Abstract
We consider a family of sequent systems with "well-behaved" logical rules in which the cut rule and/or the identity-axiom are not present. We provide a semantic characterization of the logics induced by these systems in the form of non-deterministic three-valued or four-valued matrices. The semantics is used to study some important proof-theoretic properties of these systems. These results shed light on the dual semantic roles of the cut rule and the identity-axiom, showing that they are both crucial for having deterministic finite-valued semantics.
| Original language | English |
|---|---|
| Pages (from-to) | 575-595 |
| Number of pages | 21 |
| Journal | Journal of Multiple-Valued Logic and Soft Computing |
| Volume | 21 |
| Issue number | 5-6 |
| State | Published - 2013 |
Keywords
- Cut-elimination
- Multiple-valued logics
- Non-deterministic semantics
- Proof theory
- Semantic proofs
- Sequent systems