MVL Resources

Resources for Many-Valued Logic

Reiner Hähnle

The Postscript version of this document.

This document is an updated and extended version of [Hähnle, 2001, Section 11].

Books

Classic, but dated, monographs on MVL in general are [Rosser and Turquette, 1952,Rescher, 1969]; the same holds for the collections [Dunn and Epstein, 1977,Rine, 1984].

[Malinowski, 1993] is recommended as a more recent and compact introduction into MVL. Another concise introduction, strong on algebraic aspects, is [Panti, 1998]. The volumes [Bolc and Borowik, 1992,Bolc and Borowik, 2000] are comprehensive and fairly recent, but at least the first part is, unfortunately, seriously flawed by many inaccuracies, see [Hájek and Zach, 1994].

Clearly the most comprehensive and best monograph on MVL is the recent book by Gottwald Gottwald99. The monograph [Hájek, 1998] is broader than its title may suggest--both books were of invaluable help in preparing this chapter. Substantial bibliographies are contained in [Iturrioz, 2000,Iturrioz et al., 2000,Gottwald, 2000]

There are, of course, books on more specialized areas within MVL: Among the many books on fuzzy logic I only mention [Novák, 1989,Zimmermann, 1991,Gottwald, 1993,Kruse et al., 1994,Hájek, 1998,Turunen, 1999] and the collections [Marks, 1994,Klir and Yuan, 1996], which contain material on fuzzy logic in the narrow sense. The definitive book on -norm theory is [Klement et al., 2000]. Deductive aspects of MVL are the topic of [Hähnle, 1994,Stachniak, 1996,Baaz et al., 2001]. An overview of algebraic structures related to many-valued logics is [Iturrioz et al., 2000]. Algebraic aspects of $\L$ ukasiewicz logic are treated in depth in [Cignoli et al., 1999], while philosophical aspects of MVL are discussed in [Zinov'ev, 1963,Haack, 1974,Haack, 1996]. For many-valued switching theory look at [Muzio and Wesselkamper, 1986] and the collections [Sasao, 1993,Sasao and Fujita, 1996].

Journals

There is one journal publishing articles on all aspects of many-valued logic: Multiple-Valued Logic: an International Journal, published by Gordon & Breach.

Journals with a strong emphasis on one or more aspects of MVL are Soft Computing: A Fusion of Foundations, Methodologies and Applications, published by Springer-Verlag; Mathware & Soft Computing, published by Universitat Politècnica de Catalunya; Fuzzy Sets and Systems, published by Elsevier.

Mainstream logic journals with an editorial interest in many-valued logic include Studia Logica, published by Kluwer; Journal of Applied Non-Classical Logics, published by Hermès; Journal of Logic and Computation, published by Oxford University Press; Journal of Language, Logic and Computation, published by Kluwer.

Organizations and Meetings

IEEE Computer Society has a Technical Committee on MVL [Kameyama, 1997], which also organizes the only annual conference devoted exclusively to MVL. The meeting is called International Symposium on Multiple-Valued Logic, the proceedings are published by the IEEE Computer Society Press. Papers in MVL are, of course, also presented in other logic-related conferences. A research network called Many-Valued Logics for Computer Science Applications existed in the form of an EC COST Action between 1995 and 1999 [Tassart et al., 1995]. Its final report [Iturrioz, 2000] contains a bibliography of recent work on MVL with over 600 entries.

Web Resources

Stanford Encyclopedia of Philosophy, entry for many-valued logic
Marek Perkowski's Home page on MVL
IEEE Computer Society's Technical Committee on MVL

Bibliography

Baaz et al., 2001: [Baaz et al., 2001] Baaz, M., Fermüller, C. G., and Salzer, G.
Automated deduction for many-valued logics.
In: [Robinson and Voronkov, 2001].
Bolc and Borowik, 1992: [Bolc and Borowik, 1992] Bolc, L., and Borowik, P.
Many-Valued Logics.
Vol. 1: Theoretical Foundations.
Springer-Verlag.
Bolc and Borowik, 2000: [Bolc and Borowik, 2000] Bolc, L., and Borowik, P.
Many-Valued Logics.
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Springer-Verlag.
Cignoli et al., 1999: [Cignoli et al., 1999] Cignoli, R. L. O., D'Ottaviano, I. M. L., and Mundici, D.
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Trends in Logic, vol. 7.
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Dunn and Epstein, 1977: [Dunn and Epstein, 1977] Dunn, J. M., and Epstein, G. (eds.).
Modern Uses of Multiple-Valued Logic.
Reidel, Dordrecht.
Invited Papers of 5th ISMVL Symposium 1975 with Bibliography by R. G. Wolf.
Gottwald, 1993: [Gottwald, 1993] Gottwald, S.
Fuzzy Sets and Fuzzy Logic.
Vieweg, Braunschweig.
Gottwald, 2000: [Gottwald, 2000] Gottwald, S.
A Treatise on Many-Valued Logics.
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(eds.). Atlas of many-valued structures.
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Triangular Norms.
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Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Lotfi A. Zadeh.
Advances in Fuzzy Systems, vol. 6.
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Foundations of Fuzzy System.
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Fuzzy logic technology and applications.
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Multiple-Valued Switching Theory.
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Many-Valued Logic.
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Computer Science and Multiple-Valued Logics. Second edn.
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Selected Papers from the International Symposium on Multiple-Valued Logics 1974.
Robinson and Voronkov, 2001: [Robinson and Voronkov, 2001] Robinson, A., and Voronkov, A. (eds.).
Handbook of Automated Reasoning.
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Many-Valued Logics.
Amsterdam: North-Holland.
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Logic Synthesis and Optimization.
Kluwer, Norwell/MA, USA.
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Representations of Discrete Functions.
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Resolution Proof Systems: an Algebraic Theory.
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Philosophical Problems of Many-Valued Logic.
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Reiner Hähnle
2001-08-23