2022/06/20 by Selcuk Kaan Tabakci
Arts and Humanities · Computer Science · #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Syntax, Semantics, Linguistic Variation
paper · pdf · doi:10.1007/s10992-022-09661-9
crossref issued 2022/06/20 · crossref published 2022/06/20 · crossref published-online 2022/06/20 · openalex publication_date 2022/06/20 · crossref created 2022/06/20 · crossref deposited 2022/09/20 · crossref published-print 2022/10/01 · openalex created_date 2025/10/10 · crossref indexed 2026/07/28 · openalex updated_date 2026/07/31
Abstract Frame semantics for negation on the Australian Plan accommodates many different negations, but it falls short on accommodating subminimal negation when the language contains conjunction and disjunction. In this paper, I will present a multi-relational frame semantics –multi-incompatibility frame semantics– that can accommodate subminimal negation. I will first argue that multi-incompatibility frames are in accordance with the philosophical motivations behind negation on the Australian Plan, namely its modal and exclusion-expressing nature. Then, I will prove the soundness and completeness results of a subminimal logic that consists of the multi-incompatibility semantics and a proof system with operational rules that characterize subminimal negation, conjunction and disjunction. Lastly, I will prove some key correspondence theorems that relate frame conditions to certain principles that are associated with stronger negations, which will give rise to a new kite of negations that includes subminimal negation.