41,225 research outputs found
A logic for reasoning about upper probabilities
We present a propositional logic %which can be used to reason about the
uncertainty of events, where the uncertainty is modeled by a set of probability
measures assigning an interval of probability to each event. We give a sound
and complete axiomatization for the logic, and show that the satisfiability
problem is NP-complete, no harder than satisfiability for propositional logic.Comment: A preliminary version of this paper appeared in Proc. of the 17th
Conference on Uncertainty in AI, 200
Modeling the Ellsberg Paradox by Argument Strength
We present a formal measure of argument strength, which combines the ideas
that conclusions of strong arguments are (i) highly probable and (ii) their
uncertainty is relatively precise. Likewise, arguments are weak when their
conclusion probability is low or when it is highly imprecise. We show how the
proposed measure provides a new model of the Ellsberg paradox. Moreover, we
further substantiate the psychological plausibility of our approach by an
experiment (N = 60). The data show that the proposed measure predicts human
inferences in the original Ellsberg task and in corresponding argument strength
tasks. Finally, we report qualitative data taken from structured interviews on
folk psychological conceptions on what argument strength means
Characterizing and Reasoning about Probabilistic and Non-Probabilistic Expectation
Expectation is a central notion in probability theory. The notion of
expectation also makes sense for other notions of uncertainty. We introduce a
propositional logic for reasoning about expectation, where the semantics
depends on the underlying representation of uncertainty. We give sound and
complete axiomatizations for the logic in the case that the underlying
representation is (a) probability, (b) sets of probability measures, (c) belief
functions, and (d) possibility measures. We show that this logic is more
expressive than the corresponding logic for reasoning about likelihood in the
case of sets of probability measures, but equi-expressive in the case of
probability, belief, and possibility. Finally, we show that satisfiability for
these logics is NP-complete, no harder than satisfiability for propositional
logic.Comment: To appear in Journal of the AC
Probabilistic Programming Concepts
A multitude of different probabilistic programming languages exists today,
all extending a traditional programming language with primitives to support
modeling of complex, structured probability distributions. Each of these
languages employs its own probabilistic primitives, and comes with a particular
syntax, semantics and inference procedure. This makes it hard to understand the
underlying programming concepts and appreciate the differences between the
different languages. To obtain a better understanding of probabilistic
programming, we identify a number of core programming concepts underlying the
primitives used by various probabilistic languages, discuss the execution
mechanisms that they require and use these to position state-of-the-art
probabilistic languages and their implementation. While doing so, we focus on
probabilistic extensions of logic programming languages such as Prolog, which
have been developed since more than 20 years
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