Logic-VLA: A Temporal Logic Conditioned Vision-Language-Action Model

Celina Shiyu Wang; Yiqi Zhao; Junjie Ye; Yue Wang; Jyotirmoy V. Deshmukh

cs.ROAug 20, 2026

Logic-VLA: A Temporal Logic Conditioned Vision-Language-Action Model

Authors: Celina Shiyu Wang, Yiqi Zhao, Junjie Ye, Yue Wang, Jyotirmoy V. Deshmukh

Organizations: Thomas Lord Department of Computer Science, University of Southern California

Abstract

Vision-language-action (VLA) models can follow natural-language (NL) task instructions, but such instructions may not precisely specify safety-critical or spatiotemporal requirements on the resulting behavior. We introduce Logic-VLA, a formal-requirement-aware VLA that conditions on Signal Temporal Logic (STL) specifications supplied at inference time. Logic-VLA uses a syntax-graph-based STL encoder pre-trained to capture temporal logic semantics. Policy adaptation proceeds in two stages: STL-conditioned supervised fine-tuning on satisfying demonstrations is followed by trajectory-level preference optimization over matched satisfying-violating rollout pairs using a flow-matching surrogate for Identity Preference Optimization. This formulation improves formal requirement satisfaction while preserving the nominal NL task. We evaluate Logic-VLA in closed-loop quadcopter navigation simulation across randomized photorealistic environments and test generalization to STL formulas unseen during training. Across the evaluation benchmarks, Logic-VLA improves STL satisfaction rate over an STL-blind base policy by 24.8 to 40.7 percentage points (pp) while reducing nominal NL task success by at most 1.8 pp, showing that a single VLA can adapt its behavior to varying formal requirements without requiring a separate policy for each specification.

Figures & tables

Fig. 1: Overview of Logic-VLA. Logic-VLA augments a pre-trained VLA with a structured logic conditioning pathway so that the policy jointly follows a natural-language task and a formal temporal logic requirement. The logic encoder is pre-trained from trajectory-formula pairs using robust semantics supervision (Section IV-B ). We integrate the encoder with a VLA in a post-training procedure (Section IV-C ) including 1) supervised fine-tuning using logic satisfying demonstrations and 2) trajectory-level preference optimization using matched satisfying-violating trajectory pairs.

Fig. 2: Visualization of the six natural-language navigation tasks. For each task, we show several example demonstration trajectories from the dataset $D$ in one of the ten randomized warehouse environments used in our experiments.

	Seen				Unseen Parameter				Unseen Structure
Method	STL Sat. $\uparrow$	$\rho$ Mean $\uparrow$	$\rho_{\min}$ $\uparrow$	NL Task $\uparrow$	STL Sat. $\uparrow$	$\rho$ Mean $\uparrow$	$\rho_{\min}$ $\uparrow$	NL Task $\uparrow$	STL Sat. $\uparrow$	$\rho$ Mean $\uparrow$	$\rho_{\min}$ $\uparrow$	NL Task $\uparrow$
Base	41.3	$-0.35{\pm}1.33$	-9.11	90.5	50.0	$-0.03{\pm}1.26$	-5.80	93.9	56.8	$0.07{\pm}1.51$	-6.98	89.3
STL-SFT	61.7	$0.49{\pm}1.57$	-5.09	87.2	59.5	$0.34{\pm}1.52$	-5.05	91.2	64.5	$0.71{\pm}1.86$	-4.64	85.2
Smooth Robust Semantics ( $1\times$ )	76.2	$1.62{\pm}2.92$	-5.72	68.5	71.1	$1.24{\pm}2.51$	-4.94	75.9	77.5	$2.18{\pm}3.26$	-4.92	68.6
Smooth Robust Semantics ( $2\times$ )	78.8	$2.33{\pm}3.80$	-5.79	45.0	72.1	$1.81{\pm}3.19$	-7.31	47.4	81.8	$3.34{\pm}4.24$	-3.82	42.0
Logic-VLA	82.0	$0.81{\pm}1.33$	-1.62	89.0	74.8	$0.89{\pm}1.64$	-3.79	92.2	82.0	$1.24{\pm}1.71$	-2.46	87.5

TABLE I: Evaluation Results. Comparison of Results across the baselines in Seen , Unseen Parameter , and Unseen Structure .

Fig. 3: Ablation Results. (a) Semantic pre-training vs. random encoder initialization. (b) Syntax-graph encoding vs. textual prompting. Results are shown on Seen and Unseen Parameter settings for STL satisfaction and NL task success.

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Vision-language-action models turn visual observations and natural-language instructions into actions for robots and other embodied agents.

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STeP: Signal Temporal Logic for Precise Specifications for Action Generation with Vision Language Models

Kasra Torshizi, Anukriti Singh, Sidharth Mathur, Khuzema Habib+2

Department of Computer Science University of Maryland

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Natural-language robot instructions often specify more than a coarse task goal: they may impose spatial, temporal, and logical requirements that must remain satisfied throughout execution. We present STeP, a specification-based agentic framework that uses Signal Temporal Logic (STL) as an explicit interface between high-level language reasoning and low-level robot execution. Rather than encoding such requirements implicitly in a learned policy, STeP formalizes them as task specifications that can be decomposed across multi-stage manipulation, enforced during execution, monitored online, and used as structured feedback for replanning. We evaluate STeP on standard LIBERO and LIBERO-PRO, and introduce LIBERO-Constrained, a new benchmark for manipulation tasks with spatial, temporal, and logical requirements, together with real-world tabletop experiments. On LIBERO-PRO, STeP retains 54%-89% success across five of six evaluated perturbation settings, substantially outperforming VLA and code-as-policy baselines under distribution shift. On LIBERO-Constrained, STeP achieves 80% safe success across 49 task-constraint instances; on real-world tasks, it improves safe success over a specification-free model-based baseline across all four task categories, with gains of up to 45 percentage points. These results support explicit formal specifications as a practical interface between foundation-model reasoning and reliable robot execution.

Abstract

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