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Reference graphs and semantic paradox

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In Adam Arazim & Michal Dancak (eds.), Logica Yearbook 2015. College Publications. pp. 1-15 (2016)

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  1. The Elimination of Direct Self-reference.Qianli Zeng & Ming Hsiung - 2023 - Studia Logica 111 (6):1037-1055.
    This paper provides a procedure which, from any Boolean system of sentences, outputs another Boolean system called the ‘_m_-cycle unwinding’ of the original Boolean system for any positive integer _m_. We prove that for all \(m>1\), this procedure eliminates the direct self-reference in that the _m_-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever _m_ is relatively prime to all primary periods of a Boolean paradox, this (...)
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  • Notes on Leitgeb’s What Truth Depends on.Edoardo Rivello - 2020 - Studia Logica 108 (6):1235-1262.
    In Hannes Leitgeb’s article What truth depends on the author provides a formally correct and materially adequate truth definition for the set of all grounded sentences, defined as the least fixed point of a monotone operator of semantic dependence. In this paper we will focus on the mathematical aspects of Leitgeb’s notions of dependence, grounding and truth, recasting Leitgeb’s construction in a functional setting in which we establish some new facts about these notions.
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  • Formal representations of dependence and groundedness.Edoardo Rivello - 2020 - Review of Symbolic Logic 13 (1):105-140.
    We study, in an abstract and general framework, formal representations of dependence and groundedness which occur in semantic theories of truth. Our goals are: (a) to relate the different ways in which groundedness is defined according to the way dependence is represented; and (b) to represent different notions of dependence as instances of a suitable generalisation of the mathematical notion of functional dependence.
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  • What Paradoxes Depend on.Ming Hsiung - 2018 - Synthese:1-27.
    This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I prove (...)
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  • Unwinding Modal Paradoxes on Digraphs.Ming Hsiung - 2020 - Journal of Philosophical Logic 50 (2):319-362.
    The unwinding that Cook, 767–774 2004) proposed is a simple but powerful method of generating new paradoxes from known ones. This paper extends Cook’s unwinding to a larger class of paradoxes and studies further the basic properties of the unwinding. The unwinding we study is a procedure, by which when inputting a Boolean modal net together with a definable digraph, we get a set of sentences in which we have a ‘counterpart’ for each sentence of the Boolean modal net and (...)
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  • A graph-theoretic analysis of the semantic paradoxes.Timo Beringer & Thomas Schindler - 2017 - Bulletin of Symbolic Logic 23 (4):442-492.
    We introduce a framework for a graph-theoretic analysis of the semantic paradoxes. Similar frameworks have been recently developed for infinitary propositional languages by Cook and Rabern, Rabern, and Macauley. Our focus, however, will be on the language of first-order arithmetic augmented with a primitive truth predicate. Using Leitgeb’s notion of semantic dependence, we assign reference graphs (rfgs) to the sentences of this language and define a notion of paradoxicality in terms of acceptable decorations of rfgs with truth values. It is (...)
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  • Paradoxes and contemporary logic.Andrea Cantini - 2008 - Stanford Encyclopedia of Philosophy.
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