6,209 research outputs found
Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract
In recent work, Stalnaker proposes a logical framework in which belief is
realized as a weakened form of knowledge. Building on Stalnaker's core
insights, and using frameworks developed by Bjorndahl and Baltag et al., we
employ topological tools to refine and, we argue, improve on this analysis. The
structure of topological subset spaces allows for a natural distinction between
what is known and (roughly speaking) what is knowable; we argue that the
foundational axioms of Stalnaker's system rely intuitively on both of these
notions. More precisely, we argue that the plausibility of the principles
Stalnaker proposes relating knowledge and belief relies on a subtle
equivocation between an "evidence-in-hand" conception of knowledge and a weaker
"evidence-out-there" notion of what could come to be known. Our analysis leads
to a trimodal logic of knowledge, knowability, and belief interpreted in
topological subset spaces in which belief is definable in terms of knowledge
and knowability. We provide a sound and complete axiomatization for this logic
as well as its uni-modal belief fragment. We then consider weaker logics that
preserve suitable translations of Stalnaker's postulates, yet do not allow for
any reduction of belief. We propose novel topological semantics for these
irreducible notions of belief, generalizing our previous semantics, and provide
sound and complete axiomatizations for the corresponding logics.Comment: In Proceedings TARK 2017, arXiv:1707.08250. The full version of this
paper, including the longer proofs, is at arXiv:1612.0205
Relating Knowledge and Coordinated Action: The Knowledge of Preconditions Principle
The Knowledge of Preconditions principle (KoP) is proposed as a widely
applicable connection between knowledge and action in multi-agent systems.
Roughly speaking, it asserts that if some condition is a necessary condition
for performing a given action A, then knowing that this condition holds is also
a necessary condition for performing A. Since the specifications of tasks often
involve necessary conditions for actions, the KoP principle shows that such
specifications induce knowledge preconditions for the actions. Distributed
protocols or multi-agent plans that satisfy the specifications must ensure that
this knowledge be attained, and that it is detected by the agents as a
condition for action. The knowledge of preconditions principle is formalised in
the runs and systems framework, and is proven to hold in a wide class of
settings. Well-known connections between knowledge and coordinated action are
extended and shown to derive directly from the KoP principle: a "common
knowledge of preconditions" principle is established showing that common
knowledge is a necessary condition for performing simultaneous actions, and a
"nested knowledge of preconditions" principle is proven, showing that
coordinating actions to be performed in linear temporal order requires a
corresponding form of nested knowledge.Comment: In Proceedings TARK 2015, arXiv:1606.0729
What Drives People's Choices in Turn-Taking Games, if not Game-Theoretic Rationality?
In an earlier experiment, participants played a perfect information game
against a computer, which was programmed to deviate often from its backward
induction strategy right at the beginning of the game. Participants knew that
in each game, the computer was nevertheless optimizing against some belief
about the participant's future strategy. In the aggregate, it appeared that
participants applied forward induction. However, cardinal effects seemed to
play a role as well: a number of participants might have been trying to
maximize expected utility.
In order to find out how people really reason in such a game, we designed
centipede-like turn-taking games with new payoff structures in order to make
such cardinal effects less likely. We ran a new experiment with 50
participants, based on marble drop visualizations of these revised payoff
structures. After participants played 48 test games, we asked a number of
questions to gauge the participants' reasoning about their own and the
opponent's strategy at all decision nodes of a sample game. We also checked how
the verbalized strategies fit to the actual choices they made at all their
decision points in the 48 test games.
Even though in the aggregate, participants in the new experiment still tend
to slightly favor the forward induction choice at their first decision node,
their verbalized strategies most often depend on their own attitudes towards
risk and those they assign to the computer opponent, sometimes in addition to
considerations about cooperativeness and competitiveness.Comment: In Proceedings TARK 2017, arXiv:1707.0825
Uncertainties in the solar photospheric oxygen abundance
The purpose of this work is to better understand the confidence limits of the
photospheric solar oxygen abundance derived from three-dimensional models using
the forbidden [OI] line at 6300 \AA , including correlations with other
parameters involved. We worked with a three-dimensional empirical model and two
solar intensity atlases. We employed Bayesian inference as a tool to determine
the most probable value for the solar oxygen abundance given the model chosen.
We considered a number of error sources, such as uncertainties in the continuum
derivation, in the wavelength calibration and in the abundance/strength of Ni.
Our results shows correlations between the effects of several parameters
employed in the derivation. The Bayesian analysis provides robust confidence
limits taking into account all of these factors in a rigorous manner. We obtain
that, given the empirical three-dimensional model and the atlas observations
employed here, the most probable value for the solar oxygen abundance is
. However, we note that this uncertainty does
not consider possible sources of systematic errors due to the model choice.Comment: Accepted for publication in Astronomy and Astrophysic
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