In T. Bolander, V. Hendricks & S. A. Pedersen (eds.), Self-Reference. Csli Publications (2006)
|Abstract||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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