Multi-Agent Only Knowing

Levesque introduced a notion of ``only knowing'', with the goal of capturing certain types of nonmonotonic reasoning. Levesque's logic dealt with only the case of a single agent. Recently, both Halpern and Lakemeyer independently attempted to extend Levesque's logic to the multi-agent case. Although there are a number of similarities in their approaches, there are some significant differences. In this paper, we reexamine the notion of only knowing, going back to first principles. In the process, we simplify Levesque's completeness proof, and point out some problems with the earlier definitions. This leads us to reconsider what the properties of only knowing ought to be. We provide an axiom system that captures our desiderata, and show that it has a semantics that corresponds to it. The axiom system has an added feature of interest: it includes a modal operator for satisfiability, and thus provides a complete axiomatization for satisfiability in the logic K45.Comment: To appear, Journal of Logic and Computatio

Multi-Agent Only-Knowing Revisited

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic constructs in the semantics and needs to axiomatize validity as part of the logic. It is also not clear how to generalize their ideas to a first-order case. In this paper, we propose a new account of multi-agent only-knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. We then provide, for the propositional fragment, a sound and complete axiomatization that faithfully lifts Levesque's proof theory to the many agent case. We also discuss comparisons to the earlier approach by Halpern and Lakemeyer.Comment: Appears in Principles of Knowledge Representation and Reasoning 201

Multi-Agent Only Knowing on Planet Kripke

International audienceThe idea of only knowing is a natural and intuitive notion to precisely capture the beliefs of a knowledge base. However, an extension to the many agent case, as would be needed in many applications , has been shown to be far from straightforward. For example, previous Kripke frame-based accounts appeal to proof-theoretic constructions like canonical models, while more recent works in the area abandoned Kripke semantics entirely. We propose a new account based on Moss' characteristic formulas, formulated for the usual Kripke semantics. This is shown to come with other benefits: the logic admits a group version of only knowing , and an operator for assessing the epistemic en-trenchment of what an agent or a group only knows is definable. Finally, the multi-agent only knowing operator is shown to be expressible with the cover modality of classical modal logic, which then allows us to obtain a completeness result for a fragment of the logic

Observation of vibrating systems at different time instants

In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper by A. Szij\'art\'o and J. Heged\H{u}s in which the authors ask the question of determining the initial data by only knowing the position of the string at two distinct time instants. The choice of the observation instants is crucial and the estimations rely on the Fourier series expansion of the solutions and results of Diophantine approximation.Comment: 14 page

FRW barotropic zero modes: Dynamical systems observability

The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmologies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode nor of its derivative as dynamical cosmological states. Only knowing the latter ones correspond to a rigorous dynamical observability in barotropic cosmologyComment: 10 pages, 0 figure

Learning about Developmental Disorders for Actual Support not only Knowing

People are paying more attention these days to developmental disorders. To reinforce this, the Act on Support for Persons with Developmental Disabilities was established in 2005. Over forty students attended the author\u27s class ‘Learning and Developmental Theory’ in the teacher-training course of Muroran Institute of Technology in 2011. The class included learning about developmental disorders. But only being knowledgeable about the disorders may not be sufficient. What was more expected from the students was to obtain the ability to take actions for those with the disorders. As such, the author made several attempts in the class: showing videos to help understanding the disorder, setting group discussions, writing comments to the students’ memos. In the final lecture, many students expressed their willingness to act for those with the disorders.教育改善報

Row Sport Context in PISA Like Mathematics Problem

The aim of research was to produce valid, practical and had potential-effect to mathematic literacy ability in PISA like mathematics problem in using row sports context at Asian Games 2018. The research method used development research with development studies type. The subjects of the research were the students with 15 years old of class X SMAN 10 Palembang. The techniques of collecting data were used documentation, walkthrough, test, and interview. This research produced the problem about how the students determined how many benches could be made by only knowing length and width of the boats. The results showed that the problem developed (1) valid from the suitability with the framework PISA regarding content, context, literacy process and level of questions that was connected problems with daily life accordance experts review and one to one stage (2) practical because the problem could be understood by students accordance small group stage, and (3) had a potential effect from the result of analyze the student's answer in mathematical literacy ability with representation and reasoning ability as dominant accordance field test stage