arxiv: 2510.06002 · v3 · submitted 2025-10-07 · 💻 cs.AI · cs.CL· cs.IR

Deterministic Legal Agents: A Canonical Primitive API for Auditable Reasoning over Temporal Knowledge Graphs

Hudson de Martim This is my paper

Pith reviewed 2026-05-18 09:14 UTC · model grok-4.3

classification 💻 cs.AI cs.CLcs.IR

keywords SAT-Graph APItemporal knowledge graphslegal RAGdeterministic agentsauditable reasoningprobability isolationagentic reasoningknowledge graph primitives

0 comments p. Extension

The pith

The SAT-Graph API supplies deterministic primitives that let agents execute auditable operations on temporal knowledge graphs while confining uncertainty to intent translation and narrative synthesis.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper specifies the SAT-Graph API as a canonical primitive interface that lets LLM agents interact with temporal knowledge graphs in legal settings. Agents decompose questions into execution plans and invoke atomic operations for point-in-time retrieval, provenance tracing, and impact analysis. These operations run deterministically over canonical anchors, producing an answer backed by a complete log of graph steps. Uncertainty stays limited to converting the query into a plan, anchoring semantics, and writing the final response. The design replaces single-shot semantic retrieval with an active Reason-Act-Observe cycle to preserve hierarchy, temporality, and causal provenance in high-stakes legal reasoning.

Core claim

The SAT-Graph API is a canonical primitive interface for auditable reasoning over temporal knowledge graphs, developed and illustrated in the legal domain. It exposes typed, atomic, and composable primitives that mediate between a probabilistic language model and a deterministic symbolic substrate. The design follows Probability Isolation so that uncertainty is confined to intent translation, semantic anchoring, and final narrative synthesis while structural, temporal, and causal graph traversals execute through deterministic operations over canonical anchors. The interface shifts legal RAG from single-shot Retrieve-then-Generate to active Reason-Act-Observe. An agent decomposes a legal 2u3w

What carries the argument

The SAT-Graph API, a set of typed atomic primitives for point-in-time retrieval, context reconstruction, provenance tracing, and impact analysis that operate deterministically over canonical anchors in a temporal knowledge graph.

If this is right

Agents produce answers supported by explicit, verifiable logs of every graph operation performed.
Temporal and causal relations among legal norms are traversed deterministically rather than matched probabilistically.
The same primitive set applies to any other temporally versioned, provenance-sensitive knowledge base.
Reasoning steps become explicit and decomposable before any graph access occurs.
Overall system risk decreases because structural operations no longer carry probabilistic error.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The API could be layered on existing legal databases to support contract review or regulatory monitoring with traceable steps.
Similar primitive libraries might be defined for other structured domains such as financial ledgers or clinical trial histories.
Empirical tests on real legal queries would show whether uncertainty remains confined when the underlying graph contains ambiguous or overlapping norms.

Load-bearing premise

A correctly modeled temporal knowledge graph with canonical anchors must already exist, and the deterministic primitives must be implementable without introducing new retrieval or execution vulnerabilities.

What would settle it

Implement the primitives on a sample temporal legal knowledge graph, run the same execution plan multiple times, and check whether the operation logs and structural results remain identical while any variation occurs only in the intent-translation or narrative-synthesis steps.

Figures

Figures reproduced from arXiv: 2510.06002 by Hudson de Martim.

**Figure 1.** Figure 1: From "flat-text" RAG to SAT Graph RAG This paper bridges that critical gap. We argue that enabling trustworthy legal agents requires more than a better knowledge base; it demands a formally defined and auditable interaction protocol. To this end, we introduce a formal query execution layer, which we specify as the SAT-Graph API—a canonical primitive interface for querying structure-aware, temporal graphs w… view at source ↗

**Figure 2.** Figure 2: Diagram illustrating a reasoning agent decomposing a user prompt into tasks that are executed [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: SAT-Graph Ontology Item: Represents a versioned, structural entity of a legal norm. It is instantiated as one of two concrete subtypes: Work or Work Component. • id (ID): A unique, canonical identifier (e.g. URN). • type (id): The specific item type id. • label (string): The human-readable label. • uri (string)?: (Optional) A uniform resource identifier. • parent (ID)?: (Optional) The id of its single stru… view at source ↗

read the original abstract

In high-stakes legal domains, retrieval must preserve not only semantic relevance, but also the hierarchy, temporality, and causal provenance of legal norms. Standard Retrieval-Augmented Generation (RAG), based mainly on semantic similarity over text fragments, cannot reliably provide this level of control. Prior work on SAT-Graph RAG addressed the representation problem by modeling legal materials as structure-aware temporal knowledge graphs. This paper addresses the next problem: how an LLM-based reasoning agent can interact with such a graph without reintroducing unreliable retrieval behavior. We specify the SAT-Graph API, a canonical primitive interface for auditable reasoning over temporal knowledge graphs, developed and illustrated in the legal domain. The API exposes typed, atomic, and composable primitives that mediate between a probabilistic language model and a deterministic symbolic substrate. Its design follows Probability Isolation: uncertainty is confined to intent translation, semantic anchoring, and final narrative synthesis, while structural, temporal, and causal graph traversals are executed through deterministic operations over canonical anchors. The interface shifts legal RAG from single-shot Retrieve-then-Generate to active Reason-Act-Observe. An agent decomposes a legal question into an explicit execution plan, invokes primitives for point-in-time retrieval, context reconstruction, provenance tracing, and impact analysis, and produces an answer grounded in an auditable log of graph operations. The result is a formal architectural specification, not an empirical benchmark: a secure interaction protocol that decouples legal knowledge representation from agentic reasoning. Although illustrated in law, the primitive model is domain-portable to other temporally versioned, provenance-sensitive, and authority-governed knowledge bases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper specifies a clean primitive API that lets agents run deterministic graph operations on temporal legal knowledge graphs while keeping uncertainty out of the traversals.

read the letter

The main takeaway is that the authors propose the SAT-Graph API as a set of typed, atomic primitives for point-in-time retrieval, provenance tracing, context reconstruction, and impact analysis. The design keeps graph operations fully deterministic and logs every step, pushing all probabilistic work into intent translation and final synthesis. This is a direct response to the limits of standard RAG when legal materials need hierarchy, temporality, and causal chains preserved.

Referee Report

0 major / 3 minor

Summary. The manuscript specifies the SAT-Graph API, a canonical primitive interface consisting of typed, atomic, and composable operations for deterministic interaction with temporal knowledge graphs. The design isolates uncertainty to intent translation, semantic anchoring, and narrative synthesis while executing structural, temporal, and causal traversals (point-in-time retrieval, provenance tracing, impact analysis) deterministically over canonical anchors. It reframes legal RAG as an explicit Reason-Act-Observe loop that produces answers grounded in an auditable log of graph operations, presented as a formal architectural specification rather than an empirical benchmark, with claimed portability beyond the legal domain.

Significance. If realized, the specification supplies a concrete protocol for hybrid probabilistic-symbolic reasoning that directly targets auditability and provenance requirements in high-stakes domains. The emphasis on Probability Isolation and the separation of deterministic primitives from LLM nondeterminism offers a reusable pattern for any temporally versioned, authority-governed knowledge base. The absence of empirical performance claims is appropriate for a design paper and keeps the contribution focused on interface correctness.

minor comments (3)

The abstract and introduction would benefit from an explicit statement of the minimal assumptions on the underlying temporal knowledge graph (e.g., presence of canonical anchors and complete temporal versioning) so that readers can immediately assess the scope of the specification.
Section describing the primitive signatures should include a small illustrative execution trace (even if pseudocode) showing how a multi-step legal query is decomposed into a sequence of API calls and how the resulting log is consumed for the final answer.
A short discussion of failure modes (e.g., when a requested point-in-time anchor does not exist) would clarify the contract between the agent and the substrate without altering the core deterministic guarantee.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the SAT-Graph API specification, its emphasis on probability isolation, and the recognition that the absence of empirical benchmarks is appropriate for this design-focused contribution. We accept the recommendation for minor revision and will incorporate any editorial or clarification changes in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity; forward architectural specification

full rationale

The paper is a design specification for the SAT-Graph API primitives rather than a derivation of empirical results or fitted predictions. It defines typed atomic operations for deterministic graph traversals under Probability Isolation and shifts from Retrieve-then-Generate to Reason-Act-Observe without any equations, parameter fitting, or self-referential reductions. Prior work on SAT-Graph RAG is cited only for context on the representation layer; the present paper's central claim is the coherence of the new interface itself, which stands independently as a formal protocol without reducing to inputs by construction or self-citation chains.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is a design specification. It assumes the existence of a properly structured temporal knowledge graph with canonical anchors and that deterministic operations can be realized without new vulnerabilities. No free parameters, invented entities, or ad-hoc axioms are introduced beyond standard domain assumptions about legal norms.

axioms (1)

domain assumption A correctly modeled temporal knowledge graph with canonical anchors exists and can be traversed deterministically.
Invoked in the description of Probability Isolation and the primitives for point-in-time retrieval and provenance tracing.

pith-pipeline@v0.9.0 · 5827 in / 1128 out tokens · 21108 ms · 2026-05-18T09:14:38.895997+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The SAT-Graph API... exposes typed, atomic, and composable primitives that mediate between a probabilistic language model and a deterministic symbolic substrate. Its design follows Probability Isolation: uncertainty is confined to intent translation, semantic anchoring, and final narrative synthesis, while structural, temporal, and causal graph traversals are executed through deterministic operations over canonical anchors.
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Primitives... for point-in-time retrieval, provenance tracing, impact analysis... getValidVersion(item_id, timestamp) → Version; traceCausality(version_id) → {creating_action, terminating_action}

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages · 2 internal anchors

[1]

Retrieval-augmented generation for knowledge-intensive nlp tasks

Lewis P, Perez E, Piktus A, Petroni F, Karpukhin V , Goyal N, et al. Retrieval-augmented generation for knowledge-intensive nlp tasks. In: Advances in Neural Information Processing Systems. vol. 33; 2020. p. 9459-74

work page 2020
[2]

Legal Query RAG (LQ-RAG)

Rahman SMW, Kim S, Choi H, Bhatti DS, Lee HN. Legal Query RAG (LQ-RAG). IEEE Access. 2025;PP(99):1-1

work page 2025
[3]

Optimizing Legal Text Summarization Through Dynamic Retrieval- Augmented Generation and Domain-Specific Adaptation

Ajay Mukund S, Easwarakumar KS. Optimizing Legal Text Summarization Through Dynamic Retrieval- Augmented Generation and Domain-Specific Adaptation. Symmetry. 2025;17(5):633

work page 2025
[4]

An Ontology-Driven Graph RAG for Legal Norms: A Structural, Temporal, and Deterministic Approach

De Martim H. An Ontology-Driven Graph RAG for Legal Norms: A Structural, Temporal, and Deterministic Approach; 2025. [preprint]. Accessed on: August 23, 2025. Available from: https: //arxiv.org/abs/2505.00039. arXiv preprint arXiv:2505.00039

work page internal anchor Pith review Pith/arXiv arXiv 2025
[5]

From Local to Global: A Graph RAG Approach to Query-Focused Summarization

Edge D, Trinh H, Cheng N, Bradley J, Chao A, Mody A, et al.. From local to global: A graph RAG approach to query-focused summarization; 2024. Accessed on: August 23, 2025. arXiv preprint arXiv:2404.16130. 4The SAT-Graph API specification project is publicly available at:https://github.com/hmartim/sat-graph-api 25

work page internal anchor Pith review Pith/arXiv arXiv 2024
[6]

A survey on explainable artificial intelligence (XAI): Toward medical XAI

Tjoa E, Guan C. A survey on explainable artificial intelligence (XAI): Toward medical XAI. IEEE Transactions on Neural Networks and Learning Systems. 2020;32(11):4793-813

work page 2020
[7]

The logic programming representation of the British Nationality Act

Sergot MJ, Sadri F, Kowalski RA, Kriwaczek F, Hammond P, Cory H. The logic programming representation of the British Nationality Act. In: Proceedings of the 3rd international conference on Logic programming. Springer; 1986. p. 430-53

work page 1986
[8]

Legal-bert: The muppets straight out of law school

Chalkidis I, Kamallakis M, Androutsopoulos I. Legal-bert: The muppets straight out of law school. In: Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics; 2020. p. 2898-904

work page 2020
[9]

Moving in the time: An ontology for identifying legal resources

De Oliveira Lima JA, Palmirani M, Vitali F. Moving in the time: An ontology for identifying legal resources. In: Legal Knowledge and Information Systems. Berlin: Springer Berlin Heidelberg; 2008. p. 15-24

work page 2008
[10]

Modeling the Diachronic Evolution of Legal Norms: An LRMoo-Based, Component- Level, Event-Centric Approach to Legal Knowledge Graphs; 2025

De Martim H. Modeling the Diachronic Evolution of Legal Norms: An LRMoo-Based, Component- Level, Event-Centric Approach to Legal Knowledge Graphs; 2025. [preprint]. Accessed on: August 23,

work page 2025
[11]

Available from:https://arxiv.org/abs/2506.07853

work page arXiv
[12]

A change language for ontologies and knowledge graphs

Hegde H, Vendetti J, Goutte-Gattat D, Caufield JH, Graybeal JB, Harris NL, et al. A change language for ontologies and knowledge graphs. Database. 2025;2025:baae133

work page 2025
[13]

LegalBench-RAG: A Benchmark for Retrieval-Augmented Generation in the Legal Domain; 2024

Pipitone N, Alami GH. LegalBench-RAG: A Benchmark for Retrieval-Augmented Generation in the Legal Domain; 2024

work page 2024
[14]

Retrieval-Augmented Generation for Large Language Models: A Survey; 2023

Gao Y , Xiong Y , Gao X, Jia K, Pan J, Bi Y , et al.. Retrieval-Augmented Generation for Large Language Models: A Survey; 2023

work page 2023
[15]

AGENTiGraph: A Multi-Agent Knowledge Graph Framework for Interactive, Domain- Specific LLM Chatbots

Zhao X, et al. AGENTiGraph: A Multi-Agent Knowledge Graph Framework for Interactive, Domain- Specific LLM Chatbots. In: Proceedings of the 34th ACM International Conference on Information and Knowledge Management (CIKM 2025); 2025. Forthcoming

work page 2025
[16]

ReAct: Synergizing Reasoning and Acting in Language Models; 2022

Yao S, Zhao J, Yu D, Du N, Shafran I, Narasimhan KR, et al.. ReAct: Synergizing Reasoning and Acting in Language Models; 2022

work page 2022
[17]

A Reasoning-Focused Legal Retrieval Benchmark; 2025

Zheng L, Guha N, Arifov JD, Chen ST, Siyavash SM, Manning CD, et al.. A Reasoning-Focused Legal Retrieval Benchmark; 2025. Forthcoming. Proceedings of the 4th ACM Symposium on Computer Science and Law (CS&Law ’25)

work page 2025
[18]

Legal Knowledge Graph Foundations, Part I: URI-Addressable Abstract Works (LRMoo F1 → schema.org); 2025

Martim HD. Legal Knowledge Graph Foundations, Part I: URI-Addressable Abstract Works (LRMoo F1 → schema.org); 2025. [preprint]. Accessed on: August 23, 2025. Available from: https: //arxiv.org/abs/2508.00827. 26

work page arXiv 2025