Work

Pointed Modal Abelian Logic, Algebraically

Year: 2026

Type: article

Abstract: In this article, we investigate the pointed modal logic of reals.We first establish its relational (Kripke) semantics with bounded valuations in the Abelian ℓ-group of real numbers with the distinguished negative constant -1.To study this logic algebraically, we introduce the variety of negatively pointed modal Abelian ℓ-groups, in particular we focus on the strongly pointed members thereof.Constructing complex algebras and canonical frames, we establish a Truth Lemma connecting the relational and algebraic frameworks.Since finitary axiomatizations cannot fully capture the Kripke validities of the reals we introduce further algebraic constraints, in particular including an infinitary Archimedeanstyle rule.Finally, we prove a corresponding 'infinitary algebraic completeness' result for pointed modal Abelian logic with respect to the variety of pointed modal Abelian ℓ-groups.

Source: Electronic Proceedings in Theoretical Computer Science

DOI: 10.4204/eptcs.447.29

Authors: Filip Jankovec, Wolfgang Poiger

Institutions: Czech Academy of Sciences, Czech Academy of Sciences, Institute of Computer Science

Language: English

Topic: Advanced Algebra and Logic

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W7166440370

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