Convex algebras on an interval with semicontinuous monotone operations
Logic in Computer Science
2026-03-17 v1 Logic
Abstract
In a recent work of Matteo Mio on compact quantitative equational theories (here compact means that all its consequences are derivable by means of finite proofs) convex algebras on the carrier set [0,1] whose operations are monotone and satisfy certain semicontinuity properties occurred. We fully classify those algebraic structures by giving an explicit construction of all possible convex operations on [0,1] possessing the mentioned properties. Our result thus describes exactly the range of theories to which Mio's theorem applies.
Keywords
Cite
@article{arxiv.2603.14955,
title = {Convex algebras on an interval with semicontinuous monotone operations},
author = {Ana Sokolova and Harald Woracek},
journal= {arXiv preprint arXiv:2603.14955},
year = {2026}
}