David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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In T. Bolander, V. Hendricks & S. A. Pedersen (eds.), Self-Reference. Csli Publications (2006)
One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a ﬁxpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilattice, with applications to artiﬁcial intelligence in mind. Bilattices generalize the structure Kripke used in a very natural way, while making the mathematical machinery simpler and more perspicuous. In addition, work such as that of Yablo ﬁts naturally into the bilattice setting. What I do here is present the general background of bilattices, discuss why they are natural, and show how ﬁxpoint approaches to truth in languages that allow self-reference can be applied. This is not new work, but rather is a summary of research I have done over many years.
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Citations of this work BETA
Yaroslav Shramko & Heinrich Wansing (2006). Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood. Journal of Logic, Language and Information 15 (4):403-424.
Thomas Macaulay Ferguson (2014). A Computational Interpretation of Conceptivism. Journal of Applied Non-Classical Logics 24 (4):333-367.
Heinrich Wansing (2010). The Power of Belnap: Sequent Systems for SIXTEEN ₃. [REVIEW] Journal of Philosophical Logic 39 (4):369 - 393.
Heinrich Wansing (2012). A Non-Inferentialist, Anti-Realistic Conception of Logical Truth and Falsity. Topoi 31 (1):93-100.
Dmitry Zaitsev (2009). A Few More Useful 8-Valued Logics for Reasoning with Tetralattice Eight. Studia Logica 92 (2):265 - 280.
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