24 research outputs found
Attainable Knowledge
The article investigates an evidence-based semantics for epistemic logics in
which pieces of evidence are interpreted as equivalence relations on the
epistemic worlds. It is shown that the properties of knowledge obtained from
potentially infinitely many pieces of evidence are described by modal logic S5.
At the same time, the properties of knowledge obtained from only a finite
number of pieces of evidence are described by modal logic S4. The main
technical result is a sound and complete bi-modal logical system that describes
properties of these two modalities and their interplay
Probabilistic Algorithmic Knowledge
The framework of algorithmic knowledge assumes that agents use deterministic
knowledge algorithms to compute the facts they explicitly know. We extend the
framework to allow for randomized knowledge algorithms. We then characterize
the information provided by a randomized knowledge algorithm when its answers
have some probability of being incorrect. We formalize this information in
terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a
query about a fact \phi provides evidence for \phi being true. Finally, we
discuss the extent to which this evidence can be used as a basis for decisions.Comment: 26 pages. A preliminary version appeared in Proc. 9th Conference on
Theoretical Aspects of Rationality and Knowledge (TARK'03
Evidence and plausibility in neighborhood structures
The intuitive notion of evidence has both semantic and syntactic features. In
this paper, we develop an {\em evidence logic} for epistemic agents faced with
possibly contradictory evidence from different sources. The logic is based on a
neighborhood semantics, where a neighborhood indicates that the agent has
reason to believe that the true state of the world lies in . Further notions
of relative plausibility between worlds and beliefs based on the latter
ordering are then defined in terms of this evidence structure, yielding our
intended models for evidence-based beliefs. In addition, we also consider a
second more general flavor, where belief and plausibility are modeled using
additional primitive relations, and we prove a representation theorem showing
that each such general model is a -morphic image of an intended one. This
semantics invites a number of natural special cases, depending on how uniform
we make the evidence sets, and how coherent their total structure. We give a
structural study of the resulting `uniform' and `flat' models. Our main result
are sound and complete axiomatizations for the logics of all four major model
classes with respect to the modal language of evidence, belief and safe belief.
We conclude with an outlook toward logics for the dynamics of changing
evidence, and the resulting language extensions and connections with logics of
plausibility change
Uncertainty About Evidence
We develop a logical framework for reasoning about knowledge and evidence in
which the agent may be uncertain about how to interpret their evidence. Rather
than representing an evidential state as a fixed subset of the state space, our
models allow the set of possible worlds that a piece of evidence corresponds to
to vary from one possible world to another, and therefore itself be the subject
of uncertainty. Such structures can be viewed as (epistemically motivated)
generalizations of topological spaces. In this context, there arises a natural
distinction between what is actually entailed by the evidence and what the
agent knows is entailed by the evidence -- with the latter, in general, being
much weaker. We provide a sound and complete axiomatization of the
corresponding bi-modal logic of knowledge and evidence entailment, and
investigate some natural extensions of this core system, including the addition
of a belief modality and its interaction with evidence interpretation and
entailment, and the addition of a "knowability" modality interpreted via a
(generalized) interior operator.Comment: In Proceedings TARK 2019, arXiv:1907.0833
Time-stamped claim logic
The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e., as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. We introduce the Time-Stamped Claim Logic including a sound and complete sequent calculus. In order to show how Time-Stamped Claim Logic can be used in practice, we consider a concrete cyber-attribution case study