{"ID":2835955,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.22391","arxiv_id":"2511.22391","title":"Impure Simplicial Complex and Term-Modal Logic with Assignment Operators","abstract":"Impure simplicial complexes are a powerful tool to model multi-agent epistemic situations where agents may die, but it is difficult to define a satisfactory semantics for the ordinary propositional modal language on such models, since many conceptually dubious expressions involving dead agents can be expressed in this language. In this paper, we introduce a term-modal language with assignment operators, in which such conceptually dubious expressions are syntactically excluded. We define both simplicial semantics and first-order Kripke semantics for this language, characterize their respective expressivity through notions of bisimulation, and show that the two semantics are equivalent when we consider a special class of first order Kripke models called local epistemic models. We also offer a complete axiomatization for the epistemic logic based on this language, and show that our language has a notion of assignment normal form. Finally, we discuss the behavior of a kind of intensional distributed knowledge that can be naturally expressed in our language.","short_abstract":"Impure simplicial complexes are a powerful tool to model multi-agent epistemic situations where agents may die, but it is difficult to define a satisfactory semantics for the ordinary propositional modal language on such models, since many conceptually dubious expressions involving dead agents can be expressed in this...","url_abs":"https://arxiv.org/abs/2511.22391","url_pdf":"https://arxiv.org/pdf/2511.22391v1","authors":"[\"Yuanzhe Yang\"]","published":"2025-11-27T12:16:55Z","proceeding":"cs.LO","tasks":"[\"cs.LO\",\"cs.MA\"]","methods":"[]","has_code":false}