899 research outputs found
A Dynamic Epistemic Logic with a Knowability Principle
A dynamic epistemic logic is presented in which the single agent can reason about his knowledge stages before and after announcements. The logic is generated by reinterpreting multi agent private announcements in a single agent environment. It is shown that a knowability principle is valid for such logic: any initially true Ï can be known after a certain number of announcements
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
Knowability Relative to Information
We present a formal semantics for epistemic logic, capturing the notion of knowability relative to information (KRI). Like Dretske, we move from the platitude that what an agent can know depends on her (empirical) information. We treat operators of the form K_AB (âB is knowable on the basis of information Aâ) as variably strict quantifiers over worlds with a topic- or aboutness- preservation constraint. Variable strictness models the non-monotonicity of knowledge acquisition while allowing knowledge to be intrinsically stable. Aboutness-preservation models the topic-sensitivity of information, allowing us to invalidate controversial forms of epistemic closure while validating less controversial ones. Thus, unlike the standard modal framework for epistemic logic, KRI accommodates plausible approaches to the Kripke-Harman dogmatism paradox, which bear on non-monotonicity, or on topic-sensitivity. KRI also strikes a better balance between agent idealization and a non-trivial logic of knowledge ascriptions
Two Reformulations of the Verificationist Thesis in Epistemic Temporal Logic that Avoid Fitchâs Paradox
1) We will begin by offering a short introduction to Epistemic Logic
and presenting Fitchâs paradox in an epistemicâmodal logic. (2) Then, we will
proceed to presenting three Epistemic Temporal logical frameworks creatâ
ed by Hoshi (2009)â: TPAL (Temporal Public Announcement Logic), TAPAL
(Temporal Arbitrary Public Announcement Logic) and TPAL+Pâ! (Temporal
Public Announcement Logic with Labeled Past Operators). We will show how
Hoshi stated the Verificationist Thesis in the language of TAPAL and analyze
his argument on why this version of it is immune from paradox. (3) Edgington
(1985) offered an interpretation of the Verificationist Thesis that blocks Fitchâs
paradox and we will propose a way to formulate it in a TAPALâbased lanâ
guage. The language we will use is a combination of TAPAL and TPAL+Pâ! with
an Indefinite (Unlabeled) Past Operator (TAPAL+Pâ!+P). Using indexed satisfiâ
ability relations (as introduced in (Wang 2010â; 2011)) we will offer a prospec â
tive semantics for this language. We will investigate whether the tentative reâ
formulation of Edgingtonâs Verificationist Thesis in TAPAL+Pâ!+P is free from
paradox and adequate to Edgingtonâs ideas on how âall truths are knowableâ
should be interpreted
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
Fitch's Paradox and Level-Bridging Principles
Fitchâs Paradox shows that if every truth is knowable, then every truth is known. Standard diagnoses identify the factivity/negative infallibility of the knowledge operator and Moorean contradictions as the root source of the result. This paper generalises Fitchâs result to show that such diagnoses are mistaken. In place of factivity/negative infallibility, the weaker assumption of any âlevel-bridging principleâ suffices. A consequence is that the result holds for some logics in which the âMoorean contradictionâ commonly thought to underlie the result is in fact consistent. This generalised result improves on the current understanding of Fitchâs result and widens the range of modalities of philosophical interest to which the result might be fruitfully applied. Along the way, we also consider a semantic explanation for Fitchâs result which answers a challenge raised by Kvanvig
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