Opis

• Tytuł:
  Mereological foundations of point-free geometry via multi-valued logic
• Twórca:
  Coppola, Cristina;
  Gerla, Giangiacomo
• Opis:
  We suggest possible approaches to point-free geometry based on multi-valued logic. The idea is to assume as primitives the notion of a region together with suitable vague predicates whose meaning is geometrical in nature, e.g. ‘close’, ‘small’, ‘contained’. Accordingly, some first-order multi-valued theories are proposed. We show that, given a multi-valued model of one of these theories, by a suitable definition of point and distance we can construct a metrical space in a natural way. Taking into account that interesting metrical approaches to geometry exist, this looks to be promising for a point-free foundation of the notion of space. We hope also that this way to face point-free geometry provides a tool to illustrate the passage from a naïve and ‘qualitative’ approach to geometry to the ‘quantitative’ approach of advanced science.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Data:
  2015.11.13
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Język:
  angielski
• Źródło:
  Logic and Logical Philosophy; Vol. 24 No. 4 (2015): December; 535-553;
  Logic and Logical Philosophy; Tom 24 Nr 4 (2015): December; 535-553;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Wydawca:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relacja: https://apcz.umk.pl/LLP/article/view/LLP.2015.019/7276
• Temat i słowa kluczowe:
  point-free geometry;
  multi-valued logic;
  fuzzy logic;
  continuous logic;
  metric geometry;
  mereology;
  naïve science
• Identyfikator: https://apcz.umk.pl/LLP/article/view/LLP.2015.019
• Dostawca danych:
  Akademicka Platforma Czasopism
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