 In the final quarter of the last century a host of logical papers arise from the discussion of the foundations of semantics, with a number of proposals which generalize or modify Tarski’s semantical conception of truth. Tarski notwithstanding, since 1975 the hierarchical approach has been somewhat superseded by new ideas that have rendered the ideal of logical and semantical closure in many respect accessible (especially by means of the fixed point methods used by Kripke 1975 and Martin-Woodruff; see Martin 1984). We also mention the approach stemming from Herzberger, Gupta and Belnap 1993 (see the entry  revision theory of truth),  that has connections with non-elementary parts of definability theory, set theory and higher recursion theory (Welch 2001, 2009, 2011, 2019). This has led to the general axiomatic study of revision-theoretic definitions and theories of circular definitions (see Bruni 2009, 2013b, 2015, 2019). In Standefer 2015 a connection is established between Solovay type theorem and circular definitions of revision theory and a particular modal logic RT (revision theory): a completeness theorem for this logic, analogous to Solovay’s completeness theorem for GL, is proven. The modal logic in question is built upon an operator that is naturally connected with revision-theoretic construction (hence, the name), as explained in Gupta and Standefer 2017. The proof theory of this system is studied in Standefer 2018.