Abstract
Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a general non-deterministic Kripke-style semantics is provided. This general semantics is then used to provide a constructive (and very natural), sufficient and necessary coherence criterion for the validity of the strong cut-elimination theorem in such a system. These results suggest new syntactic and semantic characterizations of basic constructive connectives.
| Original language | English |
|---|---|
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | Logical Methods in Computer Science |
| Volume | 6 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2010 |
Keywords
- Cut-elimination
- Kripke semantics
- Non-deterministic semantics
- Nonclassical logics
- Sequent calculus