کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5778196 | 1633432 | 2017 | 55 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Algebraic proof theory: Hypersequents and hypercompletions
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
منطق ریاضی
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
We continue our program of establishing connections between proof-theoretic and order-algebraic properties in the setting of substructural logics and residuated lattices. Extending our previous work that connects a strong form of cut-admissibility in sequent calculi with closure under MacNeille completions of corresponding varieties, we now consider hypersequent calculi and more general completions; these capture logics/varieties that were not covered by the previous approach and that are characterized by Hilbert axioms (algebraic equations) residing in the level P3 of the substructural hierarchy. We provide algebraic foundations for substructural hypersequent calculi and an algorithm to transform P3 axioms/equations into equivalent structural hypersequent rules. Using residuated hyperframes we link strong analyticity in the resulting calculi with a new algebraic completion, which we call hyper-MacNeille.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 3, March 2017, Pages 693-737
Journal: Annals of Pure and Applied Logic - Volume 168, Issue 3, March 2017, Pages 693-737
نویسندگان
Agata Ciabattoni, Nikolaos Galatos, Kazushige Terui,