کد مقاله کد نشریه سال انتشار مقاله انگلیسی ترجمه فارسی نسخه تمام متن
4662975 1345216 2015 9 صفحه PDF ندارد دانلود رایگان
عنوان انگلیسی مقاله
Reflecting rules: A note on generalizing the deduction theorem
ترجمه فارسی عنوان
بازتاب قوانین: نکته ای درباره تعمیم قضیه استنباط
کلمات کلیدی
روابط نتیجه انتزاعی؛ اثبات نظریه؛ قوانین مجاز؛ قضیه استنباط؛ تعویض لباس. منطق زیرساختاری؛ منطق جهانی؛ منطق موجهات
Abstract Consequence Relations; Proof-Theory; Admissible Rules; Deduction Theorem; Uniform Substitution; Substructural Logic; Universal Logic; Modal Logic
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات منطق ریاضی
چکیده انگلیسی

The purpose of this brief note is to prove a limitative theorem for a generalization of the deduction theorem. I discuss the relationship between the deduction theorem and rules of inference. Often when the deduction theorem is claimed to fail, particularly in the case of normal modal logics, it is the result of a confusion over what the deduction theorem is trying to show. The classic deduction theorem is trying to show that all so-called ‘derivable rules’ can be encoded into the object language using the material conditional. The deduction theorem can be generalized in the sense that one can attempt to encode all types of rules into the object language. When a rule is encoded in this way I say that it is reflected in the object language. What I show, however, is that certain logics which reflect a certain kind of rule must be trivial. Therefore, my generalization of the deduction theorem does fail where the classic deduction theorem didn't.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Applied Logic - Volume 13, Issue 3, September 2015, Pages 188–196
نویسندگان
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