- Tytuł:
- Cut Elimination for Extended Sequent Calculi
- Autorzy:
-
Martini, Simone
Masini, Andrea
Zorzi, Margherita - Powiązania:
- https://bibliotekanauki.pl/articles/43182562.pdf
- Data publikacji:
- 2023
- Wydawca:
- Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
- Tematy:
-
proof theory
sequent calculus
cut elimination
modal logic
2-sequents - Opis:
- We present a syntactical cut-elimination proof for an extended sequent calculus covering the classical modal logics in the \(\mathsf{K}\), \(\mathsf{D}\), \(\mathsf{T}\), \(\mathsf{K4}\), \(\mathsf{D4}\) and \(\mathsf{S4}\) spectrum. We design the systems uniformly since they all share the same set of rules. Different logics are obtained by “tuning” a single parameter, namely a constraint on the applicability of the cut rule and on the (left and right, respectively) rules for \(\Box\) and \(\Diamond\). Starting points for this research are 2-sequents and indexed-based calculi (sequents and tableaux). By extending and modifying existing proposals, we show how to achieve a syntactical proof of the cut-elimination theorem that is as close as possible to the one for first-order classical logic. In doing this, we implicitly show how small is the proof-theoretical distance between classical logic and the systems under consideration.
- Źródło:
-
Bulletin of the Section of Logic; 2023, 52, 4; 459-495
0138-0680
2449-836X - Pojawia się w:
- Bulletin of the Section of Logic
- Dostawca treści:
- Biblioteka Nauki
Artykuł