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Uncertainty measures for rough formulae in rough logic: An axiomatic approach

Yanhong She, Xiaoli He
2012 Computers and Mathematics with Applications  
To solve such a problem, a framework of uncertainty measure for formulae in rough logic is presented in this paper.  ...  Unlike the existing literatures, we adopt an axiomatic approach to study the uncertainty measure in rough logic, concretely, we define the notion of rough truth degree by some axioms, such a notion is  ...  Axiomatic definition of rough truth degree for formulae in rough logic In this section, we propose an axiomatic definition of rough truth degree, that is, we define it by some axioms.  ... 
doi:10.1016/j.camwa.2011.10.074 fatcat:awjohis25rgpzccep5rs6c5rni

On the relation between possibilistic logic and modal logics of belief and knowledge

Mohua Banerjee, Didier Dubois, Lluis Godo, Henri Prade
2017 Journal of Applied Non-Classical Logics  
relations that can account for the behavior of possibility and necessity measures.  ...  On the other hand, in the so-called meta-epistemic logic (MEL) an agent can express both all-or-nothing beliefs and explicitly ignored facts, by only using modal formulas of depth 1, and no objective ones  ...  Comparison to logics of rough sets The semantics of S5 in terms of equivalence relations (Chellas, 1980) makes it in fact the natural logical setting for rough sets (Or lowska, 1985).  ... 
doi:10.1080/11663081.2018.1439357 fatcat:s3ejaqjk6jhqdoxqytkm2npbim

Rough Sets and Rough Logic: A KDD Perspective [chapter]

Zdzisław Pawlak, Lech Polkowski, Andrzej Skowron
2000 Studies in Fuzziness and Soft Computing  
In the second part of this Chapter, we discuss rough logic and related incomplete logics from a wider perspective of logical approach in KDD.  ...  For many applications, in particular for KDD problems, it is necessary to search for relevant approximation spaces in the large space of parameterized approximation spaces.  ...  Measures of closeness of concepts We now present some approaches to closeness measures.  ... 
doi:10.1007/978-3-7908-1840-6_13 fatcat:vy35ujzaszcwvevywvjcms4wzy

AN OVERVIEW OF ROUGH SET SEMANTICS FOR MODAL AND QUANTIFIER LOGICS

CHURN-JUNG LIAU
2000 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
In particular, first order logic 12 and modal logics 13 have been widely used as a formalism for knowledge representation in artificial intelligence and an analysis tool in computer science 14,15 .  ...  Keywords: Rough set, modal logic, epistemic logic, rough quantifiers. * The preliminary versions of the paper have appeared in Ref. 1,2. 1 2 An Overview of Rough Set Semantics . . . applied to domains  ...  The other approach is to consider the approximations of a crisp or fuzzy concept in an FRAS. The result is called a fuzzy rough set.  ... 
doi:10.1142/s0218488500000071 fatcat:4ephf4rgvrfpxlk7qtmsexm6iy

An Overview of Rough Set Semantics for Modal and Quantifier Logics

C Liau
2000 International Journal of Uncertainty Fuzziness and Knowledge-Based Systems  
In particular, first order logic 12 and modal logics 13 have been widely used as a formalism for knowledge representation in artificial intelligence and an analysis tool in computer science 14,15 .  ...  Keywords: Rough set, modal logic, epistemic logic, rough quantifiers. * The preliminary versions of the paper have appeared in Ref. 1,2. 1 2 An Overview of Rough Set Semantics . . . applied to domains  ...  The other approach is to consider the approximations of a crisp or fuzzy concept in an FRAS. The result is called a fuzzy rough set.  ... 
doi:10.1016/s0218-4885(00)00007-1 fatcat:qfbkcvoytrcebd5vwohwqumbpe

Weighted logics for artificial intelligence – an introductory discussion

Didier Dubois, Lluís Godo, Henri Prade
2014 International Journal of Approximate Reasoning  
However, the systematic use of truth-tables for basic connectives in these approaches looks questionable as such notions have a strong epistemic flavor closer to ideas of uncertainty, while truth is an  ...  Uncertainty Uncertainty modeling pertains to the representation of an agent's beliefs.  ...  The same language is used to reason about other kinds of uncertainty measures like plausibility measures, belief functions, etc., see also [115] for a related general approach to reason under uncertainty  ... 
doi:10.1016/j.ijar.2014.08.002 fatcat:hri6ffyszzernoyexdemade37m

A Logic for a Critical Attitude?

Federico Boem, Stefano Bonzio
2022 Logic and Logical Philosophy  
In this paper, we claim that classical logic cannot play such a descriptive role.  ...  We propose, instead, one of the three-valued logics in the Kleene family that is often classified as the less attractive one, namely Hallden's logic.  ...  Both authors wish to thank Vincenzo Fano, Pierluigi Graziani, Stefano Calboli and the whole group Synergia of the University of Urbino, for their observations and comments on an earlier draft of this work  ... 
doi:10.12775/llp.2022.010 fatcat:m7pnvkt6krg6lapzrrebhq7jii

Quantum Logic [article]

M.L. Dalla Chiara, R. Giuntini
2001 arXiv   pre-print
We investigate some forms of quantum logic arising from the standard and the unsharp approach.  ...  We will now introduce a calculus that represents an adequate axiomatization for the logic BZL.  ...  An axiomatization of OL and OQL QL is an axiomatizable logic. Many axiomatizations are known: both in the Hilbert-Bernays style and in the Gentzen-style (natural deduction and sequent-calculi) 3 .  ... 
arXiv:quant-ph/0101028v2 fatcat:2b25tgh35na7pp7o62qit65zuy

Beyond knowing that: a new generation of epistemic logics [article]

Yanjing Wang
2016 arXiv   pre-print
We first survey what Hintikka and others did in the literature of quantified epistemic logic, and then advocate a new quantifier-free approach to study the epistemic logics of knowing-wh, which we believe  ...  We survey our recent line of work on the epistemic logics of "knowing whether", "knowing what" and "knowing how" to demonstrate the use of this new approach.  ...  The author is grateful to Hans van Ditmarsch for his very detailed comments on an early version of this paper.  ... 
arXiv:1605.01995v3 fatcat:n2vpwbpkafflxfzkjwl7lnaqzm

A simple logic for reasoning about incomplete knowledge

Mohua Banerjee, Didier Dubois
2014 International Journal of Approximate Reasoning  
Our approach offers a logical grounding to uncertainty theories like possibility theory and belief functions.  ...  In the next section, the syntax and the axiomatic setting of the logic MEL are provided.  ...  The authors also thank the anonymous reviewers for their valuable comments on previous versions.  ... 
doi:10.1016/j.ijar.2013.11.003 fatcat:ss43tf3rcra5zpdqu4wjrblosy

On similarity in fuzzy description logics

Eva Armengol, Pilar Dellunde, Àngel García-Cerdaña
2016 Fuzzy sets and systems (Print)  
For this purpose we use concrete domains in the fuzzy description logic IALCE F (D) associated either with a left-continuous or with a finite t-norm.  ...  We also prove a result relative to global similarities expressing that, in the context of the logic MTL∀, similar objects have similar properties, being these properties expressed by predicate formulas  ...  This paper is a humble tribute to the research line he has recently developed, the study of logical foundations of fuzzy description logics in connection with mathematical fuzzy logic.  ... 
doi:10.1016/j.fss.2015.11.021 fatcat:jiqok4isbvhdhcyk2zbtnxaqbq

A Fuzzy Modal Logic for Similarity Reasoning [chapter]

Lluís Godo, Ricardo O. Rodríguez
1999 Fuzzy Logic and Soft Computing  
From a technical point of view we need a fuzzy logic as base logic to deal with the fuzziness of propositions and also we need a modality to account for the notion of approximation or closeness.  ...  Therefore we propose a modal fuzzy logic with semantics based on Kripke structures where the accesibility relations are fuzzy similarity relations measuring how similar are the possible worlds.  ...  Acknowledgements The authors are grateful to Carlos Areces and Verónica Becher for valuable comments on the draft.  ... 
doi:10.1007/978-1-4615-5261-1_3 fatcat:xbdjhjnvizbk3p6ksc2gju37vm

On the Epistemic Foundation for Iterated Weak Dominance: An Analysis in a Logic of Individual and Collective attitudes

Emiliano Lorini
2013 Journal of Philosophical Logic  
A complete axiomatization as well as a decidability result for the logic are given.  ...  On the epistemic foundation for iterated weak dominance: an analysis in a logic of individual and collective attitudes.  ...  probabilities [12] , in semi-qualitative approaches, such as Spohn's theory, belief states are described by rough qualitative measures assigning orders of magnitude.  ... 
doi:10.1007/s10992-013-9297-z fatcat:gocezbxn4rempdqwt6uok6xfue

Fuzzy-Set Based Logics — an History-Oriented Presentation of their Main Developments [chapter]

Didier Dubois, Francesc Esteva, Lluís Godo, Henri Prade
2007 Handbook of the History of Logic  
Of course, the development of fuzzy sets and fuzzy logic takes its roots in concerns already encountered in non-classical logics in the first half of the century, when the need for intermediary truth-values  ...  This new trend has also put formal logic, originally developed in connection with the foundations of mathematics, in a completely new perspective, as a tool for processing information on computers.  ...  In a series of works starting in [Hájek et al., 1995] , a different logical approach to reason about uncertainty has been developed that is able to combine notions of different classical uncertainty measures  ... 
doi:10.1016/s1874-5857(07)80009-4 fatcat:s4i5zfomgzbxnfbuif5ffsesea

Some Views on Information Fusion and Logic Based Approaches in Decision Making under Uncertainty

Da Ruan, Jun Liu, Luis Martínez, Yang Xu
2010 Journal of universal computer science (Online)  
Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches.  ...  topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty.  ...  Acknowledgements This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 60474022 and 60875034), the Specialized Research Foundation for the Doctoral Program of  ... 
doi:10.3217/jucs-016-01-0003 dblp:journals/jucs/XuLMR10 fatcat:xmpnyrflcjcankp7uhi2nvhvwq
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