First-Degree Entailment and its Relatives
| Autor: | Yaroslav Shramko, Alexander Belikov, Dmitry Zaitsev |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Degree (graph theory) Logic 010102 general mathematics Binary number Of the form 06 humanities and the arts 0603 philosophy ethics and religion 01 natural sciences Logical consequence Dual (category theory) TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES History and Philosophy of Science Turnstile 060302 philosophy Preferential entailment 0101 mathematics Completeness (statistics) Mathematics |
| Zdroj: | Studia Logica. 105:1291-1317 |
| ISSN: | 1572-8730 0039-3215 |
| DOI: | 10.1007/s11225-017-9747-7 |
| Popis: | We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form $$\varphi \vdash \psi $$ , where both $$\varphi $$ and $$\psi $$ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left (or both) of the turnstile. In this way, it is possible to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations. |
| Databáze: | OpenAIRE |
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