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• W179901103 abstract "We present proofs that the following three major algorith- mic problems in Correspondence Theory are undecidable: first-order defin- ability of propositional modal formulas, modal (propositional) definability of first-order (classical predicate) formulas, and the correspondence prob- lem (equivalence on Kripke frames) for propositional modal formulas and first-order formulas. These results have been known since Chagrova's PhD thesis (4) published in 1989. However, (4) considered (propositional) intu- itionistic formulas which are much harder to deal with than the modal ones. Although the proofs from (4) provided some extra subtle results (such as the undecidability of the set of propositional formulas that are first-order definable on the class of countable frames, but not on the class of all frames; see also (9)), the technique employed was rather involved and the intuition behind was not clear (which has been mentioned by many of our colleagues). The main aim of this paper is to give simple and direct proofs for the modal case and to consider some variations of the three major problems (e.g., the case of countable frames). Our second goal is to show that in the proof of the undecidability of modal definability of first-order formulas, it is sufficient to use one simple modal formula, namely?." @default.
• W179901103 created "2016-06-24" @default.
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• W179901103 date "2006-01-01" @default.
• W179901103 modified "2023-09-23" @default.
• W179901103 title "The truth about algorithmic problems in correspondence theory" @default.
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