21,479 research outputs found
Sleeping Beauty Reconsidered: Conditioning and Reflection in Asynchronous Systems
A careful analysis of conditioning in the Sleeping Beauty problem is done,
using the formal model for reasoning about knowledge and probability developed
by Halpern and Tuttle. While the Sleeping Beauty problem has been viewed as
revealing problems with conditioning in the presence of imperfect recall, the
analysis done here reveals that the problems are not so much due to imperfect
recall as to asynchrony. The implications of this analysis for van Fraassen's
Reflection Principle and Savage's Sure-Thing Principle are considered.Comment: A preliminary version of this paper appears in Principles of
Knowledge Representation and Reasoning: Proceedings of the Ninth
International Conference (KR 2004). This version will appear in Oxford
Studies in Epistemolog
Intransitivity and Vagueness
There are many examples in the literature that suggest that
indistinguishability is intransitive, despite the fact that the
indistinguishability relation is typically taken to be an equivalence relation
(and thus transitive). It is shown that if the uncertainty perception and the
question of when an agent reports that two things are indistinguishable are
both carefully modeled, the problems disappear, and indistinguishability can
indeed be taken to be an equivalence relation. Moreover, this model also
suggests a logic of vagueness that seems to solve many of the problems related
to vagueness discussed in the philosophical literature. In particular, it is
shown here how the logic can handle the sorites paradox.Comment: A preliminary version of this paper appears in Principles of
Knowledge Representation and Reasoning: Proceedings of the Ninth
International Conference (KR 2004
Action Theory Contraction and Minimal Change
Proceedings of the 11th Conference on Principles of Knowledge Representation and Reasoning (KR'08)This work is about changing action domain descriptions in dynamic logic. We here revisit the semantics of action theory contraction, giving more robust operators that express minimal change based on a notion of distance between models. We then define syntactical contraction operators and establish their correctness w.r.t. our semantics. Finally we show that our operators satisfy the PDL-counterpart of the standard postulates for theory change adopted in the literature
A Parameterized Complexity View on Description Logic Reasoning
Description logics are knowledge representation languages that have been
designed to strike a balance between expressivity and computational
tractability. Many different description logics have been developed, and
numerous computational problems for these logics have been studied for their
computational complexity. However, essentially all complexity analyses of
reasoning problems for description logics use the one-dimensional framework of
classical complexity theory. The multi-dimensional framework of parameterized
complexity theory is able to provide a much more detailed image of the
complexity of reasoning problems.
In this paper we argue that the framework of parameterized complexity has a
lot to offer for the complexity analysis of description logic reasoning
problems---when one takes a progressive and forward-looking view on
parameterized complexity tools. We substantiate our argument by means of three
case studies. The first case study is about the problem of concept
satisfiability for the logic ALC with respect to nearly acyclic TBoxes. The
second case study concerns concept satisfiability for ALC concepts
parameterized by the number of occurrences of union operators and the number of
occurrences of full existential quantification. The third case study offers a
critical look at data complexity results from a parameterized complexity point
of view. These three case studies are representative for the wide range of uses
for parameterized complexity methods for description logic problems.Comment: To appear in the Proceedings of the 16th International Conference on
Principles of Knowledge Representation and Reasoning (KR 2018
Hunting for Tractable Languages for Judgment Aggregation
Judgment aggregation is a general framework for collective decision making
that can be used to model many different settings. Due to its general nature,
the worst case complexity of essentially all relevant problems in this
framework is very high. However, these intractability results are mainly due to
the fact that the language to represent the aggregation domain is overly
expressive. We initiate an investigation of representation languages for
judgment aggregation that strike a balance between (1) being limited enough to
yield computational tractability results and (2) being expressive enough to
model relevant applications. In particular, we consider the languages of Krom
formulas, (definite) Horn formulas, and Boolean circuits in decomposable
negation normal form (DNNF). We illustrate the use of the positive complexity
results that we obtain for these languages with a concrete application: voting
on how to spend a budget (i.e., participatory budgeting).Comment: To appear in the Proceedings of the 16th International Conference on
Principles of Knowledge Representation and Reasoning (KR 2018
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