scholarly journals Common Knowledge in Epistemic Logic With Hypotheses

10.29007/glrl ◽  
2019 ◽  
Author(s):  
Levan Uridia ◽  
Dirk Walther
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Modal Operator ◽  
The Common ◽  
Reasoning About Knowledge

We recall the epistemic logic S5r for reasoning about knowledge under hypotheses and we investigate the extension of the logic with an operator for common knowledge. The logic S5r is equipped with a modal operator of necessity that can be parameterized with hypotheses representing background assumptions while the extension with the common knowledge operator enables us to describe and reason about common knowledge among agents with possibly different background assumptions. We present an axiomatization of the logic and prove Kripke completeness and decidability results.

scholarly journals Completeness by Modal Definitions. Application to the Epistemic Logic With Hypotheses

2020 ◽  
Vol 23 (65) ◽  
pp. 1-18
Author(s):  
Levan Uridia ◽  
Dirk Walther
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Conditional Logic ◽  
Modal Operator ◽  
Distributed Knowledge ◽  
Topological Structures ◽  
The Common ◽  
Reasoning About Knowledge

We investigate the variant of epistemic logic S5 for reasoning about knowledge under hypotheses. The logic is equipped with a modal operator of necessity that can be parameterized with a hypothesis representing background assumptions. The modal operator can be described as relative necessity and the resulting logic turns out to be a variant of Chellas’ Conditional Logic. We present an axiomatization of the logic and its extension with the common knowledge operator and distributed knowledge operator. We show that the logics are decidable, complete w.r.t. Kripke as well as topological structures. The topological completeness results are obtained by utilizing the Alexandroff connection between preorders and Alexandroff spaces.

scholarly journals Small Undecidable Problems in Epistemic Planning

2018 ◽  
Author(s):  
Sébastien Lê Cong ◽  
Sophie Pinchinat ◽  
François Schwarzentruber
Keyword(s):  
Cellular Automata ◽  
Epistemic Logic ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Planning Problem ◽  
Reachability Problem ◽  
Public Action ◽  
Automatic Structure ◽  
The Common ◽  
Initial Knowledge

Epistemic planning extends classical planning with knowledge and is based on dynamic epistemic logic (DEL). The epistemic planning problem is undecidable in general. We exhibit a small undecidable subclass of epistemic planning over 2-agent S5 models with a fixed repertoire of one action, 6 propositions and a fixed goal. We furthermore consider a variant of the epistemic planning problem where the initial knowledge state is an automatic structure, hence possibly infinite. In that case, we show the epistemic planning problem with 1 public action and 2 propositions to be undecidable, while it is known to be decidable  with public actions over finite models. Our results are obtained by reducing the reachability problem over small universal cellular automata. While our reductions yield a goal formula that displays the common knowledge operator, we show, for each of our considered epistemic problems, a reduction into an epistemic planning problem for a common-knowledge-operator-free goal formula by using 2 additional actions.

scholarly journals Common Knowledge in an Epistemic Logic with Hypotheses

10.29007/43wj ◽  
2020 ◽  
Author(s):  
Levan Uridia ◽  
Dirk Walther
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Background Knowledge ◽  
Knowledge Extension ◽  
Reasoning About Knowledge

We extend epistemic logic S5r for reasoning about knowledge under hypotheses with distributive knowledge operator. This extension gives possibility to express distributive knowledge of agents with different background assumptions. The logic is important in com- puter science since it models agents behavior which already have some equipped knowledge. Extension with distributive knowledge shows to be extremely interesting since knowledge of an arbitrary agent whose epistemic capacity corresponds to any system between S4 and S5 under some restrictions can be modeled as distributive knowledge of agents with cer- tain background knowledge. We present an axiomatization of the logic and prove Kripke completeness and decidability results.

scholarly journals Common Knowledge

1992 ◽  
Vol 6 (4) ◽  
pp. 53-82 ◽  
Author(s):  
John Geanakoplos
Keyword(s):  
Common Knowledge ◽  
Economic Behavior ◽  
Infinite Chain ◽  
The Common ◽  
Reasoning About Knowledge ◽  
The Way

An event is common knowledge among a group of agents if each one knows it, if each one knows that the others know it, if each one knows that each one knows that the others know it, and so on. Thus, common knowledge is the limit of a potentially infinite chain of reasoning about knowledge. The purpose of this paper is to survey some of the implications for economic behavior of the hypotheses that events are common knowledge, that actions are common knowledge, that optimization is common knowledge, and that rationality is common knowledge. It will begin with several puzzles that illustrate the strength of the common knowledge hypothesis. It will then study how common knowledge can illuminate many problems in economics. In general, the discussion will show that a talent for interactive thinking is advantageous, but if everyone can think interactively and deeply all the way to common knowledge, then sometimes puzzling consequences may result.

El patriacado y la estructura social de la vida cotidiana

1970 ◽  
Author(s):  
Marta Postigo Asenjo
Keyword(s):  
Labor Market ◽  
Public Sphere ◽  
Civic Education ◽  
Common Knowledge ◽  
Judicial System ◽  
The Public ◽  
El Sistema ◽  
The Common ◽  
The Public Sphere ◽  
Ways Of Life

RESUMENEl sistema patriarcal no afecta exclusivamente al poder político y judicial, sino que afecta a la estructura interna de la sociedad, la identidad y las formas de vida de los individuos que en ella viven. Para comprender mejor como condiciona el sistema patriarcal las formas de vida y la visión que tienen los individuos de la realidad social, hemos de analizar el modo en que se extiende al orden institucional y lo determina mediante "tipificaciones" de hechos y de personas y mediante roles concretos, esteoreotipaciones sexiuales que obstaculizan el acceso a la esfera pública de la mujer, así como su reinserción en el mercado laboral, en suma, todo aquello que afecta al conocimiento común que comparten los miembros de una comunidad. El cambio hacia una mayor igualdad y una real democracia paritaria y compartida no es posible sin una paulatina educación y concienciación de la sociedad en su conjunto.PALABRAS CLAVEPATRIARCADO-TIPIFICACIÓN SOCIAL-IGUALDAD DE GÉNEROABSTRACTPatriarchalism is not only present in politics and the judicial system. It also affects the internal structure of society, above all the life and identitý of individuals. To understand better how it conditions their ways of life and the vision the individuals have of social reality, we should study how patriarchalism r3eaches the system of institutions and how this becomes determined by "typifications" of facts and people, and by certain roles or sexual stereotypes that hinder the access of women both to the public sphere and to tha labor market. It sum, everything that concerns the common knowledge that the members of a community share. The move towards more equality and towards a more egalitarian democracy heavily depends on the spread of civic education to the entire society.KEYWORDSPATRIARCHALISM-SOCIAL TYPIFICATION-GENDER EQUALITY

scholarly journals Playing cards with Hintikka An introduction to dynamic epistemic logic

2005 ◽  
Vol 3 ◽  
Author(s):  
H. P. Ditmarsch ◽  
W. Van Der Hoek ◽  
B. P. Kooi
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Knowledge And Beliefs ◽  
Public Announcements

This contribution is a gentle introduction to so-called dynamic epistemic logics, that can describe how agents change their knowledge and beliefs. We start with a concise introduction to epistemic logic, through the example of one, two and finally three players holding cards; and, mainly for the purpose of motivating the dynamics, we also very summarily introduce the concepts of general and common knowledge. We then pay ample attention to the logic of public announcements, wherein agents change their knowledge as the result of public announcements. One crucial topic in that setting is that of unsuccessful updates: formulas that become false when announced. The Moore-sentences that were already extensively discussed at the conception of epistemic logic in Hintikka’s ‘Knowledge and Belief ’ (1962) give rise to such unsuccessful updates. After that, we present a few examples of more complex epistemic updates.

scholarly journals The Definite and Indefinite Articles of Spanish (or Castilian) Language in Context

2019 ◽  
Vol 26 (1) ◽  
pp. 99-127
Author(s):  
Sonia Montero Gálvez
Keyword(s):  
Common Knowledge ◽  
Definite Article ◽  
Cognitive Approach ◽  
Indefinite Article ◽  
The Common ◽  
Communicative Context ◽  
The Way

The present paper addresses the contrast between the definite article (el/la/los/las) and the indefinite article (un/a/os/as) from a cognitive approach that not only poses a single meaning for each kind of article, but also highlights the pragmatic (or contextual) aspects that underlie that meaning and establish the use of one form or another. The article’s meaning is shaped by the way we conceptualize the reference: the definite article implies an inclusive reference characterized by the uniqueness of the referent, while the indefinite article implies an exclusive reference characterized by the lack of uniqueness. The possibility to choose one or other way depends on contextual aspects related to the common knowledge shared by the interlocutors, the communicative context (linguistic and situational) and the space (physical or mental) where the referent is located.

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