First-degree Entailment and Binary Consequence Systems.

This paper presents an account of Belnap and Dunn’s logic of first-degree entailment and some related logics based on a proof-theoretic machinery of binary (F MLA - F MLA) consequence systems. It is shown how the logic of first-degree entailment can be represented by various deductively equivalent systems, up to a purely structural system with transitivity as the only inference rule. A family of possible extensions of this later system is represented in a systematic manner. This is a review article, which recapitulates certain recent advances in investigating the Belnap-Dunn logic, and organizes the corresponding material from a genuinely first-degree entailment perspective.

Authors

• Yaroslav Shramko

Keywords

• First-degree entailment
• consequence system
• binary consequence
• logical frameworks
• structural reasoning
• super-Belnap logics