1,975 research outputs found
Investigating subclasses of abstract dialectical frameworks
Dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes with the price of higher computational complexity, thus an understanding of potentially easier subclasses is essential. Compared to Dung argumentation frameworks, where several subclasses such as acyclic and symmetric frameworks are well understood, there has been no in-depth analysis for ADFs in such direction yet (with the notable exception of bipolar ADFs). In this work, we introduce certain subclasses of ADFs and investigate their properties. In particular, we show that for acyclic ADFs, the different semantics coincide. On the other hand, we show that the concept of symmetry is less powerful for ADFs and further restrictions are required to achieve results that are similar to the known ones for Dung's frameworks. A particular such subclass (support-free symmetric ADFs) turns out to be closely related to argumentation frameworks with collective attacks (SETAFs); we investigate this relation in detail and obtain as a by-product that even for SETAFs symmetry is less powerful than for AFs. We also discuss the role of odd-length cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures
A Labelling Framework for Probabilistic Argumentation
The combination of argumentation and probability paves the way to new
accounts of qualitative and quantitative uncertainty, thereby offering new
theoretical and applicative opportunities. Due to a variety of interests,
probabilistic argumentation is approached in the literature with different
frameworks, pertaining to structured and abstract argumentation, and with
respect to diverse types of uncertainty, in particular the uncertainty on the
credibility of the premises, the uncertainty about which arguments to consider,
and the uncertainty on the acceptance status of arguments or statements.
Towards a general framework for probabilistic argumentation, we investigate a
labelling-oriented framework encompassing a basic setting for rule-based
argumentation and its (semi-) abstract account, along with diverse types of
uncertainty. Our framework provides a systematic treatment of various kinds of
uncertainty and of their relationships and allows us to back or question
assertions from the literature
Matching in the Pi-Calculus
We study whether, in the pi-calculus, the match prefix-a conditional operator
testing two names for (syntactic) equality-is expressible via the other
operators. Previously, Carbone and Maffeis proved that matching is not
expressible this way under rather strong requirements (preservation and
reflection of observables). Later on, Gorla developed a by now widely-tested
set of criteria for encodings that allows much more freedom (e.g. instead of
direct translations of observables it allows comparison of calculi with respect
to reachability of successful states). In this paper, we offer a considerably
stronger separation result on the non-expressibility of matching using only
Gorla's relaxed requirements.Comment: In Proceedings EXPRESS/SOS 2014, arXiv:1408.127
On Bisimulations for Description Logics
We study bisimulations for useful description logics. The simplest among the
considered logics is (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of we have any sublogic
of that extends . We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.Comment: 42 page
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