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Fuzzy Logic and the Resolution Principle

Author:

Richard C. T. LeeAuthors Info & Claims

Journal of the ACM (JACM), Volume 19, Issue 1

Pages 109 - 119

https://doi.org/10.1145/321679.321688

Published: 01 January 1972 Publication History

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References

[1]

ACKERMAN, R. Introduction to Many Valued Logics. Dover, New York, 1967.

Google Scholar

[2]

C}tANG, C. C. Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467--490.

Crossref

Google Scholar

[3]

C~ANO, C. L. Fuzzy topological spaces. J. Math. Anal. Appl. 23, 1 (1968), 182-190.

Google Scholar

[4]

CHANG, C. L., AND LEE, I:~. C. T. Symbolic logic and mechanical theorem proving. (Unpublished manuscript, 1971.)

Crossref

Google Scholar

[5]

CHANG, S.K. On the execution of fuzzy programs using finite state machines. IEEE Trans. Comp. (in press).

Digital Library

Google Scholar

[6]

Cn.~NG, S. K. Fuzzy programs, theory and applications. Proc. Brooklyn Polytechnical Institute Syrup. on Computers and Automata, Vol. XXI, 1971.

Google Scholar

[7]

DAvis, h~., AND PUTNAM, I~. A computing procedure for quantification theory. J. ACM 7 (1960), 201-205.

Digital Library

Google Scholar

[8]

GNEDENKO, B.V. The Theory of Probabilily (translated from Russian by B. R. Seekler). Chelsea, New York, 1962.

Google Scholar

[9]

GREEN, C. Application of theorem proving to problem solving. Proc. of the First International Joint Artificial Intelligence Conf., ll'ashington, D.C., 1969.

Crossref

Google Scholar

[10]

HERI~RAND, J. Recherches sur la theoria de la demonstration. Traveaux de la Societe des Sciences de Varsoria, No. 33, 1930.

Google Scholar

[11]

JEFFUEYS, H. Theory of Probability. Oxford U. Press, London, 1961.

Google Scholar

[12]

LEE, R. C.T. A completeness theorem and a computer program for finding theorems derivable from axioms. Ph.D. Thesis, Dept. of Elec. Eng. and Comput. Sci., U. of Calif., Berkeley (1967).

Crossref

Google Scholar

[13]

LEE, R. C. T., AND CHANG, C. L. Some properties of fuzzy logic. Inform. Contr. 19, 5 (Dec. 1971), 417-431.

Crossref

Google Scholar

[14]

LUKASIEWICZ, J. Logical foundations of probability theory. In Jan Lukasiewicz, Selected Works, L. Berkowski, Ed., North-Holland Publ. Co., Amsterdam, 1970, pp. 16--43.

Google Scholar

[15]

MAUINOS, P. N. Fuzzy logic and its applications to switching systems. IEEE Trans. C18, 4 (1969), 343-348.

Google Scholar

[16]

),IcCARTHY, J. Programs with common sense. In Mechanization of Thought Process, Vol. 1. Her Majesty's Stationary Office, London, 1961, pp. 75-84.

Google Scholar

[17]

,~,IcCARTHY, J ., AND HAYES, P .J . Some philosophical problems from the standpoint of artificial intelligence. In Machine Intelligence ~4, B. Meltzer and D. Michie, Eds., American Elsevier, New York, 1968, pp. 463-502.

Google Scholar

[18]

NILSSON, N.J. Learning Machines. McGraw-Hill, New York, 1965.

Google Scholar

[19]

NILSSON, N .J . Problem Solving Methods in Artificial Intelligence. McGraw-Hill, New York, 1971.

Digital Library

Google Scholar

[20]

ROBINSON, J. A. A machine-oriented logic based on the resolution principle. J. ACM 12 (1965), 23--41.

Digital Library

Google Scholar

[21]

I~OSSER, J. B., AND TURQUETTE, A.R. Many-valued Logics. North-Holland Publ. Co., Amsterdam, 1952.

Google Scholar

[22]

SLAGLE, J. R. Interpolation theorems for resolution in lower predicate calculus. J. ACM 17 (1970), 535-542.

Digital Library

Google Scholar

[23]

SLAGLE, J. R. Artificial Intelligence, the Heuristic Programming Approach. McGraw-Hill, New York, 1971.

Google Scholar

[24]

SLAQE, J. R., CHANG, C. L., AND LEE, R. C.W. Completeness theorems for semantic resolution i,1 consequence finding. Proc. of the First International Joint Artificial Intelligence Conf., Washington, D.C., 1969.

Google Scholar

[25]

WALDINGFR, P~., AND LEE, R. C.T. PROW: A step toward automatic program writing. Proc. of the First International Joint Arlificial Intelligence Conf., Washington, D.C., 1969.

Google Scholar

[26]

ZADEH, L.A. Fuzzy sets. Inform. Contr. 8 (1965), 338-353.

Crossref

Google Scholar

[27]

ZADEH, L. A. Fuzzy algorithms. Inform. Contr. 12 (1968), 94-102.

Crossref

Google Scholar

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Xu RShang CLin JShen Q(2023)Similarity Function-Assisted Dynamic Fuzzy Rule Interpolation: An Improved Approach2023 IEEE International Conference on Fuzzy Systems (FUZZ)10.1109/FUZZ52849.2023.10309764(1-6)Online publication date: 13-Aug-2023
https://doi.org/10.1109/FUZZ52849.2023.10309764
Velasco Benito GSobrino Cerdeiriña ABugarín-Diz A(2023)An empirically supported approach to the treatment of imprecision in vague reasoningInternational Journal of Approximate Reasoning10.1016/j.ijar.2023.108995161(108995)Online publication date: Oct-2023
https://doi.org/10.1016/j.ijar.2023.108995
Julián-Iranzo PSáenz-Pérez F(2023) Bousi Prolog: Design and implementation of a proximity-based fuzzy logic programming language Expert Systems with Applications10.1016/j.eswa.2022.118858213(118858)Online publication date: Mar-2023
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Index Terms

Fuzzy Logic and the Resolution Principle
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Probabilistic reasoning
      2. Vagueness and fuzzy logic
2. Mathematics of computing
  1. Discrete mathematics

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Information

Published In

Journal of the ACM Volume 19, Issue 1

Jan. 1972

192 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/321679

Editor:
Raymond E. Miller

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 January 1972

Published in JACM Volume 19, Issue 1

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Xu RShang CLin JShen Q(2023)Similarity Function-Assisted Dynamic Fuzzy Rule Interpolation: An Improved Approach2023 IEEE International Conference on Fuzzy Systems (FUZZ)10.1109/FUZZ52849.2023.10309764(1-6)Online publication date: 13-Aug-2023
https://doi.org/10.1109/FUZZ52849.2023.10309764
Velasco Benito GSobrino Cerdeiriña ABugarín-Diz A(2023)An empirically supported approach to the treatment of imprecision in vague reasoningInternational Journal of Approximate Reasoning10.1016/j.ijar.2023.108995161(108995)Online publication date: Oct-2023
https://doi.org/10.1016/j.ijar.2023.108995
Julián-Iranzo PSáenz-Pérez F(2023) Bousi Prolog: Design and implementation of a proximity-based fuzzy logic programming language Expert Systems with Applications10.1016/j.eswa.2022.118858213(118858)Online publication date: Mar-2023
https://doi.org/10.1016/j.eswa.2022.118858
Tang ZPei SPeng XZhuang FZhang XHoehndorf R(2023)Neural Multi-hop Logical Query Answering with Concept-Level AnswersThe Semantic Web – ISWC 202310.1007/978-3-031-47240-4_28(522-540)Online publication date: 6-Nov-2023
https://dl.acm.org/doi/10.1007/978-3-031-47240-4_28
Xu RShang CShen Q(2022)Towards Dynamic Fuzzy Interpolation Based on Rule Assessment2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)10.1109/FUZZ-IEEE55066.2022.9882737(1-6)Online publication date: 18-Jul-2022
https://dl.acm.org/doi/10.1109/FUZZ-IEEE55066.2022.9882737
Mutovkina N(2022)Methodology for Assessing the Risk Level of a Technical Re-equipment Project Based on Fuzzy LogicAdvances in Intelligent Systems, Computer Science and Digital Economics III10.1007/978-3-030-97057-4_2(11-21)Online publication date: 11-Mar-2022
https://doi.org/10.1007/978-3-030-97057-4_2
Nesimovic SGusic D(2021)Fuzzy Functional and Multivalued Dependencies for Frank’s Class of Additive GeneratorsInternational Journal of Circuits, Systems and Signal Processing10.46300/9106.2021.15.215(8-22)Online publication date: 18-Jan-2021
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Nesimovic SGusic D(2021)Willmott Fuzzy Implication in Fuzzy DatabasesWSEAS TRANSACTIONS ON MATHEMATICS10.37394/23206.2020.19.7219(647-661)Online publication date: 19-Jan-2021
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Gusic DAlihodzic ANesimovic S(2020)On Some Applications of h-generated Fuzzy ImplicationsWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL10.37394/23203.2020.15.4915(490-507)Online publication date: 5-Oct-2020
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Julián-Iranzo PMoreno GRiaza J(2020)The Fuzzy Logic Programming language FASILL: Design and implementationInternational Journal of Approximate Reasoning10.1016/j.ijar.2020.06.002125(139-168)Online publication date: Oct-2020
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Overview of Type-2 Fuzzy Logic Systems

A comparative study of type-1 fuzzy logic systems, interval type-2 fuzzy logic systems and generalized type-2 fuzzy logic systems in control problems