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A logic for approximate reasoning

Mingsheng Ying
1994 Journal of Symbolic Logic (JSL)  
Consequently, many logicians have proposed different systems of many-valued logic as a formalization of approximate reasoning (see, for example, Goguen [G], Gerla and Tortora [GT], Novak [No], Pavelka  ...  Classical logic is not adequate to face the essential vagueness of human reasoning, which is approximate rather than precise in nature.  ...  I am very indebted to the referee for invaluable comments, criticisms, and suggestions which considerably simplify the proofs of the main results and improve the original version of Theorem 3.3.  ... 
doi:10.2307/2275910 fatcat:oz25hkjqujf2hidynsnwbyvt6e

A Logic for Approximate First-Order Reasoning [chapter]

Frédéric Koriche
2001 Lecture Notes in Computer Science  
The purpose of this study is to handle these difficulties in a logic-oriented framework based on the paradigm of approximate reasoning.  ...  Moreover, a stepwise technique is included for improving approximations. Finally, both sound approximations and complete ones are covered.  ...  In this section we present a logic, named AFOR, for approximate first-order reasoning.  ... 
doi:10.1007/3-540-44802-0_19 fatcat:zd5tulhvnneyzmkxjwdvvs4kuq

A t-Norm Fuzzy Logic for Approximate Reasoning

Alex Tserkovny
2017 Journal of Software Engineering and Applications  
In this study, we present a systemic approach toward fuzzy logic formalization for approximate reasoning. We examine statistical characteristics of the proposed fuzzy logic.  ...  Based on this fuzzy logic we develop methods for fuzzy reasoning in which antecedents and consequents involve fuzzy conditional propositions of the form "If x is A then y is B", with A and B being fuzzy  ...  It is a well-known fact that the operation implication in a fuzzy logic was the foundation of decision making procedure for numerous approximate reasoning tasks.  ... 
doi:10.4236/jsea.2017.107035 fatcat:cqbnchc6vbc2fhhm33ef7lngji

A Fuzzy Logic Based Resolution Principal for Approximate Reasoning

Alex Tserkovny
2017 Journal of Software Engineering and Applications  
In this article, we present a systemic approach toward a fuzzy logic based formalization of an approximate reasoning methodology in a fuzzy resolution, where we derive a truth value of A from both values  ...  A current research is utilizing an approximate reasoning methodology, which is based on a similarity relation for a fuzzification, while similarity measure is utilized in fuzzy inference mechanism.  ...  approximate reasoning methodology in a fuzzy resolution.  ... 
doi:10.4236/jsea.2017.1010045 fatcat:beo5esz3yfgcdnxjgrkxd4ytfu

A simple logic for reasoning about incomplete knowledge

Mohua Banerjee, Didier Dubois
2014 International Journal of Approximate Reasoning  
In this sense MEL, even if syntactically a fragment of a known modal logic, is not really in the spirit of the standard modal logic trend for representing and reasoning about knowledge.  ...  This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 12870 To link to this article : a b s t r a c t The semantics of modal logics for reasoning about belief or  ...  Acknowledgements The first author acknowledges the support of IRIT, CNRS, for a visit during which the work was initiated.  ... 
doi:10.1016/j.ijar.2013.11.003 fatcat:ss43tf3rcra5zpdqu4wjrblosy

Towards a probability theory for product logic: States, integral representation and reasoning

Tommaso Flaminio, Lluis Godo, Sara Ugolini
2018 International Journal of Approximate Reasoning  
Finally, we axiomatize a two-tiered modal logic for probabilistic reasoning on product logic events and prove soundness and completeness with respect to probabilistic spaces, where the algebra is a free  ...  More precisely, we axiomatize a generalized notion of finitely additive probability for product logic formulas, called state, and show that every state is the Lebesgue integral with respect to a unique  ...  Finally, Section 6 is devoted to presenting a logic for probabilistic reasoning on many-valued events represented by formulas of product logic.  ... 
doi:10.1016/j.ijar.2017.11.003 fatcat:4jzlnb2zafgoznqqiw2tyshsny

Approximate databases: a support tool for approximate reasoning

Patrick Doherty, Martin Magnusson, Andrzej Szalas
2006 Journal of Applied Non-Classical Logics  
This paper describes an experimental platform for approximate knowledge databases called the Approximate Knowledge Database (AKDB), based on a semantics inspired by rough sets.  ...  local closed world nonmonotonic queries in the form of crisp or approximate logical formulas can be evaluated tractably.  ...  The techniques used are tractable, but still allow for advanced types of non-monotonic reasoning, including variants of default logics, limited circumscriptive reasoning as well as reasoning with the local  ... 
doi:10.3166/jancl.16.87-117 fatcat:r3khefzkbzgyhjjxqcwnmuddtm

A voting mechanism for fuzzy logic

J. Lawry
1998 International Journal of Approximate Reasoning  
Finally a semantics for possibility measures based on fuzzy valuations is described.  ...  It is shown that the behaviour of agents voting on the truth of sentences from a language of the propositional calculus according to such valuations can be described in terms of fuzzy logic.  ...  Petr Hajek for their many valuable comments on the ideas in this paper.  ... 
doi:10.1016/s0888-613x(98)10013-0 fatcat:7wisnsw62jhjxfhfjlqqpmeufi

A utility-valued logic for decision making

Robin Giles
1988 International Journal of Approximate Reasoning  
These entailments can provide a basis for the automatic generation of rules for expert systems.  ...  These arrays, referred to as a planes, are used for the derivation of entailments.  ...  In this paper a logic particularly appropriate for decision-making applications is described. In order to express beliefs, the notion of a sentence is replaced by that of an assertion.  ... 
doi:10.1016/0888-613x(88)90078-3 fatcat:pdagsox65za3jibr6coxpii33i

A temporal semantics for Nilpotent Minimum logic

Matteo Bianchi
2014 International Journal of Approximate Reasoning  
In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by Ł3: a completeness theorem will be shown.  ...  This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of Gödel ([Göd32], [Dum59]) and Basic Logic ([Háj98]  ...  semantics, and have contributed in a significant way to the development of this article.  ... 
doi:10.1016/j.ijar.2013.10.007 fatcat:vsli3qtjsbbcveuxz4w62ummke

A utility-valued logic for decision making

Robin Giles
1988 International Journal of Approximate Reasoning  
In this paper a logic particularly appropriate for decision-making applications is described. In order to express beliefs, the notion of a sentence is replaced by that of an assertion.  ...  Uging this method, a problem in deduction in the logic of assertions becomes a problem in linear programming, and the assertional form of resolution coincides with Fourier's method for solving such problems  ...  (It might be more, but not for reasons of formal logic.) How is this maximum to be determined? The problem can be pictured geometrically.  ... 
doi:10.1016/0888-613x(88)90104-1 fatcat:tkpmxj4wmjcvjnagjavt5hjohu

Design of a Computable Approximate Reasoning Logic System for AI

Kaidi Liu, Yancang Li, Rong Cui
2022 Mathematics  
It is a general logic system for AI to deal with uncertainty. The study has significance in theory and practice for AI and logical reasoning research.  ...  The innovation is that we proposed a discriminative weight filtering redundancy theory and designed a computable approximate reasoning logic system that combines approximate reasoning and calculation through  ...  This supporting logic is called the approximate reasoning logic. What kind of a logic is the approximate reasoning logic?  ... 
doi:10.3390/math10091447 fatcat:2m2tisktgfcqjmovmhhupckx64

A model for CAGD using fuzzy logic

J. Jacas, A. Monreal, J. Recasens
1997 International Journal of Approximate Reasoning  
This paper presents a first approach to a system based on fuzzy logic for the design of curves and surfaces in the context of computer aided geometric design.  ...  Therefore, it is natural to treat the problem in the setting of approximate reasoning.  ...  From here, Theorem 4.11 immediately follows. • SUMMARY We have presented a model to design curves and surfaces in CAGD using fuzzy approximate reasoning.  ... 
doi:10.1016/s0888-613x(96)00124-7 fatcat:lqvqi3lv65f7fil2frrbud4mla

Non-deterministic semantics for logics with a consistency operator

Arnon Avron
2007 International Journal of Approximate Reasoning  
In order to handle inconsistent knowledge bases in a reasonable way, one needs a logic which allows nontrivial inconsistent theories. Logics of this sort are called paraconsistent.  ...  In this paper we provide in a modular way simple nondeterministic semantics for 64 of the most important logics from this family.  ...  It follows that in order to handle inconsistent knowledge bases in a reasonable way, one needs an unconventional logic: a logic which allows nontrivial inconsistent theories.  ... 
doi:10.1016/j.ijar.2006.06.011 fatcat:nug7qc45e5hpdlq3p6iftedatu

REL — a logic for relative evidential support

Z. An, D.A. Bell, J.G. Hughes
1993 International Journal of Approximate Reasoning  
A formal logic--588~ for Relative Evidential Support is proposed based on the following ideas: 1. Arguments are represented direct(y and are taken as the terms for ~5 °.  ...  Our conclusion is that~qPS"S a is a suitable formalization for uncertain information.  ...  ~g'S'~-A Logic for Relative Evidential Support 215 3. LOGIC Formulae in ~S p are composed of a binary predicate "a 1 ~ a2" in which a 1 and a 2 are two arguments.  ... 
doi:10.1016/0888-613x(93)90002-u fatcat:6xq7jgfl2vfntd4az7gctyiv4a
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