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  3. Quantifiers, Propositions and Identity
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2011
      July 2011
      ISBN:
      9780511862359
      9781107010529
      DOI:
      https://doi.org/10.1017/CBO9780511862359
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.52kg, 282 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics, Logic, Categories and Sets, Logic, Philosophy, Programming Languages and Applied Logic
      Series:
      Lecture Notes in Logic (38)
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    Subjects:
    Mathematics, Logic, Categories and Sets, Logic, Philosophy, Programming Languages and Applied Logic
    Series:
    Lecture Notes in Logic (38)
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    Book description

    Many systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation of quantification. The theory is worked out for systems with quantifiers ranging over actual objects, and over all possibilia, and for logics with existence and identity predicates and definite descriptions. The final chapter develops a new admissible 'cover semantics' for propositional and quantified relevant logic, adapting ideas from the Kripke–Joyal semantics for intuitionistic logic in topos theory. This book is for mathematical or philosophical logicians, computer scientists and linguists.

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