2019
DOI: 10.1145/3325821
|View full text |Cite
|
Sign up to set email alerts
|

Abstract: This paper explores the proof theory necessary for recommending an expressive but decidable first-order system, named MAV1, featuring a de Morgan dual pair of nominal quantifiers. These nominal quantifiers called 'new' and 'wen' are distinct from the self-dual Gabbay-Pitts and Miller-Tiu nominal quantifiers. The novelty of these nominal quantifiers is they are polarised in the sense that 'new' distributes over positive operators while 'wen' distributes over negative operators. This greater control of bookkeepi… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
13
0

Year Published

2019
2019
2022
2022

Publication Types

Select...
3
2

Relationship

2
3

Authors

Journals

citations
Cited by 7 publications
(13 citation statements)
references
References 59 publications
0
13
0
Order By: Relevance
“…A proof in BV1 is a derivation of the form • P. When such a derivation exists, we say that P is provable, and write P. Cut elimination holds for BV1 as a consequence of cut-elimination for MAV1 (Horne et al 2016). A full proof appears in a companion paper (Horne et al 2018).…”
Section: The Syntax Inference Rules and Structural Rules Of Bv1mentioning
confidence: 99%
See 4 more Smart Citations
“…A proof in BV1 is a derivation of the form • P. When such a derivation exists, we say that P is provable, and write P. Cut elimination holds for BV1 as a consequence of cut-elimination for MAV1 (Horne et al 2016). A full proof appears in a companion paper (Horne et al 2018).…”
Section: The Syntax Inference Rules and Structural Rules Of Bv1mentioning
confidence: 99%
“…No further problematic cases are introduced by quantifiers. As a technical device, we define a form of restricted context called a killing context (Chaudhuri et al 2011) consisting of a hole surrounded by quantifiers ∀ and И. Splitting, proven in a companion paper as the main technical lemma required for proving cut elimination (Horne et al 2018), is formulated as follows for BV1. Traditionally, in the sequent calculus, any connective can be selected and a corresponding rule applied.…”
Section: Extending the Concept Of Left Proofs To Bv1mentioning
confidence: 99%
See 3 more Smart Citations