86 research outputs found
Belief as Willingness to Bet
We investigate modal logics of high probability having two unary modal
operators: an operator expressing probabilistic certainty and an operator
expressing probability exceeding a fixed rational threshold . Identifying knowledge with the former and belief with the latter, we may
think of as the agent's betting threshold, which leads to the motto "belief
is willingness to bet." The logic for has an
modality along with a sub-normal modality that extends
the minimal modal logic by way of four schemes relating
and , one of which is a complex scheme arising out of a theorem due to
Scott. Lenzen was the first to use Scott's theorem to show that a version of
this logic is sound and complete for the probability interpretation. We
reformulate Lenzen's results and present them here in a modern and accessible
form. In addition, we introduce a new epistemic neighborhood semantics that
will be more familiar to modern modal logicians. Using Scott's theorem, we
provide the Lenzen-derivative properties that must be imposed on finite
epistemic neighborhood models so as to guarantee the existence of a probability
measure respecting the neighborhood function in the appropriate way for
threshold . This yields a link between probabilistic and modal
neighborhood semantics that we hope will be of use in future work on modal
logics of qualitative probability. We leave open the question of which
properties must be imposed on finite epistemic neighborhood models so as to
guarantee existence of an appropriate probability measure for thresholds
.Comment: Removed date from v1 to avoid confusion on citation/reference,
otherwise identical to v
Knowledge, Justification, and Reason-Based Belief
Is knowledge definable as justified true belief ("JTB")? We argue that one
can legitimately answer positively or negatively, depending on how the notion
of justification is understood. To facilitate our argument, we introduce a
simple propositional logic of reason-based belief. We show that this logic is
sufficiently flexible to accommodate various useful features, including
quantification over reasons. We use our framework to contrast two notions of
JTB: one internalist, the other externalist. We argue that Gettier cases
essentially challenge the internalist notion but not the externalist one. In
particular, we may equate knowledge and JTB if the latter is grounded in what
we call "adequate" reasons.Comment: v3 edits acknowledgment
Logics of Temporal-Epistemic Actions
We present Dynamic Epistemic Temporal Logic, a framework for reasoning about
operations on multi-agent Kripke models that contain a designated temporal
relation. These operations are natural extensions of the well-known "action
models" from Dynamic Epistemic Logic. Our "temporal action models" may be used
to define a number of informational actions that can modify the "objective"
temporal structure of a model along with the agents' basic and higher-order
knowledge and beliefs about this structure, including their beliefs about the
time. In essence, this approach provides one way to extend the domain of action
model-style operations from atemporal Kripke models to temporal Kripke models
in a manner that allows actions to control the flow of time. We present a
number of examples to illustrate the subtleties involved in interpreting the
effects of our extended action models on temporal Kripke models. We also study
preservation of important epistemic-temporal properties of temporal Kripke
models under temporal action model-induced operations, provide complete
axiomatizations for two theories of temporal action models, and connect our
approach with previous work on time in Dynamic Epistemic Logic
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