functions by one single
sentence, those two classes are identical and constitute a subclass of the class of
partial meet multiple contractions.
Additionally, and as the rst step of the procedure that is here followed to
obtain an adequate de nition for the system of spheres-based multiple contractions,
we present a possible worlds semantics for the partial meet multiple contractions
analogous to the one proposed in [Gro88] for the partial meet contractions (by one
single sentence).
Finally, we present yet an axiomatic characterization for the new class(es) of
multiple contraction functions that are here introduced.
Description
Keywords
Belief change Theory contraction Multiple contraction Possible world semantic System of spheres Epistemic entrenchment Mathematics . Centro de Ciências Exatas e da Engenharia