Unifying logics via context-sensitiveness

Mario Piazza, Gabriele Pulcini

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

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 languageEnglish
Pages (from-to)21-40
Number of pages20
JournalJournal Of Logic And Computation
Volume27
Issue number1
DOIs
Publication statusPublished - Feb 2017

Keywords

  • Classical logic
  • Context-sensitiveness
  • Cut-elimination
  • Non-monotonicity
  • Paraconsistency
  • Proof-theory

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