Inquisitive first-order logic is neither compact nor recursively axiomatizable
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917356399230976 |
|---|---|
| author | Ciardelli, Ivano Kontinen, Juha |
| author_facet | Ciardelli, Ivano Kontinen, Juha |
| contents | Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which extends classical first-order logic with a question-forming disjunction and a question-forming existential quantifier. This logic makes it possible to formalize a broad range of questions, and to capture their logical relations to each other and to statements. Since its introduction in 2009, two central questions about the meta-theoretic properties of InqBQ have been open: the first is whether entailment is compact, in the sense that any conclusion that follows from a set of premises already follows from a finite subset of these premises; the second is whether the set of validities is recursively enumerable and, thus, whether the logic admits a recursive axiomatization. We settle these questions in the negative: entailment in InqBQ is not compact, and the set of validities of InqBQ is not recursively enumerable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inquisitive first-order logic is neither compact nor recursively axiomatizable Ciardelli, Ivano Kontinen, Juha Logic Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which extends classical first-order logic with a question-forming disjunction and a question-forming existential quantifier. This logic makes it possible to formalize a broad range of questions, and to capture their logical relations to each other and to statements. Since its introduction in 2009, two central questions about the meta-theoretic properties of InqBQ have been open: the first is whether entailment is compact, in the sense that any conclusion that follows from a set of premises already follows from a finite subset of these premises; the second is whether the set of validities is recursively enumerable and, thus, whether the logic admits a recursive axiomatization. We settle these questions in the negative: entailment in InqBQ is not compact, and the set of validities of InqBQ is not recursively enumerable. |
| title | Inquisitive first-order logic is neither compact nor recursively axiomatizable |
| topic | Logic |
| url | https://arxiv.org/abs/2603.20845 |