Hybrid Deduction–Refutation Systems

Valentin Goranko
2019 Axioms  
Hybrid deduction–refutation systems are deductive systems intended to derive both valid and non-valid, i.e., semantically refutable, formulae of a given logical system, by employing together separate derivability operators for each of these and combining 'hybrid derivation rules' that involve both deduction and refutation. The goal of this paper is to develop a basic theory and 'meta-proof' theory of hybrid deduction–refutation systems. I then illustrate the concept on a hybrid derivation
more » ... of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations.
doi:10.3390/axioms8040118 fatcat:ar4xhq35yjcsvjxa7hnz5fqvim