Recently, Professor Ming Hsiung published his paper, “Kripke’s Fixed Points and Leitgeb’s Semantic Dependence,” in the international journal The Review of Symbolic Logic. The journal was founded by the Association for Symbolic Logic (ASL) and, together with The Journal of Symbolic Logic and Bulletin of Symbolic Logic, is one of the major journals published under the auspices of the ASL. It is indexed in internationally recognized databases, including A&HCI and SCIE. 

=====Abstract===== 

Kripke’s fixed-point theory of truth relies essentially on the monotonicity of valuation schemes in order to guarantee the existence of fixed points for the truth predicate. Under non-monotonic valuation schemes, Kripke’s jump may fail to generate a monotonic sequence, and fixed points need not exist. Inspired by Leitgeb’s dependence-based reconstruction of fixed points in classical two-valued semantics, this paper investigates whether analogous constructions are possible in three-valued semantics, including under non-monotonic valuation schemes. To this end, we generalize Leitgeb’s semantic dependence relation to three-valued semantics using partial predicates. On this basis, we define a dependence jump operation and a conditional dependence jump, and show how these operations induce monotonic sequences for the truth predicate under arbitrary three-valued valuation schemes. We compare the least fixed points generated by these jumps with those obtained from Kripke’s original jump across a range of standard valuation schemes, including Kleene, supervaluational, Łukasiewicz, and Gödel schemes. Finally, we show that the resulting notion of semantic dependence yields a uniform formal characterization of self-referentiality in three-valued semantics, thereby extending well-known two-valued results to Kripkean truth theories. 

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Ming Hsiung, Kripke’s Fixed Points and Leitgeb’s Semantic Dependence, The Review of Symbolic Logic, Volume 19, Issue 3, pp. 559–585, September 2026.
DOI:10.1017/S1755020326101178 

Article link: https://doi.org/10.1017/S1755020326101178

Report: HSIUNG Ming

Initial Review: HU Yang

Secondary Review: WU Su

Final Review: HSIUNG Ming