16,333 research outputs found
Subset space logic with arbitrary announcements
National audienceIn this paper we introduce public announcements to Subset Space Logic (SSL). In order to do this we have to change the original semantics for SSL a little and consider a weaker version of SSL without the cross axiom. We present an axiomatization, prove completeness and show that this logic is PSPACE-complete. Finally, we add the arbitrary announcement modality which expresses “true after any announcement”, prove several semantic results, and show completeness for a Hilbert-style axiomatization of this logic
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
A logic for reasoning about ambiguity
Standard models of multi-agent modal logic do not capture the fact that
information is often \emph{ambiguous}, and may be interpreted in different ways
by different agents. We propose a framework that can model this, and consider
different semantics that capture different assumptions about the agents'
beliefs regarding whether or not there is ambiguity. We examine the expressive
power of logics of ambiguity compared to logics that cannot model ambiguity,
with respect to the different semantics that we propose.Comment: Some of the material in this paper appeared in preliminary form in
"Ambiguous langage and differences of belief" (see arXiv:1203.0699
The Logic of Joint Ability in Two-Player Tacit Games
Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality
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