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Argument-based Belief in Topological Structures

Chenwei Shi, Sonja Smets, Fernando R. Velázquez-Quesada
2017 Electronic Proceedings in Theoretical Computer Science  
Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction.  ...  In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through  ...  In such structures, the semantic interpretation of a modality for this neighborhood-based belief is given by M, x |= B ϕ iff ϕ M ∈ N B The following lemma states that every topological argumentation model  ... 
doi:10.4204/eptcs.251.36 fatcat:2zjcz4biv5hzxj7z6zuqvmbdge

Some non-classical approaches to the Brandenburger–Keisler paradox

Can Başkent
2015 Logic Journal of the IGPL  
Now, a semantics for the interactive belief structures can be given.  ...  Briefly, in this article, we first show that adopting the non-well-founded set theory makes a significant change in the structure of the paradox.  ...  Topological structures play an essential role in various paraconsistent logics and algebraic structures.  ... 
doi:10.1093/jigpal/jzv001 fatcat:kvosfrcjg5bzfjnzcbvoycwayi

Some Non-Classical Approaches to the Branderburger-Keisler Paradox [article]

Can Baskent
2011 arXiv   pre-print
In this paper, we discuss a well-known self-referential paradox in foundational game theory, the Brandenburger - Keisler paradox.  ...  We show that the paradox persists in both frameworks for category theoretical reasons, but, with different properties.  ...  We now step by step construct the BK argument in paraconsistent topological setting. We will call such a belief model a paraconsistent topological belief model.  ... 
arXiv:1107.4929v1 fatcat:d52qphlc4nff5kmzyzunnz43um

Hierarchies of beliefs for compact possibility models

Thomas Mariotti, Martin Meier, Michele Piccione
2005 Journal of Mathematical Economics  
In this paper, we construct a universal type space for a class of possibility models by imposing topological restrictions on the players' beliefs.  ...  The resulting type space is universal, in the sense that any compact and continuous possibility structure can be uniquely represented within it.  ...  A topological model of beliefs Compact possibility structures The restrictions that we shall impose on S, T and R are topological.  ... 
doi:10.1016/j.jmateco.2003.11.009 fatcat:vguxdqym6ff4vfgpgkyfebsu4u

Type space on a purely measurable parameter space

Mikl�s Pint�r
2005 Economic Theory  
In all four papers the structure of beliefs is inherited from the topology of lower ranked beliefs spaces or the parameter space, moreover beliefs are modeled by compact regular probability measures.  ...  In this paper we show that at very natural assumptions upon the structure of the beliefs, the universal type space does exist.  ...  Remark 20 This Theorem shows the importance of pointwise convergence topology. If T is a topological space, then the weak or weak* topology is weaker then our structure on ∆(σ(A T )).  ... 
doi:10.1007/s00199-004-0501-9 fatcat:btifkodmibggpf7rzk4niajnxy

Justified Belief and the Topology of Evidence [chapter]

Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün, Sonja Smets
2016 Lecture Notes in Computer Science  
We introduce a new topological semantics for evidence, evidencebased belief, knowledge and learning.  ...  This setting generalizes (and in a sense improves on) the evidence models for belief due to van Benthem and Pacuit, as well as our own previous work on (a topological semantics for) Stalnaker's doxasticepistemic  ...  The fact that arguments are open in the generated topology encodes the principle that any argument should be evidence-based: whenever an argument is correct, then it is supported by some factive evidence  ... 
doi:10.1007/978-3-662-52921-8_6 fatcat:ii6c75wugvdc7lqo5soxxmuux4

Topological structures of complex belief systems

Josué-Antonio Nescolarde-Selva, José-Luis Usó-Doménech
2013 Complexity  
Consequence 7: Substantive beliefs have an abstract or ideal topological structure 4 .  ...  In order to establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures.  ...  Hugh Gash for his important collaboration in this work, especially English corrections and scientific recommendations.  ... 
doi:10.1002/cplx.21455 fatcat:bi5yzvhhu5dq7agldlvzlwoypu

Page 2273 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
This makes it possible to use arrow structures as a semantic base for a special polymodal logic, called in the paper BAL (basic arrow logic).  ...  Summary: “A drawback of existing epistemic logics in their in- ability to deal with entrenchment of beliefs. All beliefs have equal status; none can be held more firmly than others.  ... 

Page 241 of Behavior Research Methods Vol. 27, Issue 2 [page]

1995 Behavior Research Methods  
structures (Ranney et al., in press).  ...  Intercoder reliabilities arise by contrasting (1) correlations among activation sets and (2) the node¬ link topologies and structures yielded by the various en¬ coders of the same protocol; see Figure  ... 

The Use of Multilegged Arguments to Increase Confidence in Safety Claims for Software-Based Systems: A Study Based on a BBN Analysis of an Idealized Example

Bev Littlewood, David Wright
2007 IEEE Transactions on Software Engineering  
The use of multilegged arguments to increase confidence in safety claims for software-based systems: A study based on a BBN analysis of an idealized example.  ...  The use of multilegged arguments to increase confidence in safety claims for software-based systems: A study based on a BBN analysis of an idealized example.  ...  Acknowledgement This work was partially supported by the DIRC project ('Interdisciplinary Research Collaboration in Dependability of Computer-Based Systems') funded by UK Engineering and Physical Sciences  ... 
doi:10.1109/tse.2007.1002 fatcat:qmwajiculfetfkpumuzkswsciy

Page 2103 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
We use argument structures as the basis of our general proposal for argument aggregation. “There are a number of frameworks for modelling argumenta- tion in logic.  ...  We then motivate and formalise the notion of argument trees and argument structures which provide a way of exhaustively collating arguments and counter-arguments.  ... 

A Topological Approach to Full Belief

Alexandru Baltag, Nick Bezhanishvili, Aybüke Özgün, Sonja Smets
2018 Journal of Philosophical Logic  
We then propose a solution consisting in interpreting belief in a similar way based on hereditarily extremally disconnected spaces, and axiomatize the belief logic of hereditarily extremally disconnected  ...  In this paper, we provide a topological semantics for belief, in particular, for Stalnaker's notion of belief defined as 'epistemic possibility of knowledge', in terms of the closure of the interior operator  ...  We compare our new semantics with the older topological interpretation of belief in terms of Cantor derivative, giving several arguments in favour of our semantics.  ... 
doi:10.1007/s10992-018-9463-4 pmid:30956353 pmcid:PMC6423016 fatcat:se5zhba22ja7fg7z4wga7swlae

Constructing flexible dynamic belief networks from first-order probabilistic knowledge bases [chapter]

Sabine Glesner, Daphne Koller
1995 Lecture Notes in Computer Science  
In contrast to common dynamic belief networks, the structure of our networks is more flexible and better adapted to the given situation.  ...  In particular, we define decision tree representations of conditional probability tables that can be used to decrease the size of the created belief networks.  ...  Their knowledge base represents the topology and conditional probability tables of a first-order belief network in the FOPL language.  ... 
doi:10.1007/3-540-60112-0_25 fatcat:jkbt5lvuxveylftbuxwvw2dz2m

Reasoning about Evidence using Bayesian Networks [chapter]

Hayson Tse, Kam-Pui Chow, Michael Kwan
2012 IFIP Advances in Information and Communication Technology  
This paper presents methods for analyzing the topology of a Bayesian belief network created to qualify and quantify the strengths of investigative hypotheses and their supporting digital evidence.  ...  The methods are applied to review a Bayesian belief network constructed for a criminal case involving Bit-Torrent file sharing, and explain the causal effects underlying the legal arguments.  ...  The interactions are reflected by the causal structure or topology of a Bayesian belief network.  ... 
doi:10.1007/978-3-642-33962-2_7 fatcat:3jffpu2aprgxxngstm3ylbwkpq

The generic possibility of full surplus extraction in models with large type spaces

Alia Gizatulina, Martin Hellwig
2017 Journal of Economic Theory  
We interpret the McAfee-Reny condition as a much stronger version of injectiveness of belief functions and prove genericity by arguments similar to those used to prove the classical embedding theorem for  ...  McAfee and Reny (1992) have given a necessary and sufficient condition for full surplus extraction in naive type spaces with a continuum of payoff types.  ...  By standard arguments, in both topologies, M(T −i ) is also complete. 22 Thus, with both topologies, E * (T i , M(T −i )) is also dense in C(T i , M(T −i )).  ... 
doi:10.1016/j.jet.2017.05.009 fatcat:kckpavl43rfp5olwcmgdv7s4xa
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