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Formalising and Implementing Grassroots Social Contracts: From Legal Text to Grassroots Platforms (Full Version)

James Golike, Andy Lewis-Pye, Ehud Shapiro

arXiv:2609.06231v2cs.CYcs.DCcs.HCcs.PL

TL;DR

Existing contract languages bind parties at formation and maintain one global contract state, leaving the paper’s question about independently formed groups and their later interaction unaddressed. The paper defines grassroots social contracts, formalises them as act schemas, and compiles qualifying schemas into transactions; it proves their protocols grassroots and volitionally so, with decidable sufficient conditions.

  • Problem

    The paper asks how a contract can induce systems over finite sets of people and support interaction between independently formed groups, a question existing languages with one global state cannot pose.

    Source: §1 · p. 5

  • Method

    The paper specifies contract acts as schemas, checks Introduction, Provenance, and Volition, then compiles qualifying schemas into volition-guarded atomic transactions.

    Source: §1 · pp. 3, 5

  • Results

    Independently adopted communities can later merge, any two parties may come into relation without permission, and every act participant is a party.

    Source: §1 · p. 3, §11 · p. 29

  • Takeaways & Limitations

    The three decidable schema conditions are sufficient to certify a contract as grassroots, though they are not necessary.

    Source: §11 · p. 30

    The conditions are sufficient but not necessary, and a characterization of all grassroots contracts remains open.

    Source: §11 · p. 30

Abstract

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Two centuries ago Pierre-Joseph Proudhon envisioned a social contract that is (1) an agreement of man with man; (2) reciprocal; (3) imposing no obligation upon the parties except that which results from their personal promise; (4) subject to no external authority; (5) freely accepted and signed by all the participants; (6) of the nature of a contract of exchange. He also envisioned a property of social contracts, analogous to a property of digital platforms we term grassroots: that one could "make a contract with all, as ... with some"; digitally, that a grassroots platform can have multiple instances, which may coalesce by mutual consent. We define grassroots social contracts as social contracts meeting these conditions and that (7) people are free to deal with each other; and (8) there is no external register of people. We show that a grassroots social contract can be transformed into a working grassroots platform through an abstraction cascade, from the contract text to formal act schemas, verified syntactically to be grassroots, and then to volition-guarded multiagent atomic transactions. Act schemas are a formal language for the acts the contract describes, each naming the parties' roles, which of them must will the act, and its precondition and effect at each role. Any contract written in this language meets the eight conditions, provided it is syntactically grassroots, satisfying three decidable conditions, Introduction, Provenance and Volition. We prove that the protocol realising a syntactically grassroots contract is grassroots, and volitionally so. Clauses of a grassroots social contract are of three legal types: a breach of an enforced clause is impossible with a correct implementation; a breach of an attested or undertaken clause can be taken to court, with signed evidence for an attested clause. We illustrate them with a grassroots social graph and grassroots currencies.

1. Introduction

The paper formalises Proudhon’s reciprocal, freely adopted social contract as a grassroots protocol whose instances can form and coalesce without external authority. It gives decidable conditions for turning contract text into schemas and transactions, proves the resulting protocol grassroots, and distinguishes clause types by their enforceability and records.

1. Introduction

  • Proudhon’s contract is reciprocal and freely accepted, while its grassroots extension lets independent platform instances coalesce by mutual consent.The paper adds that people are free to deal with one another and that there is no external register of people.Source: §1 · p. 2
  • Grassroots protocols allow any two parties to come into relation without permission, let independently adopted communities merge, and require every act participant to be a party.No registry issues identifiers, no log orders acts, and no authority timestamps them.Source: §1 · pp. 2–3
  • Act schemas specify parties’ roles, required volition, and each role’s preconditions and effects; Introduction, Provenance, and Volition make a contract syntactically grassroots.The conditions are sufficient for the eight contract conditions and are decidable; a checker certifies the two contracts in the paper.Source: §1 · p. 3
  • A syntactically grassroots contract compiles into a polite set of volition-guarded transactions, and its protocol is proved grassroots and volitionally so.The Introduction, Provenance, and Volition conditions are decidable; the compilation and checker are algorithmic, while rendering legal text as schemas remains a matter of judgement.Source: §1 · pp. 3–4
  • Enforced clauses cannot be breached by a correct implementation, while attested and undertaken breaches can be taken to court, with signed evidence for attested clauses.For attested clauses, the contract records the breach; for undertaken clauses, it records who made the undertaking, whose performance occurs outside the contract.Source: §1 · p. 4
  • The paper illustrates the framework with a social graph carrying signed items and a currency of personal coins, both certified from their schemas.The cascade proceeds from legal text to act schemas and then volition-guarded transactions; prior work describes the steps from transactions to a working app.Source: §1 · pp. 3–5

2. Two Grassroots Social Contracts

The paper carries two contracts through its formalisation: a social graph with signed items and a currency of personal coins. Their clauses illustrate how acts and non-act commitments are represented in the contract language.

2. Two Grassroots Social Contracts

  • The section introduces two example contracts—a social graph carrying signed items and a currency of personal coins—for the later syntax, compilation, and certification.The paper presents their clauses in prose before formalising their acts.Source: §2 · pp. 5–6

2.1. The Social Graph with Signed Items

  • The social graph contract covers friendship, ending friendship, signing an item, forwarding it to a friend, and a confidence commitment to disclose only by forwarding.The forwarding clause warrants personal knowledge of the party from whom the item was received; the warranty and confidence clause describe no act of their own.Source: §2.1 · pp. 6–7

2.2. Currencies

  • A personal coin names its issuer, and the currency contract covers minting, swapping, paying, redeeming, and an issuer’s obligation to accept coins at advertised prices.The first four clauses determine transactions; the issuer’s obligation describes no act and gives a coin its worth.Source: §2.2 · p. 7
  • A swap exchanging an Alice-coin for a Bob-coin opens a mutual credit line, leaving each party holding a coin issued by the other.A coin can be handed on, so a holding may name an issuer its holder has never transacted with; certification relies on traceable provenance, with conservation of money as a special case.Source: §2.2 · p. 7

3. Act Schemas

The section formalizes contract clauses as role-specific act schemas, illustrates their operation in social-graph and currency contracts, and identifies the syntactic conditions for grassroots realisation.

3.2. The Syntax of a Schema

  • Act schemas formalize acts with named roles, required and forbidden atoms, state changes, and optional role-specific willingness guards.A schema is a template whose role identities are supplied when parties sign; each role has its own preconditions and effects.Source: §3 · p. 7, §3.2 · p. 8

3.1. Atoms and States

  • A local state is a multiset of atoms describing its holder’s records, such as friends or coins held.Atoms take people or speech acts as arguments; the holder is not itself an argument of its state’s atoms.Source: §3.1 · pp. 7–8

3.3. The Schemas of the Social Graph

  • In the social graph, friendship requires both parties’ will and ends for both, while forwarding records the forwarder without preventing a false warranty.A signed item is authored by its signer; forwarding leaves a record naming the forwarder with the recipient.Source: §3.3 · p. 9

3.4. The Schemas of the Currency

  • A currency swap can create a mutual credit line, while coins record an issuer’s undertaking only after passing to another holder.Pay and swap can move an issuer’s coin without asking the issuer; minting alone records nothing against the issuer.Source: §3.4 · p. 10

3.5. The Conditions Every Act-Schema Contract Meets

  • Every act-schema contract satisfies conditions (1), (2), (4), and (5), but it need not satisfy the remaining conditions.An act affecting a state does so only for a party in a schema role; schemas single out no person, and contract adoption and signing determine who is bound. Contracts without an act connecting strangers fail Introduction.Source: §3.5 · pp. 10–11

3.6. What We Prove

  • Grassroots syntax requires an unobstructed introductory act, traceable provenance, and volition, expressed as decidable conditions on the contract text.Introduction permits strangers to relate by mutual will; provenance requires records naming people to be traceable to someone present or already recorded by a party to the act.Source: §3.6 · pp. 11–12
  • The protocol realising a syntactically grassroots contract is volitionally grassroots, and a checker can decide whether the contract meets the syntactic conditions.The checker evaluates finite conditions on schemas, including introductory-act reachability and role-graph connectivity.Source: §3.6 · pp. 11, 13

4. Volition-Guarded Transactions and Grassroots Protocols

This section defines volition-guarded transactions and protocols, then characterizes grassroots protocols by independence, continued opportunity to interact, and mutual consent at first interaction.

4. Volition-Guarded Transactions and Grassroots Protocols

  • A volition-guarded transaction pairs a machine-state change with guards whose holders must be willing for it to occur.A protocol is a family of transition systems, one for each finite participant set; correctness requires safe runs and liveness.Source: §4 · pp. 13–14
  • A correct run is safe when each step is a transition and live when no enabled class remains enabled forever without being taken.Volitional machine transactions occur when the transaction’s guards all hold their class.Source: §4 · pp. 13–14
  • Instances are connected components of the interaction graph, whose edges mark pairs that have interacted in a run prefix.Disjoint instances coalesce when they are separate components in an earlier prefix and belong to one component in a later prefix.Source: §4 · p. 14
  • A protocol is grassroots when correct runs of disjoint groups can interleave and groups that have not interacted can still interact.The first interaction must be guarded by a member of each group for the protocol to be volitionally grassroots; instances can then coalesce.Source: §4 · p. 14

5. Compiling Schemas into Transactions

The section compiles schemas into volition-guarded multiagent transactions and establishes properties of the resulting protocol, including that only schema parties change state and no party is privileged.

5.1. The Compilation

  • Compilation maps each act schema to a volition-guarded multiagent atomic transaction, with guards supplied by the schema’s guarding roles.At each binding, required atoms must be present and forbidden atoms absent; the transaction applies the schema’s additions and deletions.Source: §5.1 · pp. 14–15
  • The compilation is well defined: its transaction set meets the required closure-disjointness and countable-equivalence conditions.A schema with no guarding role yields transactions with empty guards, which are eventually taken when machine-enabled.Source: §5.1 · p. 15

5.2. Two Examples

  • Befriending compiles to a transaction guarded by Alice and Bob; a swap of their own issued coins is their mutual credit line.Different admissible states yield instances of the same befriending act; a swap of a coin for one of the same issue changes no state.Source: §5.2 · p. 16

5.3. Every Participant Is a Party

  • Every changed agent is assigned to a schema role, and permuting participants preserves runs and reachable configurations.Thus no party is privileged: any reachable configuration remains reachable after any permutation of the participants.Source: §5.3 · pp. 16–17

6. Polite Sets of Volition-Guarded Transactions

The section characterizes politeness as a transaction-set condition sufficient for a protocol to be volitionally grassroots. Openness supports interaction between agents, while closure ensures consent when participants are not already in one instance.

6. Polite Sets of Volition-Guarded Transactions

  • Openness lets two agents reach a configuration where an act between them can be enabled; closure requires unguarded acts to involve agents already in one instance.The act still requires all its guards to be willing.Source: §6 · p. 18
  • A protocol over a polite set of volition-guarded transactions is volitionally grassroots.Politeness means the set is both open and closed.Source: §6 · p. 18
  • Openness yields cross-group interaction, while closure prevents an unwilled transaction from joining separate instances.Together these properties establish interactivity and consent, the conditions behind the theorem.Source: §6 · pp. 17, 19

7. Conditions Sufficient for Openness and Closure

The section proves that a syntactically grassroots contract realizes a volitionally grassroots protocol by establishing openness and closure. It applies the conditions to the social graph and currency contracts.

7. Conditions Sufficient for Openness and Closure

  • The protocol realizing a syntactically grassroots contract is volitionally grassroots.The proof obtains openness and closure for its transactions, then applies the politeness theorem.Source: §7 · pp. 19, 21
  • An unobstructed introductory act supports openness, while traceable-provenance edges cannot cross instances, supporting closure.Openness lets any two people start an instance without permission; closure requires unguarded acts to remain within one instance.Source: §7 · pp. 20–22

7.1. The Social Graph Certified

  • The social graph contract is syntactically grassroots, and its realizing platform is therefore volitionally grassroots.Befriending is an unobstructed introductory act; friend-recording graph components define instances, and forwarded items can name an author who did not transact with the recipient.Source: §7.1 · p. 22

7.2. The Currency Certified

  • The currency contract is syntactically grassroots, and its realizing platform is therefore volitionally grassroots.Coin provenance tracks transfer from the issuer; pay deletes a coin from the payer, whereas forwarding keeps the item.Source: §7.2 · pp. 22–23

8. Clauses and Their Modalities

The section classifies clauses by whether the protocol can determine or breach them and what record it leaves. The three modalities are enforced, attested, and undertaken, but they do not cover every clause.

8. Clauses and Their Modalities

  • Clauses are enforced when no contract transaction can breach them, attested when breach is possible and witnessed against the obligor, and undertaken when performance lies outside the protocol but is recorded.The three modalities describe what the realization does with a clause, not kinds of obligation.Source: §8 · pp. 23–24
  • A clause whose breach is unwitnessed, or whose obligation leaves no identifiable record, falls outside all three modalities.The modalities are exclusive but not exhaustive.Source: §8 · p. 24
  • Guarding a predicate enforces its consent clause, while the examples classify friendship clauses as enforced and forwarding and mutual-credit-line clauses as undertaken.A mutual credit line is witnessed against both parties; the clause that a coin enters a holding only by its issuer’s will has no modality.Source: §8 · p. 24
  • Attestation depends on an act’s effects naming its author; signed speech acts can provide that record, and the paper’s warranty example is attested through forwarding.A later promised performance is never attested because failure to perform is not itself an act of the contract.Source: §8 · p. 25

9. Signing the Contract

Joining requires signing an undertaking to keep the contract toward other participants and presenting it to each participant encountered. The code enforces presentation and carries certified-code commitments.

9. Signing the Contract

  • A participant signs an undertaking to keep the contract and presents it to every participant with whom they interact.The code or hosting platform refuses an interaction when a participant has not presented the undertaking.Source: §9 · p. 25
  • In a presenting run, every agent in an instance of at least two agents has presented its undertaking to another agent in that instance.This follows because an interaction creates an edge in the instance’s interaction graph and presentation is required for each interaction.Source: §9 · pp. 25–26
  • The creator and compiler certify the code, and each party undertakes to run that certified code.The creator certifies that the code realizes the contract and the compiler certifies that the compiled code is the creator’s; the certifications are signed warranties, not contract clauses.Source: §9 · p. 26

10. Related Work

The related work spans formal contract languages, monitoring, self-governance, and regulation; this paper instead checks grassroots properties from contract text and distinguishes three legal clause types. It also situates grassroots contracts among neighboring instruments and identifies assumptions common in related formalisms.

Contracts as formal objects

  • Contract automata, rule-based encodings, and smart-contract comparisons model clauses operationally, but the paper focuses on deriving grassroots properties from acts in contract text.Prior approaches include timed contract automata and defeasible rules with violation and reparation chains.Source: §10 · pp. 26, 29

Contract languages

  • Related contract languages often fix parties or rely on global clocks, monitors, or ledgers, while this work studies contracts over finite sets of people without those resources.Symboleo assigns roles during execution and presupposes a monitor; Stipula fixes parties in its constructor and carries a global clock.Source: §10 · pp. 26–27

Standard-form contracting and self-governance

  • Grassroots contracts differ from bilateral adhesion agreements by having no drafting proprietor, while commons scholarship addresses shared resources rather than relationships.The paper also contrasts party-held records with monitoring approaches that rely on trusted observers and timestamps.Source: §10 · pp. 28–29

Terms a machine can evaluate

  • A three-way clause division distinguishes unbreachable clauses from breaches that can be recorded against an identifiable obligor, unlike binary machine-enforceability divisions.The second class matters because remedies require a provable breach and an identifiable obligor.Source: §10 · p. 28

Grassroots systems

  • The paper adds transaction politeness, decidable conditions on legal text, and a three-way account of clause realization to grassroots systems work.Politeness is sufficient for protocol grassrootsness; the text conditions establish it from acts, and schemas determine how clauses are handled.Source: §10 · p. 29

Neighbouring instruments

  • Unlike a licence, bylaws, conduct code, or membership terms, a grassroots contract presupposes neither prior rights nor an association, admitting proprietor, or membership register.Its obligations are owed mutually by each party to every other and derive from no party’s prior entitlement.Source: §10 · p. 29

11. Conclusion

The conclusion presents an algorithmic route from legal text through act schemas to a volitionally grassroots protocol, with the schemas also governing how clauses are realized. It identifies unresolved questions about necessity and further invariants.

Conclusion

  • The legal text becomes act schemas and then volition-guarded transactions over local states, whose atoms record exactly their named participants.Three decidable schema conditions suffice for the realizing protocol to be volitionally grassroots; rendering text as schemas remains the judgment-dependent step.Source: §11 · pp. 29–30
  • The same schemas classify clauses as unbreachable, breaches recorded against an answerable party, or undertakings recorded with their giver.Attestation and undertaking both require a record held by another party; they differ in whether the breach is itself an act of the contract.Source: §11 · p. 30
  • In the social graph, befriending creates an edge only between its two willing parties, while coin transfers can point to people not directly transacted with.For coins, conservation of money is the condition preventing an edge from joining separate instances.Source: §11 · p. 30
  • Openness lets anyone start an instance without permission, while closure removes the need for registries, ordering logs, or timestamping authorities.The resulting community requires no permission to form, authority to operate, or proprietor to govern it.Source: §11 · p. 30
  • The schema conditions are sufficient but not necessary, and which further invariants follow from schemas remains open.A future characterization could identify which contracts are grassroots and whether schemas imply invariants beyond examples such as money conservation.Source: §11 · p. 30

A. The Framework of Volition-Guarded Multiagent Atomic Transactions

The appendix recalls the volition-guarded multiagent transaction framework so the paper’s formal statements can be read without consulting another paper. It defines willingness at the level of transaction classes and illustrates different guard requirements in the social graph.

Framework overview

  • The appendix restates prior framework material and omits its proofs, which are available in the cited earlier work.Its stated purpose is to make the paper’s Section 6 statements and proofs readable without recourse to another paper.Source: A. The Framework of Volition-Guarded… · p. 33
  • A volition-guarded transaction is a machine transaction whose guards specify which participating people must be willing for it to occur.A volitional state is a set of equivalence classes of transactions a person is willing their machine to take part in.Source: A. The Framework of Volition-Guarded… · p. 33
  • In the social graph, befriending requires both parties’ willingness, whereas unfriending requires either party’s willingness.People may change their volitional states freely, and taking an equivalent transaction fulfills the corresponding will.Source: A. The Framework of Volition-Guarded… · p. 33

A.1. Agents, Machines and Volition-Guarded Transactions

The framework models people operating machines through local states and volitional states, with atomic asynchronous transactions changing participating machines. Equivalence classes let willingness apply across transactions representing the same act in different configurations.

Agents, machines and transactions

  • A machine transaction changes a configuration over its participants, and a volition-guarded transaction pairs it with the subset of participants required to be willing.Participants may be active, with changing states, or stationary, whose states serve only as preconditions.Source: §A.1 · pp. 33–34
  • A guarded transaction can occur only when its designated guards are willing, and atomic asynchronous execution does not depend on nonparticipants’ states.A guard set containing both parties requires both; separate single-party guards allow either party’s volition to suffice.Source: §A.1 · p. 34
  • Transaction equivalence groups transactions with the same participants, allowing a person to will a class rather than one configuration-specific transaction.All befriending transactions between the same two people form one class, and taking one member fulfills that will.Source: §A.1 · p. 34
  • An agent state pairs a volitional state with a machine state, and an agent configuration assigns such a state to each agent.The framework uses a set of agents and machine states with a designated initial state.Source: §A.1 · pp. 33–34
  • A volitional machine transaction requires participating agents to have the transaction class in their volitional states, then removes that class when the transaction occurs.Volition changes let a person independently add or remove willing transaction classes.Source: §A.1 · p. 34

A.2. Transition Systems and the Induced Volitional System

This section defines correctness for transition systems and constructs the volitional multiagent system induced by guarded transactions. It explains how liveness classes, transaction closure, machine preconditions, and agents’ volitions shape its runs.

A.2. Transition Systems and the Induced Volitional System

  • A run is correct when it is safe and live: every step is a valid transition, and no enabled liveness class is indefinitely ignored.A finite safe run can be extended to a correct run.Source: §A.2 · p. 35
  • A partial equivalence partitions only some transitions into liveness classes; transitions outside its domain may occur but are never required.The definition of correctness therefore imposes liveness obligations only on transitions in those classes.Source: §A.2 · p. 35
  • A machine transaction over a subgroup induces multiagent transitions in which agents outside that subgroup remain stationary.Transaction closure lifts machine transitions to configurations over the larger agent set.Source: §A.2 · p. 35
  • When distinct transactions have disjoint P-closures, each resulting transition has a unique inducing transaction, preserving the relation between transaction classes.The closure relation remains a partial equivalence when the original relation is one.Source: §A.2 · pp. 35–36
  • The induced volitional system gives each agent a state combining its volitions with a machine state, and allows volition changes or volitional machine transitions.Volition changes remain outside the liveness-class relation.Source: §A.2 · p. 36
  • A guarded transaction is enabled only when its machine precondition holds and its guard’s agents will its class; an empty guard requires no volitions.Volition changes carry no liveness obligation, leaving personal choices free.Source: §A.2 · p. 36

A.3. Protocols, Grassroots Protocols and Coalescence

A protocol supplies a compatible transition system for each agent set. It is grassroots when independent groups can interleave correctly and can still interact later; the section also states a coalescence result for instances.

A.3. Protocols, Grassroots Protocols and Coalescence

  • A protocol assigns a transition system to every agent set, with local-state sets and initial states compatible as the agent set grows.The local-states function is monotone in the agent set.Source: §A.3 · p. 36
  • In a grassroots protocol, disjoint groups can operate independently while the combined system also offers behaviors unavailable to either group alone.Obliviousness captures noninterference during interleaving; the combined system can nevertheless provide additional behavior.Source: §A.3 · p. 37
  • For disjoint agent groups, an interleaving advances one group at a time while preserving each group’s own run states.The combined configuration is well-defined because the component state spaces and initial configurations agree across agent sets.Source: §A.3 · p. 37
  • A protocol is grassroots when it is both oblivious and interactive: independent groups’ correct runs can interleave correctly, and interaction remains possible after any interaction-free prefix.The interaction requirement applies at every such prefix, not only at the initial configuration.Source: §A.3 · p. 37
  • Any two disjoint instances in a prefix of a correct run of a grassroots protocol can coalesce in a correct continuation.The proposition applies to instances within a larger agent set.Source: §A.3 · p. 37

A.4. Volitional Transactions-Based Protocols

This section builds protocols from volition-guarded transactions and establishes conditions for their safety, obliviousness, and volitional interaction. Volition constrains how otherwise independent groups first couple.

A.4. Volitional Transactions-Based Protocols

  • A volitional transactions-based protocol assigns each agent set the volitional multiagent system induced by its transactions.The transaction set for an agent set includes transactions supported by the local-state function within that set.Source: §A.4 · pp. 37–38
  • In a group’s own system, agents will only transactions internal to that group, so a transaction reaching another group cannot be willed there.This invariant is used in the proofs of the protocol properties.Source: §A.4 · p. 38
  • Every finite prefix of an interleaving of correct runs from disjoint groups is a safe run of their combined system.Source: §A.4 · p. 38
  • A volitional transactions-based protocol is oblivious if no class spanning two disjoint groups is ever enabled during their interleaved correct runs.Source: §A.4 · p. 38
  • Volitional grassrootsness requires the first interaction between disjoint groups in a safe interactive run to be induced by a transaction willed by members of both groups.The volitional condition constrains coupling that a member might otherwise initiate in the combined system.Source: §A.4 · p. 38
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