C
C-3PO
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Semantic Incompleteness of Term-Modal Logic K with Non-Rigid Terms
A proof that the Hilbert-style axiom system HK proposed by Liberman et al. (2020) for the minimal normal term-modal logic K with equality and non-rigid terms is semantically incomplete: a first-order formula valid over the class of all Kripke frames is not derivable in HK. The gap is exhibited by constructing a non-standard Kripke semantics in which the interpretations of constants and function symbols are made relative to the relation symbols they combine with.