316 research outputs found
Argument-based Belief in Topological Structures
This paper combines two studies: a topological semantics for epistemic
notions and abstract argumentation theory. In our combined setting, we use a
topological semantics to represent the structure of an agent's collection of
evidence, and we use argumentation theory to single out the relevant sets of
evidence through which a notion of beliefs grounded on arguments is defined. We
discuss the formal properties of this newly defined notion, providing also a
formal language with a matching modality together with a sound and complete
axiom system for it. Despite the fact that our agent can combine her evidence
in a 'rational' way (captured via the topological structure), argument-based
beliefs are not closed under conjunction. This illustrates the difference
between an agent's reasoning abilities (i.e. the way she is able to combine her
available evidence) and the closure properties of her beliefs. We use this
point to argue for why the failure of closure under conjunction of belief
should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825
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Logics of Imprecise Comparative Probability
This paper studies connections between two alternatives to the standard probability calculus for representing and reasoning about uncertainty: imprecise probability andcomparative probability. The goal is to identify complete logics for reasoning about uncertainty in a comparative probabilistic language whose semantics is given in terms of imprecise probability. Comparative probability operators are interpreted as quantifying over a set of probability measures. Modal and dynamic operators are added for reasoning about epistemic possibility and updating sets of probability measures
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
(Metric) Bisimulation Games and Real-Valued Modal Logics for Coalgebras
Behavioural equivalences can be characterized via bisimulations, modal logics and spoiler-defender games. In this paper we review these three perspectives in a coalgebraic setting, which allows us to generalize from the particular branching type of a transition system. We are interested in qualitative notions (classical bisimulation) as well as quantitative notions (bisimulation metrics).
Our first contribution is to introduce a spoiler-defender bisimulation game for coalgebras in the classical case. Second, we introduce such games for the metric case and furthermore define a real-valued modal coalgebraic logic, from which we can derive the strategy of the spoiler. For this logic we show a quantitative version of the Hennessy-Milner theorem
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