Multiagent GLP: Secure Decentralized Logic Programming

• Multiagent GLP (maGLP) is a secure, concurrent logic programming framework that integrates atomic SRSW channels for deterministic inter-agent communication.
• It extends classical logic programming by adding paired writer/reader variables and cryptographic identity verification, enabling robust decentralized applications.
• The system ensures safety through acyclicity, monotonicity, and blockchain-like immutability, providing provable security in distributed, multiagent environments.

Multiagent Grassroots Logic Programs (maGLP) refers to a secure, concurrent, multiagent logic programming language designed to implement grassroots platforms—distributed applications operated by cryptographically identified peers on their own devices, with no privileged global resource, and robust to the challenges of open deployment including security, concurrency, and decentralization. The central innovation of maGLP is the extension of classic logic programming with atomic, paired single-reader/single-writer (SRSW) logic variables that act as secure channels of communication among autonomous agents, whose identities are anchored by public key cryptography. This combines rigorous semantic control familiar from logic programming and linear logic with security, interoperability, and provable safety suited for decentralized platforms (Shapiro, 17 Oct 2025, Shapiro, 6 Feb 2026).

1. Syntax and Semantic Foundations

maGLP builds on standard logic programming (LP) syntactic structures but introduces new constructs and conventions:

• Variables and SRSW Structure: There are two sorts of variables: writers ($V$) and their paired readers ($V?$), forming the set $\mathcal{V} = V \cup V?$. Each variable is restricted to single assignment and single consumption within the system, crucial for ensuring SRSW and preventing ambiguity or state clashes.
• Agent Universe: Each agent $p \in \Pi$ (with $\Pi$ countable) is identified by a public key $pk_p$.
• Terms, Atoms, and Clauses: Terms may be variables (writer or reader), constants, or compound function applications. Atom and goal multisets are extended accordingly. Each clause $H :– B$ must conform to the SRSW constraint: every variable (as writer or reader) appears at most once. Complete program $M$ is a finite set of such clauses.
• Configurations: Each agent maintains a local asynchronous resolvent $(G_p, \sigma_p)$, with $G_p$ its current goal multiset and $\sigma_p$ a substitution containing pending reader assignments. A global configuration $c$ is a tuple of such local states, one per participating agent.

The single-assignment SRSW discipline, grounded in these definitions, guarantees both structural soundness and communication determinism in a multiagent context (Shapiro, 17 Oct 2025, Shapiro, 6 Feb 2026).

2. Multiagent Operational Semantics

maGLP employs a transactions-based transition system with the following operation primitives:

1. Reduce$_p$: A unary (local) reduction. Agent $p$ selects a goal $A \in G_p$, matches against the first applicable clause (using writer-only unification), generating new goals and reader substitutions; updates are applied to the local state.
2. Communicate$_{p \rightarrow q}$: Binary communication. When agent $p$ holds an assignment $X? := T$ in its substitution and agent $q$ has $X?$ as a goal, the assignment is transferred and applied.
3. Network$_{p \rightarrow q}$: Handles routing of channel messages so that SRSW variable assignments synchronize correctly between agents.

A run of maGLP is a fair interleaving of these transactions, with nondeterministic scheduling—no strict global scheduler is mandated. Initial configurations use anonymous variables, ensuring that agents start identically but retain local uniqueness (Shapiro, 17 Oct 2025).

3. Cryptographically Secure Communication

Security is a first-class concern in maGLP, achieved by tightly coupling logic variable assignments to cryptographic operations:

• Agent Identities and Keys: Each agent possesses a $(pk_p, sk_p)$ keypair; their public key serves as global identity.
• Message Security: Every inter-agent communication (including variable assignment propagation) is encapsulated as follows:

$$E_{M,p,q} = \mathsf{Encrypt}_{pk_q} \big( \mathsf{Sign}_{sk_p} \big( \mathsf{Attest}_M(E) \big) \big)$$

Here, $\mathsf{Attest}_M(E)$ attests that the agent runs a specific GLP module $M$, and the combination of encryption and signature ensures confidentiality, authenticity, and code provenance.

• Assumptions: The model relies on standard public-key assumptions: signature unforgeability, encryption confidentiality, and attestation soundness.

This design enables agents to verify identities, code integrity, and the validity of every state transition or communication event, neutralizing impersonation or code injection attacks in distributed settings (Shapiro, 17 Oct 2025).

4. Safety Properties and Decentralized Correctness

Key safety and semantic properties of maGLP are direct generalizations of their single-agent GLP antecedents, made robust in a multiagent setting:

• Deductiveness: Every finite maGLP run’s cumulative effect is a logical deduction from the initial program $M$, after reader/writer erasure. Resolution and communication preserve logical soundness.
• SRSW Preservation: If SRSW holds initially, it remains invariant—no variable is duplicated or reassigned within any agent or across the system.
• Acyclicity: Cyclic terms are statically precluded by occurs checks and SRSW constraints, preventing circular data flows and logical paradoxes.
• Monotonicity: Any goal reducible at some point remains reducible (perhaps modulo reader instantiation) in all subsequent states, provided it is not yet reduced.

These invariants guarantee that race conditions, aliasing, and data corruption—common pitfalls in concurrent and distributed computation—are structurally and semantically excluded (Shapiro, 17 Oct 2025, Shapiro, 6 Feb 2026).

5. Grassroots and Blockchain-Like Properties

maGLP formalizes and proves the grassroots property, ensuring that the behavior and protocol composition of any coalition of agents $P$ remains coherent and correct as additional agents join or cooperate. Specifically:

• Grassroots Protocol: For any nonempty subset $P \subset P' \subseteq \Pi$, the system satisfies both obliviousness ($T(P) \uparrow P' \subseteq T(P')$) and interactivity (new agents can induce system state traces impossible in smaller coalitions).
• GLP Streams as Blockchains: The structure of SRSW assignments and attested communications yield blockchain analogues:
  • Immutability (no re-binding),
  • Unforkability (by SRSW uniqueness),
  • Non-repudiation (via signature and attestation),
  • Acyclicity (structure preserves ordered, append-only extension).
• Interlaced Streams: Each agent’s stream can reference multiple predecessors, yielding blocklace structures, generalizing conventional blockchains to multi-parent, multi-agent cooperative data logs.

These constructs replace energy-intensive proof-of-work with semantic and cryptographic guarantees, suited for cooperative, distributed systems (Shapiro, 17 Oct 2025).

6. Implementation-Ready Transition Systems (madGLP)

The abstract semantics of maGLP are refined for implementation as madGLP—a multiagent, deterministic operational semantics:

• Agent Local State: Each agent stores a deterministic queue of active goals, tables of suspended and failed goals, a global writers table mapping shared variables, and explicit queues of outgoing/incoming messages.
• Algorithmic Structure: Reduce, Send, and Receive operations are fully deterministic at the agent level; overall system evolution is globally nondeterministic, reflecting true asynchronous distributed deployment.
• Refinement Mapping: A formal mapping $\pi$ connects states of madGLP to the abstract maGLP semantics, guaranteeing liveness, completeness, and full semantic compatibility (subject to asynchronous message delivery).

This approach provides a mathematically grounded, machine-verifiable specification suitable for AI-generated, platform-independent implementations, including for smartphones communicating peer-to-peer using WebRTC or TCP/IP, and using data structures such as active queues, writer tables, and serialized message formats (Shapiro, 6 Feb 2026).

7. Example: Secure Grassroots Social Graph Construction

The flexibility and security of maGLP enable expressive distributed application development. The grassroots social graph application is illustrative:

• Initialization: Each agent starts with authenticated user and network channels; anonymous variables ensure fresh local context.
• Cold-Call and Friend-Mediated Introduction: Logic code for cold-call and mediated introduction protocols establishes new social links, exchanging attested, signed messages along SRSW-typed channels.
• Code Assurance: All communications encapsulate $E_{M,p,q}$ envelopes; receiving agents perform attestation and signature verification before accepting state changes or peer links.

This pattern enables authenticated, trust-minimized social networking without central control, instantiating the core vision of grassroots platforms (Shapiro, 17 Oct 2025).

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References:

• Grassroots Logic Programs: A Secure, Multiagent, Concurrent, Logic Programming Language (Shapiro, 17 Oct 2025)
• Implementing Grassroots Logic Programs with Multiagent Transition Systems and AI (Shapiro, 6 Feb 2026)