Time as Structure: Temporal Dependency Graphs for Verifiable Deadline Computation over Legal Documents

Miss a filing deadline by one day and the claim is barred, however strong the case. Computing that deadline is rarely simple: the period runs from a triggering event, is counted by a statutory convention, and may be suspended by a mandatory conciliation window. We ask whether a language model should answer such questions directly, or read the document and leave the arithmetic to code. We extract dated facts and their dependencies into a temporal dependency graph and compute deadlines from it with a calendar-correct engine. On UK Employment Appeal Tribunal judgments the engine reproduces six of seven timeliness rulings, and matches the judges' own dates to the day. The strongest of four language models, asked the same cases, gets the arithmetic right and the answer wrong: in six of twenty-one responses its stated verdict contradicts its own thinking, and every contradiction runs the same way, calling a late claim timely. To test the systems at scale we move the dismissal date across the statutory boundary, generating 427 cases whose answers are computed rather than annotated. On the cases both systems answer, the pipeline is right 90.2% of the time against 61.2% for direct answering. The limit is extraction: on contracts the errors are almost never in the arithmetic, but in choosing which event the period starts from.

sLTN: Structural Logic Tensor Networks

Logic Tensor Networks (LTN) provide a neurosymbolic framework in which first-order logic is interpreted through tensor operations, enabling logical constraints to be integrated with differentiable learning. However, the original formulation of LTN is primarily suited to data represented as flat collections of individuals, and does not explicitly capture structural organization such as temporal order, sequential position, or graph connectivity. We introduce sLTN, an extension of LTN that makes structural dimensions first-class elements of the language. Structural dimensions represent named tensor axes associated with domain-specific organization, such as time steps, sequence positions, or graph nodes. They can be quantified explicitly, related through structural relations, and used to express temporal, sequential, and relational constraints directly at the logical level. We formalize the syntax and fuzzy tensor semantics of sLTN and show that, in the absence of structural dimensions, the framework recovers the original LTN semantics as a special case. We further describe a PyTorch implementation based on a declarative signature, formula parsing, and tensorial interpretation. The framework is illustrated on representative temporal and sequential reasoning examples. This paper serves as a companion to the sltn library, available at https://github.com/logictensornetworks/sltn.

Maximum Satisfiability of Simple Temporal Problems

The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints. As STP data can be inconsistent, we study MAXSTP: compute a maximum-cardinality consistent subset of constraints. This extension is NP-hard, and we analyze its parameterized complexity under measures that capture practically relevant instance features: the number of variables $n$ (instance scale), the maximum coefficient magnitude $k$ (numeric range), and structural parameters of the constraint graph such as treewidth $tw$ (decomposability) and vertex cover size $vc$ (density). We show that MAXSTP is W[1]-hard parameterized by $n$, implying that $n$ and parameters that depend on $n$ (including $tw$ and $vc$) are insufficient for fixed-parameter tractability. For combined parameters, we give an $O^*(k^n)$-time algorithm, yielding single-exponential solvability for fixed $k$. While $k+tw$ remains W[1]-hard, MAXSTP is in XP via an $O^*((n\cdot k)^{tw})$ algorithm. Our results suggest that MAXSTP is often computationally harder than optimizing qualitative CSPs. We verify that many such problems (including RCC-8 and Allen's algebra) are FPT when parameterized by $n$ or $tw$. However, we also demonstrate that FPT algorithms for MAXSTP are indeed possible but with other parameters such as $k + vc$.

Learning Structural Convergence: A Neuro-Symbolic Benchmark for Temporal Reasoning

High-complexity operational environments require methods that detect and anticipate temporally distributed patterns rather than classify isolated events. This paper introduces TRACTA (Temporal Reasoning and Capability-Trajectory Analysis), a controlled synthetic benchmark for temporal structural reasoning in high-complexity event-driven systems, instantiated through Multi-Domain Operations (MDO)-like scenarios. The benchmark includes three tasks: early_warning, pattern_detection, and run_classification, and compares raw-event neural models, a contract-lite semantic baseline, and a neuro-symbolic configuration operating on semantically grounded trajectories. Results show that raw event-level learning remains informative, but learned temporal modeling over semantic capability and contextual direct-impact trajectories achieves the highest aggregate point estimates, with the largest margins on the temporal tasks. Ablation analysis indicates that capability dynamics, contextual impacts, and temporal structure contribute complementary information. Shortcut diagnostics indicate that the most direct cross-run global-identifier shortcut is controlled in the primary neural input view, while residual shallow signals remain. Overall, the findings support a bounded methodological conclusion: in controlled synthetic settings, semantically grounded trajectories provide an effective representation for temporal structural reasoning, supporting further investigation of semantic interfaces between event data, structured representations, and temporal learning.

WaveformQA: Benchmarking LLM Temporal Reasoning on Digital Waveforms

Large Language Models (LLMs) have demonstrated strong capabilities in code generation and reasoning, yet their ability to perform temporal reasoning over digital waveform data remains largely unexplored. Although reasoning over digital waveforms is a critical bottleneck in design verification, existing benchmarks primarily evaluate hardware description language (HDL) code generation and use waveforms only as supplementary context. This paper presents WaveformQA, an open-source question-answering benchmark for evaluating LLM temporal reasoning over digital waveforms. The benchmark comprises 360 questions with programmatically generated ground truths across eight categories of varying difficulty, including questions targeting multi-signal correlation and event ordering. Waveforms are generated from open-source design implementations, ensuring reproducibility and grounding the benchmark in real hardware behavior. Evaluation of frontier LLMs reveals that while models achieve reasonable accuracy on simple queries, performance degrades due to context window limitations and reasoning difficulties on complex temporal and multi-step questions. In addition, we show that an event-time JSON representation of waveforms improves LLM reasoning accuracy versus the standardized value change dump (VCD) format. The open-source framework supports extending to new question categories and importing new waveform sources, enabling researchers to rapidly prototype temporal reasoning experiments.

When Do LLMs Apply the Wrong Law? Diagnosing LLM Failures in Temporal Legal Reasoning

Legal reasoning tasks such as legal judgment prediction (LJP) require identifying the temporally correct version of the law governing a case -- a capability we term temporal applicable-law determination. However, whether large language models (LLMs) can reliably perform this task remains unexplored. In this paper, we construct a benchmark to evaluate LLMs on temporal applicable-law determination, and systematically investigate why they fail at temporal legal reasoning. Our experiments reveal four key findings. First, LLMs exhibit a strong bias toward applying the most recently enacted law, regardless of when the legally relevant facts occurred. Second, this bias does not stem from an inability to understand that laws have temporal scope, nor from a lack of knowledge about historical statutes. Third, we provide behavioral evidence that reinforcement-learning-shaped explicit reasoning may be a key mechanism: while improving general reasoning ability, it reduces the diversity of reasoning paths, causing models to converge on applying the current law. Fourth, this produces a counterintuitive inverse relationship: models with stronger general reasoning ability tend to perform worse on temporal legal reasoning. Our findings offer concrete guidance for future work on improving LLM performance in temporally grounded legal reasoning.

A Temporal Reasoning Benchmarking Framework for LRMs via Difficulty-controlled and Dynamic Test Generation

Defining the reasoning boundaries and ensuring the reliability of Large Reasoning Models (LRMs) remains a critical challenge. Current benchmarks primarily rely on static datasets susceptible to data contamination or synthetic tasks lacking fine-grained difficulty control. Furthermore, standard outcome-based evaluations often conceal reasoning flaws by neglecting the reasoning process. To address these limitations, we introduce TRACE, a testing framework that models temporal reasoning as constraint satisfaction problems via Allen's Interval Algebra. This approach enables precise regulation of logical complexity and incorporates a Trace-Based Verification Oracle to validate reasoning faithfulness. Using this framework, we construct TRACEBench, an extensive benchmark comprising 1,200 synthesized test instances across graded difficulty levels. We employ TRACE to evaluate eight widely used LRMs on TRACEBench. The results confirm a strong negative correlation between model performance and our difficulty metric (Pearson's r approximately -0.96), validating the effectiveness of our difficulty control mechanism. Moreover, our trace-based analysis exposes significant discrepancies between reasoning validity and final answers, revealing a high spurious guessing rate of approximately 28% in mid-sized models. In addition, we diagnose scale-dependent failure modes, ranging from Degenerative Loops in small models to Reasoning Explosion in advanced architectures. TRACE thus provides a robust, automated platform for benchmarking the true temporal reasoning capabilities of LRMs.