Work

Compact Quantitative Theories of Convex Algebras

Year: 2025

Type: article

Abstract: We introduce the concept of compact quantitative equational theory. A quantitative equational theory is defined to be compact if all its consequences are derivable by means of finite proofs. We prove that the theory of interpolative barycentric (also known as convex) quantitative algebras of Mardare et. al. is compact. This serves as a paradigmatic example, used to obtain other compact quantitative equational theories of convex algebras, each axiomatizing some distance on finitely supported probability distributions.

Source: Electronic Notes in Theoretical Informatics and Computer Science

DOI: 10.46298/entics.16876

Author: Matteo Mio

Institutions: École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Funder: Agence Nationale de la Recherche

Award: Quantitative Reasoning Methods for Probabilistic Logics