Grassroots Logic Programs (GLP)

• Grassroots Logic Programs (GLP) are secure, decentralized logic frameworks that use single-reader/single-writer variables and cryptographic protocols for exclusive, authenticated communication.
• They enforce concurrency through an asynchronous transition system that guarantees deadlock-free, immutable, and non-repudiable message exchanges between agents.
• GLP underpins decentralized applications such as grassroots social networks, cryptocurrencies, and federated governance by ensuring secure, verifiable, and scalable multiagent interactions.

Grassroots Logic Programs (GLP) are a class of logic programming languages and frameworks designed to support secure, multiagent, and concurrent computation for decentralized applications on grassroots platforms. In this context, “grassroots” denotes systems that are built and governed by networked, cryptographically-identified individuals, prioritizing autonomy, security, and composability, and enabling organic federation of independently deployed instances. GLP extends the standard operational model of logic programming by integrating concurrency, secure communication via cryptographic protocols, and rigorous safety properties, establishing a foundation for grassroots social networks, cryptocurrencies, and democratic federations (Shapiro, 17 Oct 2025).

1. Formal Structure and Operational Model

GLP generalizes classical logic programming—traditionally formalized by transition systems on goals and clauses—by introducing paired single-reader/single-writer (SRSW) logic variables. Each variable pair designates an exclusive communication channel: one writer (producer) and one reader (consumer). In a GLP computation, operational reduction proceeds nondeterministically across goals while strictly enforcing pairing constraints. The model ensures that:

• Each writer variable is assigned exactly once by one process (no writer-to-writer aliasing),
• Each reader variable is assigned a value via an explicit message from its unique paired writer,
• Any message between agents is encrypted, signed, and digitally attested, supporting end-to-end integrity and identity verification.

Formally, a GLP system specifies an asynchronous transition system:

$\mathrm{GLP} = (C, c_0, T)$

where $C$ is a set of asynchronous resolvents (pairs of active goals and reader substitutions), $c_0$ is the initial resolvent, and $T$ consists of transitions representing goal reduction or communication of writer assignments.

2. Security, Cryptography, and Attestation

A defining feature of GLP is the system-level integration of cryptographic primitives into its operational semantics. Secure message passing in GLP is achieved by:

• Encrypting each message from writer to reader with the recipient’s public key,
• Appending a digital signature generated with the sender’s private key,
• Attaching an attestation: $$\mathrm{attestation}(X, \mathrm{att}(\mathrm{Agent}, \mathrm{Module}))$$ and module guard predicates, enabling code integrity and provenance verification.

An assignment (communication event) is thus transmitted in the form $E_{M,p,q} = (X?:=T)$, where $M$ encodes the module (program identity), $p$ the sender, and $q$ the recipient. The security guarantees are:

• Integrity: Unauthorized modification of messages is detectable by signature verification,
• Confidentiality: Only the designated recipient can decrypt the message,
• Non-repudiation: Assignment origins are irrefutable due to digital signatures,
• Code provenance and compliance: Attestation predicates verify that code versions and agents adhere to agreed protocols.

This infrastructure enables correct participants to authenticate identities, establish secure channels, and detect or exclude faulty/malicious code without reliance on a trusted third party.

3. Concurrency, Multiagent Execution, and Asynchronous Streams

GLP operational semantics permit both single-agent concurrency (multiple goals reduced in parallel subject to SRSW invariance) and true multiagent computation. In the multiagent case, each agent maintains a local program state, and inter-agent communication occurs by transferring assignments via secure, paired variable channels. The resulting system is modeled as a multiagent transition system (TS):

$\mathrm{TS} = (C, c_0, T)$

with $C$ a set of states (asynchronous resolvents per agent), and $T$ containing transitions for local goal reduction and for “Communicate” events (writer-to-reader assignment transmission).

This structure ensures:

• Deadlock-free coordination: Each communication is point-to-point between unique writer/reader pairs,
• Determinism at channel level: Absence of race conditions due to SRSW discipline,
• Safety against denial-of-service and equivocation attacks: Since assignment equivocation (i.e., multiple concurrent values per writer) is structurally impossible.

As agents independently evolve their local state and exchange variable assignments, the global execution forms a distributed directed acyclic graph (DAG) of events, denoted in the literature as a “blocklace.”

4. SRSW Variables and Safety Properties

SRSW (single-reader/single-writer) variable pairing constitutes a primitive for safe, exclusive communication. In every well-formed clause (or goal), every variable appears at most once in a writer and at most once in a reader position. GLP enforces the following invariants:

• SRSW Preservation: All reduction and communication steps maintain this strict pairing; violations are precluded by syntactic and operational checks.
• Acyclicity: Writers cannot be bound to terms containing their own paired reader; the “occurs check” is extended accordingly to prevent cyclic term graphs.
• Monotonicity: If a goal is reducible at time $t$, it (or an instance via reader substitutions) remains reducible at all subsequent steps.
• Computation as Deduction: For any computation $G_0 \leadsto_{\mathcal{P}, \sigma} G_n$ in program $\mathcal{P}$, it holds that $$\mathcal{P} \models G_0 \sigma \rightarrow G_n \sigma$$.

These properties collectively guarantee that GLP computations correspond to valid deductions in the underlying logic, and that the behavior remains consistent across both sequential and concurrent reductions.

5. Blockchain-like Security Guarantees and Stream Structure

GLP streams possess key properties that are directly analogous to those enforced by blockchain systems:

Property	GLP Mechanism	Explanation
Immutability	SRSW, single-assign.	Once a writer is assigned, the value cannot change; no conflicting writes are possible.
Unforkability	SRSW, acyclicity	Each variable assignment event occurs exactly once per channel; forks are structurally prohibited.
Non-repudiation	Digital signatures	Assignment records are signed and attributed to the originating agent.
Blocklace	Concurrent streams	Distributed execution forms a DAG of assignments and reductions, supporting consistency and history.

Interlaced GLP computation forms a “blocklace” (Editor’s term), which generalizes a blockchain to allow high concurrency and compound event relationships, without requiring resource-intensive global consensus or proof-of-work mechanisms.

6. Grassroots Social Graph Protocol and Applications

A principal application of GLP is the implementation of a grassroots social graph—a decentralized, authenticated, cryptographically-secured network of user connections. The protocol is defined by GLP clauses implementing:

• Cold-call introduction (establishing new connections directly via network messages),
• Peer-mediated introductions (establishing trust chains based on existing connections),
• Attestation predicates for code and identity integrity.

Connection establishment involves transmission of encrypted, signed offers containing unbound response variables; UI-level and protocol-level negotiation ensure only authenticated, attested channels are added to the social graph. All communication events are validated via cryptographic attestation, and updates are merged and tagged, supporting asynchronous state propagation across distributed devices.

GLP has been demonstrated as a foundation for:

• Secure distributed social networks,
• Federated or cooperative cryptocurrencies (leveraging blocklace structure for asset/ledger management),
• Grassroots democratic federations with anonymous, verifiable voting protocols,
• Smartphone-ready implementations using transition systems (e.g., irGLP, IRmaGLP) compatible with platforms such as Dart/Flutter, and TEE integration for cryptographic operations.

7. Relationship to Earlier Grassroots Logic Programming and Extensions

GLP, in its contemporary formulation, extends traditional “grassroots” logic programming frameworks—previously concerned with community-based agreement and joint fixpoints—by supplying a concrete operational model with explicit concurrency, secure message-passing, and attestation. Earlier frameworks modelled collective agreement by fixed-point semantics over agent-coupled logic programs, sometimes with social conditions (as in SOLP (0805.3518)). In contrast, GLP provides:

• Language-level constructs for secure channel communication,
• A direct mapping of program variables to cryptographically protected streams,
• Operational and cryptographic safety guarantees critical for adversarial environments and decentralized control.

The GLP paradigm thus bridges foundational logic programming principles with the practical and security exigencies of emergent grassroots platforms, supporting robust and scalable distributed applications in untrusted, federated environments.

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In summary, Grassroots Logic Programs (GLP) formalize a logic programming-based approach to secure, concurrent, multiagent systems. By intertwining SRSW logic variables, cryptographic attestation, and rigorous operational semantics, GLP provides a theoretically and practically robust substrate for decentralized social, economic, and governance infrastructure on grassroots platforms (Shapiro, 17 Oct 2025).