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This paper formalizes a deterministic, multiagent logic programming framework where AI agents (specifically Claude) are used to translate mathematical specifications into Dart implementations for workstations and smartphones. The approach leverages a single-occurrence invariant to ensure correctness in concurrent systems, effectively bridging formal logic with practical AI-driven software development. For technical audiences, the key takeaway is the validation of an automated pipeline that converts abstract logical models into executable code while maintaining rigorous proof of correctness.
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Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI (Full Version)

arXiv2 min read

arXiv:2602.06934v4 Announce Type: replace-cross Abstract: Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its paired reader, and may contain additional readers and/or writers. This enables the concise expression of rich multidirectional communication modalities. The language was introduced together with concurrent (cGLP) and multiagent (maGLP) operational semantics. Here, we derive from these (\ia)~dGLP, a deterministic counterpart of cGLP, and (\ib)~madGLP, a counterpart of maGLP in which deterministic agents communicate solely by asynchronous message passing, and prove them correct against their abstract counterparts. maGLP shared variable pairs spanning agents can be implemented as local variables paired by \emph{global links}, with correctness following from disjoint substitution commutativity (a consequence of GLP's single-occurrence invariant). We further prove that madGLP is grassroots. Both dGLP and madGLP serve as formal specifications for an AI-driven implementation discipline (math $\to$ informal spec $\to$ Dart) employed and described here: from dGLP, AI (Claude) developed a workstation-based GLP implementation in Dart, and from madGLP it is developing a smartphone-based multiagent one.

Abstract:Grassroots Logic Programs (GLP) is a concurrent logic programming language in which logic variables are partitioned into paired readers and writers. An assignment is produced at most once via a writer and consumed at most once via its paired reader, and may contain additional readers and/or writers. This enables the concise expression of rich multidirectional communication modalities. The language was introduced together with concurrent (cGLP) and multiagent (maGLP) operational semantics. Here, we derive from these (\ia)~dGLP, a deterministic counterpart of cGLP, and (\ib)~madGLP, a counterpart of maGLP in which deterministic agents communicate solely by asynchronous message passing, and prove them correct against their abstract counterparts. maGLP shared variable pairs spanning agents can be implemented as local variables paired by \emph{global links}, with correctness following from disjoint substitution commutativity (a consequence of GLP's single-occurrence invariant). We further prove that madGLP is grassroots. Both dGLP and madGLP serve as formal specifications for an AI-driven implementation discipline (math $\to$ informal spec $\to$ Dart) employed and described here: from dGLP, AI (Claude) developed a workstation-based GLP implementation in Dart, and from madGLP it is developing a smartphone-based multiagent one.

Programming Languages (cs.PL); Artificial Intelligence (cs.AI); Distributed, Parallel, and Cluster Computing (cs.DC); Logic in Computer Science (cs.LO); Multiagent Systems (cs.MA)

arXiv:2602.06934 [cs.PL]

(or arXiv:2602.06934v4 [cs.PL] for this version)

Full text under the publisher's open licence · 213 words

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