A monadic logic of ordered abelian groups
Official URL
Abstract
A many-valued modal logic with connectives interpreted in the ordered additive group of real numbers is introduced as a modal counterpart of the one-variable fragment of a (monadic) first-order real-valued logic. It is shown that the logic is decidable and admits an interpretation of the one-variable fragment of first-order Lukasiewicz logic. Completeness of an axiom system for the modal-multiplicative fragment is established via a Herbrand theorem for its first-order counterpart. A functional representation theorem is then proved for a class of monadic lattice-ordered abelian groups and used to establish completeness of an axiom system for the full logic.
Date Issued
2020-07-01
Publication Type
Book Section
Subject(s)
Language(s)
en
Editor(s)
Olivetti, Nicola | |
Verbrugge, Rineke | |
Negri, Sara | |
Sandu, Gabriel |
Additional Credits
Publisher
College Publications
ISBN
978-1-84890-341-8
Book Title
Access(Rights)
restricted