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 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 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 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 Multi-Agent Abstract Argumentation Frameworks With Incomplete Knowledge of Attacks

2021 ◽  
Author(s):  
Andreas Herzig ◽  
Antonio Yuste Ginel
Keyword(s):  
Epistemic Logic ◽  
Partial Information ◽  
Common Knowledge ◽  
Higher Order ◽  
Dynamic Epistemic Logic ◽  
Second Order ◽  
The State ◽  
Incomplete Knowledge ◽  
Abstract Argumentation ◽  
Multi Agent

We introduce a multi-agent, dynamic extension of abstract argumentation frameworks (AFs), strongly inspired by epistemic logic, where agents have only partial information about the conflicts between arguments. These frameworks can be used to model a variety of situations. For instance, those in which agents have bounded logical resources and therefore fail to spot some of the actual attacks, or those where some arguments are not explicitly and fully stated (enthymematic argumentation). Moreover, we include second-order knowledge and common knowledge of the attack relation in our structures (where the latter accounts for the state of the debate), so as to reason about different kinds of persuasion and about strategic features. This version of multi-agent AFs, as well as their updates with public announcements of attacks (more concretely, the effects of these updates on the acceptability of an argument) can be described using S5-PAL, a well-known dynamic-epistemic logic. We also discuss how to extend our proposal to capture arbitrary higher-order attitudes and uncertainty.

A Conformity Measure Using Background Knowledge for Association Rules

2009 ◽  
pp. 100-115 ◽  
Author(s):  
Hacène Cherfi ◽  
Amedeo Napoli ◽  
Yannick Toussaint
Keyword(s):  
Association Rules ◽  
Domain Knowledge ◽  
Common Knowledge ◽  
Background Knowledge ◽  
Quality Measures ◽  
Numerical Approach ◽  
Domain Model ◽  
Classification Methods ◽  
Knowledge Domain ◽  
Semantic Techniques

A text mining process using association rules generates a very large number of rules. According to experts of the domain, most of these rules basically convey a common knowledge, that is, rules which associate terms that experts may likely relate to each other. In order to focus on the result interpretation and discover new knowledge units, it is necessary to define criteria for classifying the extracted rules. Most of the rule classification methods are based on numerical quality measures. In this chapter, the authors introduce two classification methods: the first one is based on a classical numerical approach, that is, using quality measures, and the other one is based on domain knowledge. They propose the second original approach in order to classify association rules according to qualitative criteria using domain model as background knowledge. Hence, they extend the classical numerical approach in an effort to combine data mining and semantic techniques for post mining and selection of association rules. The authors mined a corpus of texts in molecular biology and present the results of both approaches, compare them, and give a discussion on the benefits of taking into account a knowledge domain model of the data.

Logics for reasoning about knowledge and belief

1989 ◽  
Vol 4 (2) ◽  
pp. 119-139 ◽  
Author(s):  
Han Reichgelt
Keyword(s):  
Epistemic Logic ◽  
Autoepistemic Logic ◽  
Theorem Provers ◽  
Reasoning About Knowledge

AbstractAI researchers are becoming increasingly aware of the importance of reasoning about knowledge and belief. This paper reviews epistemic logic, a logic designed specifically for this type of reasoning. I introduce epistemic logic, and discuss some of the philosophical problems associated with it. I then compare two different styles of implementing theorem provers for epistemic logic. I also briefly discuss autoepistemic logic, a form of epistemic logic intended to model an agent's introspective reasoning, i.e. an agent's reasoning about its own beliefs. Finally, I discuss some of the proposals in the AI literature that are aimed at avoiding some of the philosophical problems that dog both epistemic and autoepistemic logic. This paper is not a full introduction to the field. Rather, it is intended to give the reader some flavour of the problems that research in this area faces, as well as some of the proposals for solving these problems.

scholarly journals ARROW UPDATE LOGIC

2011 ◽  
Vol 4 (4) ◽  
pp. 536-559 ◽  
Author(s):  
BARTELD KOOI ◽  
BRYAN RENNE
Keyword(s):  
Epistemic Logic ◽  
Belief Change ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Epistemic Access ◽  
Multi Agent ◽  
Logic Approach ◽  
Action Models ◽  
Information Change ◽  
Update Logic

We presentArrow Update Logic, a theory of epistemic access elimination that can be used to reason about multi-agent belief change. While the belief-changing “arrow updates” of Arrow Update Logic can be transformed into equivalent belief-changing “action models” from the popular Dynamic Epistemic Logic approach, we prove that arrow updates are sometimes exponentially more succinct than action models. Further, since many examples of belief change are naturally thought of from Arrow Update Logic’s perspective of eliminating access to epistemic possibilities, Arrow Update Logic is a valuable addition to the repertoire of logics of information change. In addition to proving basic results about Arrow Update Logic, we introduce a new notion of common knowledge that generalizes both ordinary common knowledge and the “relativized” common knowledge familiar from the Dynamic Epistemic Logic literature.

scholarly journals THE EXPRESSIVITY OF FACTUAL CHANGE IN DYNAMIC EPISTEMIC LOGIC

2013 ◽  
Vol 7 (2) ◽  
pp. 208-221 ◽  
Author(s):  
LOUWE B. KUIJER
Keyword(s):  
Epistemic Logic ◽  
Common Knowledge ◽  
Dynamic Epistemic Logic ◽  
Public Announcements

AbstractA commonly used dynamic epistemic logic is one obtained by adding commonknowledge and public announcements to a basic epistemic logic. It is known from Kooi (2007) that adding public substitutions to such a logic adds expressivity over the class K of models. Here I show that substitutions also add expressivity over the classes KD45, S4 and S5 of models. Since the combination of common knowledge, public announcements and substitutions, was shown in Kooi (2007) to be equally expressive to relativized common knowledge these results also show that relativized common knowledge is more expressive than common knowledge and public announcements over KD45, S4 and S5. These results therefore extend the result from van Benthem et al. (2006) that shows that relativized common knowledge is more expressive than common knowledge and public announcements over K.

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