Next Article in Journal
Numerical Solutions of Coupled Burgers’ Equations
Next Article in Special Issue
Synthetic Tableaux with Unrestricted Cut for First-Order Theories
Previous Article in Journal
On One Problems of Spectral Theory for Ordinary Differential Equations of Fractional Order
Previous Article in Special Issue
Deduction in Non-Fregean Propositional Logic SCI
Open AccessArticle

Hybrid Deduction–Refutation Systems

1
Department of Philosophy, Stockholm University, SE-10691 Stockholm, Sweden
2
Visiting professorship at Department of Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
Axioms 2019, 8(4), 118; https://doi.org/10.3390/axioms8040118
Received: 27 August 2019 / Revised: 8 October 2019 / Accepted: 10 October 2019 / Published: 21 October 2019
(This article belongs to the Special Issue Deductive Systems)
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 system of natural deduction for classical propositional logic, for which I show soundness and completeness for both deductions and refutations. View Full-Text
Keywords: deductive refutability; refutation systems; hybrid deduction–refutation rules; derivative hybrid rules; soundness; completeness; natural deduction; meta-proof theory deductive refutability; refutation systems; hybrid deduction–refutation rules; derivative hybrid rules; soundness; completeness; natural deduction; meta-proof theory
MDPI and ACS Style

Goranko, V. Hybrid Deduction–Refutation Systems. Axioms 2019, 8, 118.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop