RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
Video Library
Archive
Most viewed videos

Search
RSS
New in collection





You may need the following programs to see the files






The eighth International сonference "Advances in Modal Logic" (AiML 2010)
August 25, 2010 11:50, Moscow
 


Cut-elimination and proof search for bi-intuitionistic tense logic

Rajeev Goré, Linda Postniece, Alwen Tiu
Video records:
Windows Media 228.8 Mb
Flash Video 383.0 Mb
MP4 383.0 Mb

Number of views:
This page:407
Video files:132

Rajeev Goré, Linda Postniece, Alwen Tiu


Видео не загружается в Ваш браузер:
  1. Установите Adobe Flash Player    

  2. Проверьте с Вашим администратором, что из Вашей сети разрешены исходящие соединения на порт 8080
  3. Сообщите администратору портала о данной ошибке

Abstract: We consider an extension of bi-intuitionistic logic with the traditional modalities $\lozenge$, $\square$, $\blacklozenge$ and $\blacksquare$ from tense logic Kt. Proof theoretically, this extension is obtained simply by extending an existing sequent calculus for bi-intuitionistic logic with typical inference rules for the modalities used in display logics. As it turns out, the resulting calculus, LBiKt, seems to be more basic than most intuitionistic tense or modal logics considered in the literature, in particular, those studied by Ewald and Simpson, as it does not assume any a priori relationship between the modal operators $\lozenge$ and $\square$. We recover Ewald's intuitionistic tense logic and Simpson's intuitionistic modal logic by modularly extending LBiKt with additional structural rules. The calculus LBiKt is formulated in a variant of display calculus, using a form of sequents called nested sequents. Cut elimination is proved for LBiKt, using a technique similar to that used in display calculi. As in display calculi, the inference rules of LBiKt are “shallow” rules, in the sense that they act on top-level formulae in a nested sequent. The calculus LBiKt is ill-suited for backward proof search due to the presence of certain structural rules called “display postulates” and the contraction rules on arbitrary structures. We show that these structural rules can be made redundant in another calculus, DBiKt, which uses deep inference, allowing one to apply inference rules at an arbitrary depth in a nested sequent. We prove the equivalence between LBiKt and DBiKt and outline a proof search strategy for DBiKt. We also give a Kripke semantics and prove that LBiKt is sound with respect to the semantics, but completeness is still an open problem. We then discuss various extensions of LBiKt.

Language: English

SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru
 
Contact us:
 Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2017