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Generalisation of first-order logic to nonatomic domains

Journal of Symbolic Logic 50 (3):815-838 (1985)

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Region-based topology.Peter Roeper - 1997 - Journal of Philosophical Logic 26 (3):251-309.details A topological description of space is given, based on the relation of connection among regions and the property of being limited. A minimal set of 10 constraints is shown to permit definitions of points and of open and closed sets of points and to be characteristic of locally compact T2 spaces. The effect of adding further constraints is investigated, especially those that characterise continua. Finally, the properties of mappings in region-based topology are studied. Not all such mappings correspond to point (...) Download Export citation Bookmark 62 citations
First- and second-order logic of mass terms.Peter Roeper - 2004 - Journal of Philosophical Logic 33 (3):261-297.details Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation. Download Export citation Bookmark 2 citations
The Aristotelian Continuum. A Formal Characterization.Peter Roeper - 2006 - Notre Dame Journal of Formal Logic 47 (2):211-232.details While the classical account of the linear continuum takes it to be a totality of points, which are its ultimate parts, Aristotle conceives of it as continuous and infinitely divisible, without ultimate parts. A formal account of this conception can be given employing a theory of quantification for nonatomic domains and a theory of region-based topology. Download Export citation Bookmark 7 citations

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