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paraconsistent logic and query answering in inconsistent databases

Journal of Applied Non-Classical logics 2024年第1期34卷 133-154页

作者： Middelburg, C.A. Informatics Institute Faculty of Science University of Amsterdam Amsterdam Netherlands

This paper concerns the paraconsistent logic LPQ⊃,F and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a con... 详细信息

This paper concerns the paraconsistent logic LPQ^⊃,F and an application of it in the area of relational database theory. The notions of a relational database, a query applicable to a relational database, and a consistent answer to a query with respect to a possibly inconsistent relational database are considered from the perspective of this logic. This perspective enables among other things the definition of a consistent answer to a query with respect to a possibly inconsistent database without resort to database repairs. In an earlier paper, LPQ^⊃,F is presented with a sequent-style natural deduction proof system. In this paper, a sequent calculus proof system is presented instead because such proof systems are generally considered more suitable as the basis of proof search procedures than natural deduction proof systems and proof search procedures can serve as the core of algorithms for computing consistent answers to queries. © 2024 Informa UK Limited, trading as Taylor & Francis Group.

关键词： consistent query answering inconsistent database paraconsistent logic Relational database sequent calculus

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On the strongest three-valued paraconsistent logic contained in classical logic and its dual

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JOURNAL OF logic AND COMPUTATION 2021年第2期31卷 597-611页

作者： Middelburg, C. A. Univ Amsterdam Fac Sci Informat Inst Sci Pk 904 NL-1098 XH Amsterdam Netherlands

LP superset of,F is a three-valued paraconsistent propositional logic that is essentially the same as J3. It has the most properties that have been proposed as desirable properties of a reasonable paraconsistent propositional logic. However, it follows easily from already published results that there are exactly 8192 different three-valued paraconsistent propositional logics that have the properties concerned. In this paper, properties concerning the logical equivalence relation of a logic are used to distinguish LP superset of,F from the others. As one of the bonuses of focusing on the logical equivalence relation, it is found that only 32 of the 8192 logics have a logical equivalence relation that satisfies the identity, annihilation, idempotent and commutative laws for conjunction and disjunction. For most properties of LP superset of,F that have been proposed as desirable properties of a reasonable paraconsistent propositional logic, its paracomplete analogue has a comparable property. In this paper, properties concerning the logical equivalence relation of a logic are also used to distinguish the paracomplete analogue of LP superset of,F from the other three-valued paracomplete propositional logics with those comparable properties.

关键词： paraconsistent logic three-valued logic logical consequence logical equivalence paracomplete logic

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A basic system of paraconsistent Nelsonian logic of conditionals

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JOURNAL OF logic LANGUAGE AND INFORMATION 2024年第4-5期33卷 299-337页

作者： Olkhovikov, Grigory K. Ruhr Univ Bochum Dept Philosophy I Univ Str 150 D-44780 Bochum Germany

We define a Kripke semantics for a conditional logic based on the propositional logic N4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{N4}$$\end{document}, the paraconsistent variant of Nelson's logic of strong negation;we axiomatize the minimal system induced by this semantics. The resulting logic, which we call N4CK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{N4CK}$$\end{document}, shows strong connections both with the basic intuitionistic logic of conditionals IntCK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{IntCK}$$\end{document} introduced earlier in (Olkhovikov, 2023) and with the N4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{N4}$$\end{document}-based modal logic FSKd\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textsf{FSK}<^>d$$\end{document} introduced in (Odintsov and Wansing, 2004) as one of the possible counterparts to the classical modal system K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upg

关键词： Conditional logic Strong negation paraconsistent logic Strong completeness Modal logic Constructive logic

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Consistent IoT Systems: A Perspective Based on paraconsistent Descriptive logic 20

Consistent IoT Systems: A Perspective Based on Paraconsisten...

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International Conference on Intelligent Environments (IE)

作者： Perez-Gaspar, Miguel Gomez, Javier Barcenas, Everardo Garcia, Francisco Univ Nacl Autonoma Mexico Dept Telecommun Mexico City DF Mexico Univ Nacl Autonoma Mexico Dept Comp Engn Mexico City DF Mexico

ISBN: (纸本)9798350386806;9798350386790

Internet of Things (IoT) devices generate vast and often contradictory data streams. This poses a challenge for IoT systems, which must make accurate and reliable decisions based on this data. paraconsistent descriptive logic (PDL) is a branch of non-classical logic that can handle inconsistencies without compromising data reliability. We propose the integration of PDL into IoT systems to improve data coherence and reliability. We also introduce a Consistency Theorem that establishes rules for managing inconsistencies systematically and in a controlled way. Our efforts aim to pave the way for more robust, reliable, and user-friendly IoT systems.

关键词： Internet of Things data inconsistency paraconsistent logic consistency theorem

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paraconsistent logic Programming in Three and Four-Valued logics

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Bulletin of Symbolic logic 2022年第2期28卷 260-260页

作者： Kleidson Êglicio Carvalho da Silva Oliveira University of Campinas Brazil 2017.

From the interaction among areas such as Computer Science, Formal logic, and Automated Deduction arises an important new subject called logic Programming. This has been used continuously in the theoretical study and practical applications in various fields of Artificial Intelligence. After the emergence of a wide variety of non-classical logics and the understanding of the limitations presented by first-order classical logic, it became necessary to consider logic programming based on other types of reasoning in addition to classical reasoning. A type of reasoning that has been well studied is the paraconsistent, that is, the reasoning that tolerates contradictions. However, although there are many paraconsistent logics with different types of semantics, their application to logic programming is more delicate than it first appears, requiring an in-depth study of what can or cannot be transferred directly from classical first-order logic to other types of *** on studies of Tarcisio Rodrigues on the foundations of paraconsistent logic Programming (2010) for some logics of Formal Inconsistency (LFIs), this thesis intends to resume the research of Rodrigues and place it in the specific context of LFIs with three- and four-valued semantics. This kind of logics are interesting from the computational point of view, as presented by Luiz Silvestrini in his Ph.D. thesis entitled “A new approach to the concept of quase-truth” (2011), and by Marcelo Coniglio and Martín Figallo in the article “Hilbert-style presentations of two logics associated to tetravalent modal algebras” [Studia logica (2012)]. Based on original techniques, this study aims to define well-founded systems of paraconsistent logic programming based on well-known logics, in contrast to the ad hoc approaches to this question found in the *** prepared by Kleidson Êglicio Carvalho da Silva Oliveira.E-mail: kecso10@***: http://***/jspui/handle/REPOSIP/322632

关键词： logic programming paraconsistent logic Many-valued logics

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Predictive Controller Based on paraconsistent Annotated logic for Synchronous Generator Excitation Control

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ENERGIES 2023年第4期16卷 1934页

作者： Da Silva Filho, Joao Inacio de Oliveira, Raphael Adamelk Bispo Rodrigues, Marcos Carneiro Cortes, Hyghor Miranda Rocco, Alexandre Mario, Mauricio Conceicao Garcia, Dorotea Vilanova Abe, Jair Minoro Torres, Claudio Rodrigo Ricciotti, Viviane B. Duarte Ricciotti, Antonio Carlos Duarte de Carvalho Jr, Arnaldo Lambert-Torres, Germano St Cecilia Univ UNISANTA Lab Appl Paraconsistent Log Oswaldo Cruz St 288 BR-11045907 Santos SP Brazil Univ Paulista Grad Program Prod Engn Jose Maria Whitaker Ave 320 BR-04057000 Sao Paulo SP Brazil Paula Souza State Ctr Technol Educ CEETEPS Postgrad Program Management & Technol Prod Syst Bandeirantes St 169 BR-01124010 Sao Paulo SP Brazil Fed Univ Rondonia Acad Dept Elect Engn BR-76801058 Porto Velho Brazil Fed Inst Educ Sci & Technol Sao Paulo IFSP BR-11533160 Cubatao SP Brazil Gnarus Inst BR-37500052 Itajuba MG Brazil

This study presents a new Model Predictive Controller (MPC), built with algorithms based on paraconsistent Annotated logic (PAL), with application examples in the excitation control of a synchronous generator. PAL is a non-classical evidential and propositional logic that is associated with a Hasse lattice, and which presents the property of accepting the contradiction in its foundations. In this research, the algorithm was constructed with a version of the PAL that works with two information signals in the degrees of evidence format and, therefore, is called paraconsistent Annotated logic with annotation of two values (PAL2v). For the validation of the algorithmic structure, the computational tool MATLAB((R)) Release 2012b, The MathWorks, Inc., Natick, MA, United States was used. Simulations were performed which compared the results obtained with PPC-PAL2v to those obtained in essays with the AVR (Automatic Voltage Regulator) controls in conjunction with the PSS (Power System Stabilizer) and the conventional MPC of fixed weights. The comparative results showed the PPC-PAL2v to display superior performance in the action of the excitation control of the synchronous generator, with a great efficiency in response to small signals.

关键词： paraconsistent logic paraconsistent annotated logic power grids stability control predictive models energy efficiency power system stability

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Sequent calculus for 3-valued paraconsistent logic QMPT0

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logic JOURNAL OF THE IGPL 2019年第4期27卷 507-521页

作者： Nide, Naoyuki Goto, Yuki Fujita, Megumi Nara Womens Univ Div Human Life & Environm Sci Nara 6308506 Japan Kobe Univ Grad Sch Syst Informat Kobe Hyogo 6578501 Japan Natl Inst Informat Principles Informat Res Div Tokyo 1018430 Japan

We present a sequent calculus of a paraconsistent logic QMPT0, which has the paraconsistent-type excluded middle law (PEML) as an initial sequent. Our system shows that the presence of PEML is essentially important for QMPT0. It also has special rules when the set of constant symbols is finite. We also discuss the cut-elimination property of our system.

关键词： paraconsistent logic sequent calculus

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paraconsistent Annotated logic Algorithms Applied in Management and Control of Communication Network Routes

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SENSORS 2021年第12期21卷 4219-4219页

作者： Da Silva Filho, Joao Inacio Abe, Jair Minoro Marreiro, Alessandro de Lima Gonzalez Martinez, Angel Antonio Torres, Claudio Rodrigo Rocco, Alexandre Cortes, Hyghor Miranda Mario, Mauricio Conceicao Tavares Pacheco, Marcos Tadeu Garcia, Dorotea Vilanova Blos, Mauricio Fontoura Univ Santa Cecilia Lab Appl Paraconsistent Log Oswaldo Cruz St 288 BR-11045100 Santos SP Brazil Univ Paulista Grad Program Prod Engn Jose Maria Whitaker Ave 320 BR-04057000 Sao Paulo SP Brazil

This paper presents a computational method based on non-classical logic dedicated to routing management and information stream control in communication networks. paraconsistent logic (PL) was used to create an algorithmic structure whose main property is to accept contradiction. Moreover, a computational structure, the denominated paraconsistent data analyzer (PDA(PAL2v)), was constructed to perform routing management in communication networks. Direct comparisons of PDA(PAL2v) with a classical logic system that simulates routing conditions were made in the laboratory. In the conventional system, the paraconsistent algorithms were considered as binary logic gates, and in the tests, the same adjustment limits of PDA(PAL2v) were applied. Using a database with controlled insertion of noise, we obtained an efficacy of 97% in the detection of deteriorated packets with PDA(PAL2v) and 72% with the conventional simulation system. Functional tests were carried out, showing that PDA(PAL2v) is able to assess the conditions and degradation of links and perform the analysis and correlation of various inputs and variables, even if the signals have contradictory values. From practical tests in the laboratory, the proposed method represents a new way of managing and controlling communication network routes with good performance.

关键词： paraconsistent logic routing management system communication networks adaptive algorithms paraconsistent analysis network

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Hybrid PI controller constructed with paraconsistent annotated logic

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CONTROL ENGINEERING PRACTICE 2019年 84卷 112-124页

作者： Coelho, Marcelo Saraiva da Silva Filho, Joao Inacio Cortes, Hyghor Miranda de Carvalho, Arnaldo, Jr. Blos, Mauricio Fontoura Mario, Mauricio Conceicao Rocco, Alexandre Santa Cecilia Univ UNISANTA Lab Appl Paraconsistent Log Oswaldo Cruz St 288 BR-11045000 Santos City SP Brazil SENAI Coll Santos Bras Cuba St 344 BR-11013162 Santos City SP Brazil

In this work a new type of hybrid PI controller is presented using the paraconsistent logic (PL) as the basis for the mathematical and logical treatment of the signals corresponding to the control variables. This control has the conventional actions PI (Proportional and Integral) together with the logical actions structured in the concepts of paraconsistent logic. Compared to conventional techniques, this new type of Hybrid PI Controller with paraconsistent logic responded well to the various tests performed in the control loop. The tests and the technical validations were done with evidences that prove the efficiency of the paraconsistent concepts.

关键词： Level control mesh Process control paraconsistent logic Hybrid PI control Algorithm

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paraconsistent logic with Multiple Fuzzy Linguistic Truth-values 9

Paraconsistent Logic with Multiple Fuzzy Linguistic Truth-va...

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9th International Conference on Agents and Artificial Intelligence (ICAART)

作者： Wang, Manren Luo, Xudong Sun Yat Sen Univ Dept Philosophy Zhuhai Zhuhai Peoples R China Sun Yat Sen Univ Inst Log & Cognit Dept Philosophy Guangzhou Guangdong Peoples R China

ISBN: (纸本)9789897582202

This paper extends the two-valued paraconsistent logic into an one in which a proposition takes a truth-value from a set of multiple fuzzy linguistic terms. More specifically, we propose the corresponding inference rule and semantics, and finally prove the soundness of our new fuzzy logical system and its completeness. Moreover, we use an example to illustrate the applicability of our logic system in real life.

关键词： Knowledge Presentation and Reasoning Uncertainty in AI Soft Computing paraconsistent logic Fuzzy logic Multi-valued logic Linguistic Truth-value

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