Comparing More Revision and Fixed-Point Theories of Truth

Abstract

Kremer presented three approaches of comparing fixed-point and revision theories of truth in Kremer (Journal of Philosophical Logic, 38(4), 363–403, 2009). Using these approaches, he established the relationships among ten fixed-point theories suggested by Kripke in (Journal of Philosophy, 72(19), 690–716, 1975) and three revision theories presented by Gupta and Belnap in (1993). This paper continues Kremer’s work. We add five other revision theories to the comparisons, including the theory proposed by Gupta in (Journal of Philosophical Logic, 11(1), 1–60, 1982), the theory proposed by Herzberger in (Journal of Philosophical Logic, 11(1), 61–102, 1982), the theory based on fully-varied revision sequences (and stability) proposed by Gupta and Belnap in (1993), the theory proposed by Yaqūb in (1993), and the theory based on weakly consistent revision sequences (and stability). We show that, the notion of Thomason model defined by Belnap’s limit rule is not equivalent to the one defined by Gupta’s limit rule, and that the theory based on fully-varied revision sequences is ≤2-equivalent to the one based on the greatest intrinsic fixed point of σ.