Tootfinder

Symmetry breaking for inductive logic programming
Andrew Cropper, David M. Cerna, Matti J\"arvisalo
https://arxiv.org/abs/2508.06263 https://arxiv.org…

Symmetry breaking for inductive logic programming
The goal of inductive logic programming is to search for a hypothesis that generalises training data and background knowledge. The challenge is searching vast hypothesis spaces, which is exacerbated because many logically equivalent hypotheses exist. To address this challenge, we introduce a method to break symmetries in the hypothesis space. We implement our idea in answer set programming. Our experiments on multiple domains, including visual reasoning and game playing, show that our approach …

Compositional Inductive Invariant Inference via Assume-Guarantee Reasoning
Ian Dardik, Eunsuk Kang
https://arxiv.org/abs/2509.06250 https://arxiv.org/pdf/2…

Compositional Inductive Invariant Inference via Assume-Guarantee Reasoning
A common technique for verifying the safety of complex systems is the inductive invariant method. Inductive invariants are inductive formulas that overapproximate the reachable states of a system and imply a desired safety property. However, inductive invariants are notoriously complex, which makes inductive invariant inference a challenging problem. In this work, we observe that inductive invariant formulas are complex primarily because they must be closed over the transition relation of an en…

Inductive Learning for Possibilistic Logic Programs Under Stable Models
Hongbo Hu, Yisong Wang, Yi Huang, Kewen Wang
https://arxiv.org/abs/2510.07069 https://

Inductive Learning for Possibilistic Logic Programs Under Stable Models
Possibilistic logic programs (poss-programs) under stable models are a major variant of answer set programming (ASP). While its semantics (possibilistic stable models) and properties have been well investigated, the problem of inductive reasoning has not been investigated yet. This paper presents an approach to extracting poss-programs from a background program and examples (parts of intended possibilistic stable models). To this end, the notion of induction tasks is first formally defined, its…

Newton to Einstein: Axiom-Based Discovery via Game Design
Pingchuan Ma, Benjamin Tod Jones, Tsun-Hsuan Wang, Minghao Guo, Michal Piotr Lipiec, Chuang Gan, Wojciech Matusik
https://arxiv.org/abs/2509.05448

Newton to Einstein: Axiom-Based Discovery via Game Design
This position paper argues that machine learning for scientific discovery should shift from inductive pattern recognition to axiom-based reasoning. We propose a game design framework in which scientific inquiry is recast as a rule-evolving system: agents operate within environments governed by axioms and modify them to explain outlier observations. Unlike conventional ML approaches that operate within fixed assumptions, our method enables the discovery of new theoretical structures through syst…

iFinder: Structured Zero-Shot Vision-Based LLM Grounding for Dash-Cam Video Reasoning
Manyi Yao, Bingbing Zhuang, Sparsh Garg, Amit Roy-Chowdhury, Christian Shelton, Manmohan Chandraker, Abhishek Aich
https://arxiv.org/abs/2509.19552

iFinder: Structured Zero-Shot Vision-Based LLM Grounding for Dash-Cam Video Reasoning
Grounding large language models (LLMs) in domain-specific tasks like post-hoc dash-cam driving video analysis is challenging due to their general-purpose training and lack of structured inductive biases. As vision is often the sole modality available for such analysis (i.e., no LiDAR, GPS, etc.), existing video-based vision-language models (V-VLMs) struggle with spatial reasoning, causal inference, and explainability of events in the input video. To this end, we introduce iFinder, a structured …

Investigating Advanced Reasoning of Large Language Models via Black-Box Interaction
Congchi Yin, Tianyi Wu, Yankai Shu, Alex Gu, Yunhan Wang, Jun Shao, Xun Jiang, Piji Li
https://arxiv.org/abs/2508.19035

Investigating Advanced Reasoning of Large Language Models via Black-Box Interaction
Existing tasks fall short in evaluating reasoning ability of Large Language Models (LLMs) in an interactive, unknown environment. This deficiency leads to the isolated assessment of deductive, inductive, and abductive reasoning, neglecting the integrated reasoning process that is indispensable for humans discovery of real world. We introduce a novel evaluation paradigm, \textit{black-box interaction}, to tackle this challenge. A black-box is defined by a hidden function that maps a specific set…

Monoid Structures on Indexed Containers
Michele De Pascalis, Tarmo Uustalu, Niccol\`o Veltr\`i
https://arxiv.org/abs/2509.25879 https://arxiv.org/pdf/2509.…

Monoid Structures on Indexed Containers
Containers represent a wide class of type constructions relevant for functional programming and (co)inductive reasoning. Indexed containers generalize this notion to better fit the scope of dependently typed programming. When interpreting types to be sets, a container describes an endofunctor on the category of sets while an I-indexed container describes an endofunctor on the category Set^I of I-indexed families of sets. We consider the monoidal structure on the category of I-indexed containe…

Fuzzy, Symbolic, and Contextual: Enhancing LLM Instruction via Cognitive Scaffolding
Vanessa Figueiredo
https://arxiv.org/abs/2508.21204 https://arxiv.org/…

Fuzzy, Symbolic, and Contextual: Enhancing LLM Instruction via Cognitive Scaffolding
We study how architectural inductive biases influence the cognitive behavior of large language models (LLMs) in instructional dialogue. We introduce a symbolic scaffolding mechanism paired with a short-term memory schema designed to promote adaptive, structured reasoning in Socratic tutoring. Using controlled ablation across five system variants, we evaluate model outputs via expert-designed rubrics covering scaffolding, responsiveness, symbolic reasoning, and conversational memory. We present …

Monotone Neural Control Barrier Certificates
Alireza Nadali, Ashutosh Trivedi, Majid Zamani, Saber Jafarpour
https://arxiv.org/abs/2508.12178 https://arxiv…

Monotone Neural Control Barrier Certificates
This work presents a neurosymbolic framework for synthesizing and verifying safety controllers in high-dimensional monotone dynamical systems using only linear sample complexity, without requiring explicit models or conservative Lipschitz bounds. The approach combines the expressiveness of neural networks with the rigor of symbolic reasoning via barrier certificates, functional analogs of inductive invariants that formally guarantee safety. Prior data-driven methods often treat dynamics as blac…

Polynomial-Time Exact Algorithm for Non-preemptive Single-Machine Scheduling with Heterogeneous Release and Processing Times
Xiaoyang Duan, Peixin Zhao
https://arxiv.org/abs/2508.18272

Polynomial-Time Exact Algorithm for Non-preemptive Single-Machine Scheduling with Heterogeneous Release and Processing Times
This paper addresses the non-preemptive single-machine scheduling problem with heterogeneous release and processing times, where minimizing total waiting time is NP-hard. We introduce a novel waiting-time formula that preserves global information, which derive a specific structural condition that transforms the problem into a tractable form. Leveraging this formula, we develop a structure-driven analytical framework that uses inductive reasoning to characterize the feasible solution space. This…