Citation-Aware Symbolic Reasoning

• Citation-aware symbolic reasoning is a framework that integrates citation graph structures with segmented content analysis to systematically link scientific claims via explicit symbolic logic.
• It leverages machine-evaluated confidence scores to construct and prune multi-hop evidence chains, thereby ensuring coherent and verifiable literature synthesis.
• The SciRAG implementation demonstrates improved accuracy and transparency by combining adaptive retrieval, citation-aware ranking, and outline-guided synthesis.

Citation-aware symbolic reasoning is a mechanistic approach to literature-based scientific question answering in which a system systematically leverages the structure of the citation graph, organizes support at the content-segment level, and deploys explicit symbolic logic to reason over connections between documents. By integrating directed citation information with segment-level conceptual relationships—each quantified with machine-evaluated confidence—citation-aware symbolic reasoning produces interpretable, high-confidence chains of evidence that underlie answer synthesis, ranking, and attribution. A contemporary open-source instantiation is realized in the SciRAG framework, which combines adaptive retrieval, citation-aware symbolic reasoning, and outline-guided synthesis to ensure more accurate, coherent, and verifiable scientific literature synthesis (Ding et al., 18 Nov 2025).

1. Formalization of the Citation and Relation Graphs

The citation-aware symbolic reasoning component builds on a structured, two-level graph formalism. The key objects are as follows:

• Paper (node) set: $V = \{p_1, p_2, \ldots, p_N\}$ is the set of candidate papers retrieved and expanded after the initial stage.
• Segments: Each paper $p_i$ is partitioned into content segments $$\text{seg}(p_i) = \{s_{i,1}, s_{i,2}, \ldots, s_{i,m_i}\}$$, and each $s_{i,k}$ is tagged with a conceptual role $r(s_{i,k}) \in R$ (e.g., $T$ = theory, $E$ = experiment, $M$ = method, $A$ = application).
• Citation edge set: $E \subseteq V \times V$ includes both backward (if $p_i$ cites $p_j$) and forward (if $p_j$ cites $p_i$) edges. Every edge $e = (i \rightarrow j)$ is annotated by direction $d_e \in \{\text{BWD}, \text{FWD}\}$, hop distance $h_e \in \mathbb{N}$ (usually $h_e \leq 1$ per expansion), and a support weight $w_{ij} \in [0,1]$ computed as $w_{ij} = \mathrm{LLMScore}(p_i, p_j)$.
• Segment-level relation graph: $G_{\text{seg}} = (S, L)$, where $S = \bigcup_{i=1}^N \text{seg}(p_i)$, and $L \subseteq S \times S$ consists of links $\ell = (s_{i,k} \rightarrow s_{j,l})$ established whenever an LLM prompt affirms that $s_{i,k}$ conceptually supports $s_{j,l}$. Each link $\ell$ is labeled with the roles of both segments and given a confidence score $\lambda_{(i,k),(j,l)} \in [0,1]$, denoted as $[i]r(s_{i,k}) \rightarrow [j]r(s_{j,l}) : \lambda$.

2. Algorithmic Procedure: Graph Construction, Traversal, and Ranking

SciRAG’s citation-aware symbolic reasoning is executed via a multi-stage, LLM-orchestrated pipeline that can be formalized as follows:

function CitationAwareReasoning(q, P0): # 1. Citation graph expansion adjudicated by an LLM if LLMJudge(q, P0) == false: P ← ExpandGraph(P0) # one-hop backward & forward else: P ← P0 # 2. Content segmentation and role tagging for p in P: seg(p) ← TagSegments(p) # e.g., abstract → [T, E, M, A, ...] # 3. Build the segment-level relation graph G_seg ← BuildRelationGraph({seg(p) | p in P}) # For all pairs (si,k, sj,l), prompt LLM: # "Does si,k support sj,l? If so, λ in [0,1] and label [i]r→[j]r’." # 4. Prune low-confidence and contradictory chains G_pruned ← PruneChains(G_seg) # Remove edge/chain if min_{ℓ in c} λ_ℓ < θ_min or if LLM notes contradiction # 5. Compute and assign paper ranks by strongest scoring chains for p in P: Rank(p) ← max_{c ends in seg(p)} Score(c) where Score(c) = (1/|c|) ∑_{ℓ in c} λ_ℓ # 6. Return top-K papers return TopK(P, Rank)

Relevant formulas:

• Graph expansion: $$P = P_0 \cup \bigcup_{p \in P_0} (\text{BackwardNeighbors}(p) \cup \text{ForwardNeighbors}(p))$$
• Chain confidence: For a chain $c = (\ell_1, \ell_2, ..., \ell_L)$, $\text{Conf}(c) = \min_{m=1..L} \lambda_{\ell_m}$
• Chain score: $$\text{Score}(c) = \frac{1}{L} \sum_{m=1}^L \lambda_{\ell_m}$$
• Paper ranking: $$\text{Rank}(p_i) = \max_{c \text{ ends in any } s \in \text{seg}(p_i)} \text{Score}(c)$$

This procedure yields document rankings and segment chains forming the backbone of reasoning and synthesis.

3. Symbolic Reasoning Logic, Pruning, and Inference

The symbolic reasoning component comprises the following major logic rules:

• Segment tagging: Abstracts are partitioned into segments, each classified into roles $r \in \{T, E, M, A, ...\}$ via prompt-based LLM inference.
• Link construction: For every ordered pair $(s_{i,k}, s_{j,l})$, an LLM is prompted to judge conceptual support, returning a labeled link $[i]r \rightarrow [j]r'$ with confidence $\lambda$.
• Chain assembly: Residual links combine to form multi-hop chains $$c: [i_1]r_1 \rightarrow [i_2]r_2 \rightarrow \ldots \rightarrow [i_L]r_L$$, modeling transitive support from theory, through method and experiment, to application across the corpus.
• Pruning: Any link with $\lambda < \theta_{\text{min}}$ (empirically, $\theta_{\text{min}} \approx 0.5$) is removed. Chains are also pruned if the LLM flags logical contradictions (e.g., an experimental result contradicting a cited theory).
• Inference and ranking: Papers inherit their highest-scoring chain, and only those participating in multi-segment, high-confidence, contradiction-free chains are prioritized.

This logic ensures that the output answer and citations are underpinned by explicit, machine-verifiable reasoning paths.

4. Role in the SciRAG Literature Synthesis Pipeline

Citation-aware symbolic reasoning is integrated as a middle layer in the overall SciRAG workflow (Ding et al., 18 Nov 2025):

• Adaptive retrieval: The system queries standard dense or snippet-based retrievers, then invokes citation-aware symbolic reasoning on the initial set (and any citation-expansion results). If the most promising chains do not satisfy the LLM judge, deeper search (e.g., further citation hops) is triggered.
• Outline-guided synthesis: Final selected segments and their supporting chains are used to build a hierarchical answer plan, structured by roles (e.g., Theory → Method → Experiment → Application). Outline synthesis operates strictly over the pruned, symbolically justified reasoning graph.
• Consistency enforcement: During backtracking and refinement, any segment or answer element unsupported by valid chains, or flagged as contradictory, is excised, guaranteeing logical coherence and high transparency.

This integration yields answers where every claim and citation can be traced to explicit, confidence-weighted, multi-paper proof chains, significantly improving trustworthiness in scientific QA systems.

5. Empirical Performance and Illustrative Examples

Citation-aware symbolic reasoning yields substantial empirical advantages in factuality and citation quality:

• Toy Example: For papers $\{p_1, p_2, p_3, p_4\},$ with roles $[p_1:T,E],$ $[p_2:M],$ $[p_3:E],$ $[p_4:A],$ LLM-derived links create chains such as $[1]T \rightarrow [3]E$ $(\lambda=0.90),$ $[3]E \rightarrow [4]A$ $(\lambda=0.80),$ and $[2]M \rightarrow [4]A$ $(\lambda=0.70)$. Highest chain scores (e.g., Score$(c_1) = 0.85)$ surface $p_1, p_3, p_4$ and de-prioritize less-well-integrated $p_2$, exemplifying interpretable, role-coherent chain construction.
• Ablation on SciFact: Full SciRAG (including symbolic reranking) achieves Correctness = 84.1%. Removing symbolic reranking leads to a 10.7-point drop (Correctness = 73.4%), directly demonstrating the impact of citation-aware symbolic pruning and ranking.
• Citation metrics: Strict citation F1 on SciFact improves from 44.1 to 52.9 with symbolic reasoning, indicating that the system reduces spurious attributions and surfaces multi-hop, indirectly supported evidence chains.

These results validate that citation-aware symbolic reasoning is essential for producing more accurate, transparent, and verifiable syntheses in scientific literature QA (Ding et al., 18 Nov 2025).

6. Significance and Implications for Scientific Information Aggregation

Citation-aware symbolic reasoning, as implemented in SciRAG, addresses fundamental limitations of dense retrieval and typical retrieval-augmented generation (RAG) approaches, which often ignore citation topology, lack segmented conceptual reasoning, and cannot guarantee proof coherence or proper attribution. The structured, segment-level symbolic graph enables adaptive traversal, fine-grained support tracing, and multi-paper argumentative synthesis.

A plausible implication is that such frameworks can serve as a new foundation for large-scale, trustworthy scientific knowledge aggregation, offering structured transparency, resistance to hallucinated citations, and the ability to handle complex multi-hop, multi-source queries within rapidly expanding literatures (Ding et al., 18 Nov 2025).