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  1. Vague Objects and Vague Identity: New Essays on Ontic Vagueness.K. Akiba (ed.) - 2014 - Dordrecht, Netherland: Springer.
    This unique anthology of new, contributed essays offers a range of perspectives on various aspects of ontic vagueness. It seeks to answer core questions pertaining to onticism, the view that vagueness exists in the world itself. The questions to be addressed include whether vague objects must have vague identity, and whether ontic vagueness has a distinctive logic, one that is not shared by semantic or epistemic vagueness. The essays in this volume explain the motivations behind onticism, such as the plausibility (...)
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  • Non-Archimedean fuzzy and probability logic.Andrew Schumann - 2008 - Journal of Applied Non-Classical Logics 18 (1):29-48.
    In this paper the non-Archimedean multiple-validity is proposed for basic fuzzy logic BL∀∞ that is built as an ω-order extension of the logic BL∀. Probabilities are defined on the class of fuzzy subsets and, as a result, for the first time the non-Archimedean valued probability logic is constructed on the base of BL∀∞.
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  • Mathematical fuzzy logics.Siegfried Gottwald - 2008 - Bulletin of Symbolic Logic 14 (2):210-239.
    The last decade has seen an enormous development in infinite-valued systems and in particular in such systems which have become known as mathematical fuzzy logics. The paper discusses the mathematical background for the interest in such systems of mathematical fuzzy logics, as well as the most important ones of them. It concentrates on the propositional cases, and mentions the first-order systems more superficially. The main ideas, however, become clear already in this restricted setting.
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  • Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part II: Category Theoretic Approaches.Siegfried Gottwald - 2006 - Studia Logica 84 (1):23-50.
    For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.
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  • Castles Built on Clouds: Vague Identity and Vague Objects.Benjamin L. Curtis & Harold W. Noonan - 2014 - In Ken Akiba & Ali Abasnezhad (eds.), Vague Objects and Vague Identity: New Essays on Ontic Vagueness. Dordrecht, Netherland: Springer. pp. 305-326.
    Can identity itself be vague? Can there be vague objects? Does a positive answer to either question entail a positive answer to the other? In this paper we answer these questions as follows: No, No, and Yes. First, we discuss Evans’s famous 1978 argument and argue that the main lesson that it imparts is that identity itself cannot be vague. We defend the argument from objections and endorse this conclusion. We acknowledge, however, that the argument does not by itself establish (...)
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  • Interpreting lattice-valued set theory in fuzzy set theory.P. Hajek & Z. Hanikova - 2013 - Logic Journal of the IGPL 21 (1):77-90.
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