Convex algebras on an interval with semicontinuous monotone operations
Year: 2026
Type: article
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.
Authors: Ana Sokolova, Harald Woracek
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7138110674