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Logic for update products and steps into the past
, 2007
"... This paper provides a sound and complete proof system for a language Le+Y that adds to Dynamic Epistemic Logic (DEL) a discrete previoustime operator as well as single symbol formulas that partially reveal the most recent event that occured. The completeness theorem is by filtration followed by mod ..."
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This paper provides a sound and complete proof system for a language Le+Y that adds to Dynamic Epistemic Logic (DEL) a discrete previoustime operator as well as single symbol formulas that partially reveal the most recent event that occured. The completeness theorem is by filtration followed by model unravelling and other model transformations. Decidability follows from the completeness proof. The degree to which it is important to include the additional single symbol formulas is addressed in a discussion about the difficulties of the completeness for a language LY that only adds the previoustime operator to DEL. Discussion is also given regarding the completeness for a language obtained by removing common knowledge operators from Le+Y.
Simulation and information: Quantifying over epistemic events, Knowledge Representation for Agents and MultiAgent Systems
, 2009
"... We introduce a multiagent logic of knowledge with time where Fϕ stands for ‘there is an informative event after which ϕ’. Formula Fϕ is true in a model iff it is true in all its refinements (i.e., ‘atoms ’ and ‘back ’ are satisfied; the dual of simulation). The logic is ‘almost ’ normal, and positi ..."
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We introduce a multiagent logic of knowledge with time where Fϕ stands for ‘there is an informative event after which ϕ’. Formula Fϕ is true in a model iff it is true in all its refinements (i.e., ‘atoms ’ and ‘back ’ are satisfied; the dual of simulation). The logic is ‘almost ’ normal, and positive knowledge is preserved. The meaning of Fϕ is also “after the agents become aware of new factual information, ϕ is true, ” and on finite models it is also “there is an event model (M, s) after which ϕ. ” The former provides a correspondence with bisimulation quantifiers in a setting with epistemic operators. 1
doi:10.1111/j.17552567.2011.01119.x Everything is Knowable – How to Get to Know Whether a Proposition is Truetheo_1119 1..22
, 2012
"... Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known af ..."
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Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch’s and Moore’s results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful ’ as ‘known after its announcement ’ and ‘knowable ’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition j that is not known after its announcement but there is another announcement after which j is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: �(Kj ⁄ K¬j). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable ’ as ‘known after an announcement’. Keywords: modal logic, knowability, Fitch’s paradox, dynamic epistemics, public announcements 1. Successful – the Historical Record
A Uniform Logic of Information Dynamics
"... Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a nonuniform dynamic epistemic ..."
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Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a nonuniform dynamic epistemic logic is Public Announcement Logic (PAL), and a wellknown open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PALKω, as well as standard extensions thereof, e.g., PALTω, PALS4ω, and PALS5ω. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
Subset space logic with arbitrary announcements
"... Abstract. In 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 ..."
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Abstract. In 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 PSPACEcomplete. Finally, we add the arbitrary announcement modality which expresses “true after any announcement”, prove several semantic results, and show completeness for a Hilbertstyle axiomatization of this logic. 1
Moorean Phenomena in Epistemic Logic
, 2010
"... ◮ Under what conditions does a true piece of information remain true when it is received by an agent? ..."
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◮ Under what conditions does a true piece of information remain true when it is received by an agent?
Exploring the tractability border in epistemic tasks
 SYNTHESE
, 2012
"... We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it po ..."
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We analyse the computational complexity of comparing informational structures. Intuitively, we study the complexity of deciding queries such as the following: Is Alice’s epistemic information strictly coarser than Bob’s? Do Alice and Bob have the same knowledge about each other’s knowledge? Is it possible to manipulate Alice in a way that she will have the same beliefs as Bob? The results show that these problems lie on both sides of the border between tractability (P) and intractability (NPhard). In particular, we investigate the impact of assuming information structures to be partitionbased (rather than arbitrary relational structures) on the complexity of various problems. We focus on the tractability of concrete epistemic tasks and not on epistemic logics describing them.