An abstract approach to reasoning about games with mistaken and changing beliefs

We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour in games with mistaken and changing beliefs leaving aside normative questions concerning whether the agents are behaving “rationally”; we focus on what agents do in a game. In this paper, we are not concerned with the reasoning process of the (ideal) economic agent; rather, our intended application is artificial agents, e.g., autonomous agents interacting with a human user or with each other as part of a computer game or in a virtual world. We give a story of mistaken beliefs that is a typical example of the situation in which we should want our formal setting to be applied. Then we give the definitions for our formal system and how to use this setting to get a backward induction solution. We then apply our semantics to the story related earlier and give an analysis of it. Our final section contains a discussion of related work and future projects. We discuss the advantages of our approach over existing approaches and indicate how it can be connected to the existing literature

UvA-DARE (Digital Academic Repository) Logic and the Simulation of Interaction and Reasoning: Introductory Remarks

Logic and the simulation of interaction and reasoning: Introductory remarks Löwe, B. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. Abstract. This introductory note provides the background for the symposium "Logic and the Simulation of Interaction and Reasoning", its motivations and the 15 papers presented at the symposium

The educator’s role in Higher Education: position papers from a project of the Special Interest Group Higher Education of the Worshipful Company of Educators

The Company of Educators was set up in the year 2017 and currently has over thirty members who are Freemen and Liverymen of the company interested in Higher Education, Higher Education policy, research, and research training. Topics of interest include educational methods and concepts for universities, training of doctoral students, training of skills relevant for higher education; mentoring and career development of junior academics. The group is chaired by Benedikt Löwe. So far, the SIGHE had two meetings, one at Christ's College, Cambridge, on 3 November 2017 and one at New College, Oxford, on 20 January 2018. During these meetings, SIGHE decided on a number of projects that would define and inform the discussion of the members of the group. The first project, entitled The educator’s role in Higher Education: What distinguishes it from other educational sectors?, is coordinated by James Crabbe and Max Weaver. The two coordinators have produced two position papers that constitute this document. The position papers are to be seen as personal statements of their respective authors rather than a description of the position of the SIGHE, let alone the company. They are supposed to provoke useful reflection and discussion. The authors of the papers encourage readers to contact them directly and discuss the content of the papers

An abstract approach to reasoning about games with mistaken and changing beliefs

We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour in games with mistaken and changing beliefs leaving aside normative questions concerning whether the agents are behaving “rationally”; we focus on what agents do in a game. In this paper, we are not concerned with the reasoning process of the (ideal) economic agent; rather, our intended application is artificial agents, e.g., autonomous agents interacting with a human user or with each other as part of a computer game or in a virtual world. We give a story of mistaken beliefs that is a typical example of the situation in which we should want our formal setting to be applied. Then we give the definitions for our formal system and how to use this setting to get a backward induction solution. We then apply our semantics to the story related earlier and give an analysis of it. Our final section contains a discussion of related work and future projects. We discuss the advantages of our approach over existing approaches and indicate how it can be connected to the existing literature

Enabling mathematical cultures: introduction

Funder: Universität Hamburg (1037

Constructing illoyal algebra-valued models of set theory

AbstractAn algebra-valued model of set theory is called loyal to its algebra if the model and its algebra have the same propositional logic; it is called faithful if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphisms of the algebra result in models that are not faithful and apply this to construct three classes of illoyal models: tail stretches, transposition twists, and maximal twists.</jats:p

Inhabitants of interesting subsets of the Bousfield lattice

In 1979, Bousfield defined an equivalence relation on the stable homotopy category. The set of Bousfield classes has some important subsets such as the distributive lattice DL of all classes 〈E〉which are smash idempotent and the complete Boolean algebra cBA of closed classes. We provide examples of spectra that are in DL, but not in cBA; in particular, for every prime p, the Bousfield class of the Eilenberg–MacLane spectrum 〈HFp〉 is in DL∖cBA