@inbook{4aa47b81489942598d90fc66385fb436,

title = "G{\"o}del, Escher, Bell: Contextual Semantics of Logical Paradoxes",

abstract = "Quantum physics exhibits various non-classical and paradoxical features. Among them are non-locality and contextuality (e.g. Bell{\textquoteright}s theorem or the Einstein-Podolsky-Rosen paradox). Since they are expected to constitute a key resource in quantum computation, several approaches have been proposed to provide high-level expressions for them. In one of these approaches, Abramsky and others use the mathematics of algebraic topology and characterize non-locality and contextuality as the same type of phenomena as M. C. Escher{\textquoteright}s impossible figures. This article expands this topological insight and demonstrates that logical paradoxes arising from circular references (of the sort formalized by G{\"o}del{\textquoteright}s fixed-point or diagonalization lemma) share the same topological structure as the quantum paradoxes, by reformatting the topological model of contextuality into a semantics of logical paradoxes. This topological semantics indeed provides a unifying perspective from which previous approaches of philosophers and logicians to logical paradoxes can be understood as diverse ways of fine-tuning topologies to model paradoxes.",

keywords = "Categorical semantics, Circularity, Contextuality, Logical paradox, Presheaf, Quantum physics, Topology",

author = "Kohei Kishida",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2023",

doi = "10.1007/978-3-031-24117-8_14",

language = "English (US)",

series = "Outstanding Contributions to Logic",

publisher = "Springer",

pages = "531--572",

booktitle = "Outstanding Contributions to Logic",

address = "Germany",

}