کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4661739 1633456 2015 32 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
First order S4 and its measure-theoretic semantics
ترجمه فارسی عنوان
S4 مرتبه نخست و معناشناسی اندازه گیری نظری آن
کلمات کلیدی
منطق مودال؛ منطق مودال کمی ؛ FOS4؛ معناشناسی توپولوژیکی؛ جامعیت، جبر اندازه گیری
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

The first order modal logic FOS4 is a combination of the axioms and rules of inference of propositional S4 and classical first order logic with identity. We give a topological and measure-theoretic semantics for FOS4 with expanding domains. The latter extends the measure-theoretic semantics for propositional S4 introduced by Scott and studied in [3] and [6], and [8]. The main result of the paper is that FOS4 is complete for the measure-theoretic semantics with countable expanding domains. More formally, FOS  4 is complete for the Lebesgue measure algebra, MM, or algebra of Borel subsets of the real line modulo sets of measure zero, with countable expanding domains. A corollary to the main result is that first order intuitionistic logic FOH   is complete for the frame of open elements in MM with countable expanding domains. We also show that FOS4 is not complete for the real line or the infinite binary tree with limits with countable expanding domains.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 166, Issue 2, February 2015, Pages 187–218
نویسندگان
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