Abstract
The goal of this article is to design a uniform proof-theoretical framework encompassing classical, non-monotonic and paraconsistent logic. This framework is obtained by the control sets logical device, a syntactical apparatus for controlling derivations. A basic feature of control sets is that of leaving the underlying syntax of a proof system unchanged, while affecting the very combinatorial structure of sequents and proofs. We prove the cut-elimination theorem for a version of controlled propositional classical logic, i.e. the sequent calculus for classical propositional logic to which a suitable system of control sets is applied. Finally, we outline the skeleton of a new (positive) account of non-monotonicity and paraconsistency in terms of concurrent processes.
Original language | English |
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Pages (from-to) | 21-40 |
Number of pages | 20 |
Journal | Journal Of Logic And Computation |
Volume | 27 |
Issue number | 1 |
DOIs | |
Publication status | Published - Feb 2017 |
Keywords
- Classical logic
- Context-sensitiveness
- Cut-elimination
- Non-monotonicity
- Paraconsistency
- Proof-theory