Autonomous vehicles require highly sophisticated decision-making to determine their motion. This paper describes how such functionality can be achieved with a practical rule engine learned from expert driving decisions. We propose an algorithm to create and maintain a rule-based behaviour planner, using a two-layer rule-based theory. The first layer determines a set of feasible parametrized behaviours, given the perceived state of the environment. From these, a resolution function chooses the most conservative high-level maneuver. The second layer then reconciles the parameters into a single behaviour. To demonstrate the practicality of our approach, we report results of its implementation in a level-3 autonomous vehicle and its field test in an urban environment.

Hospitalizations that follow closely on the heels of one or more emergency department visits are often symptoms of missed opportunities to form a proper diagnosis. These diagnostic errors imply a failure to recognize the need for hospitalization and deliver appropriate care, and thus also bear important connotations for patient safety. In this paper, we show how data mining techniques can be applied to a large existing hospitalization data set to learn useful models that predict these upcoming hospitalizations with high accuracy. Specifically, we use an ensemble of logistics regression, na\"ive Bayes and association rule classifiers to successfully predict hospitalization within 3, 7 and 14 days of an emergency department discharge. Aside from high accuracy, one of the advantages of the techniques proposed here is that the resulting classifier is easily inspected and interpreted by humans so that the learned rules can be readily operationalized. These rules can then be easily distributed and applied directly by physicians in emergency department settings to predict the risk of early admission prior to discharging their emergency department patients.

Despite the impressive performance in a variety of complex tasks, modern large language models (LLMs) still have trouble dealing with some math problems that are simple and intuitive for humans, such as addition. While we can easily learn basic rules of addition and apply them to new problems of any length, LLMs struggle to do the same. Instead, they may rely on similar cases seen in the training corpus for help. We define these two different reasoning mechanisms as "rule-based reasoning" and "case-based reasoning". Since rule-based reasoning is essential for acquiring systematic generalization ability, we aim to explore exactly whether transformers use rule-based or case-based reasoning for math problems. Through carefully designed intervention experiments on five math tasks, we confirm that transformers are performing case-based reasoning, no matter whether scratchpad is used, which aligns with the previous observations that transformers use subgraph matching/shortcut learning to reason. To mitigate such problems, we propose a Rule-Following Fine-Tuning (RFFT) technique to teach transformers to perform rule-based reasoning. Specifically, we provide explicit rules in the input and then instruct transformers to recite and follow the rules step by step. Through RFFT, we successfully enable LLMs fine-tuned on 1-5 digit addition to generalize to up to 12-digit addition with over 95% accuracy, which is over 40% higher than scratchpad. The significant improvement demonstrates that teaching LLMs to use rules explicitly helps them learn rule-based reasoning and generalize better in length.

Knowledge graph (KG) completion aims to find out missing triples in a KG. Some tasks, such as link prediction and instance completion, have been proposed for KG completion. They are triple-level tasks with some elements in a missing triple given to predict the missing element of the triple. However, knowing some elements of the missing triple in advance is not always a realistic setting. In this paper, we propose a novel graph-level automatic KG completion task called Triple Set Prediction (TSP) which assumes none of the elements in the missing triples is given. TSP is to predict a set of missing triples given a set of known triples. To properly and accurately evaluate this new task, we propose 4 evaluation metrics including 3 classification metrics and 1 ranking metric, considering both the partial-open-world and the closed-world assumptions. Furthermore, to tackle the huge candidate triples for prediction, we propose a novel and efficient subgraph-based method GPHT that can predict the triple set fast. To fairly compare the TSP results, we also propose two types of methods RuleTensor-TSP and KGE-TSP applying the existing rule- and embedding-based methods for TSP as baselines. During experiments, we evaluate the proposed methods on two datasets extracted from Wikidata following the relation-similarity partial-open-world assumption proposed by us, and also create a complete family data set to evaluate TSP results following the closed-world assumption. Results prove that the methods can successfully generate a set of missing triples and achieve reasonable scores on the new task, and GPHT performs better than the baselines with significantly shorter prediction time. The datasets and code for experiments are available at https://github.com/zjukg/GPHT-for-TSP.

In Explainable AI, rule extraction translates model knowledge into logical rules, such as IF-THEN statements, crucial for understanding patterns learned by black-box models. This could significantly aid in fields like disease diagnosis, disease progression estimation, or drug discovery. However, such application domains often contain imbalanced data, with the class of interest underrepresented. Existing methods inevitably compromise the performance of rules for the minor class to maximise the overall performance. As the first attempt in this field, we propose a model-agnostic approach for extracting rules from specific subgroups of data, featuring automatic rule generation for numerical features. This method enhances the regional explainability of machine learning models and offers wider applicability compared to existing methods. We additionally introduce a new method for selecting features to compose rules, reducing computational costs in high-dimensional spaces. Experiments across various datasets and models demonstrate the effectiveness of our methods.

We study how to subvert language models from following the rules. We model rule-following as inference in propositional Horn logic, a mathematical system in which rules have the form "if $P$ and $Q$, then $R$" for some propositions $P$, $Q$, and $R$. We prove that although transformers can faithfully abide by such rules, maliciously crafted prompts can nevertheless mislead even theoretically constructed models. Empirically, we find that attacks on our theoretical models mirror popular attacks on large language models. Our work suggests that studying smaller theoretical models can help understand the behavior of large language models in rule-based settings like logical reasoning and jailbreak attacks.

Large language models (LLMs) have achieved impressive human-like performance across various reasoning tasks. However, their mastery of underlying inferential rules still falls short of human capabilities. To investigate this, we propose a logic scaffolding inferential rule generation framework, to construct an inferential rule base, ULogic, comprising both primitive and compositional rules across five domains. Our analysis of GPT-series models over a rule subset reveals significant gaps in LLMs' logic understanding compared to human performance, especially in compositional and structural complex rules with certain bias patterns. We further distill these rules into a smaller-scale inference engine for flexible rule generation and enhancing downstream reasoning. Through a multi-judger evaluation, our inference engine proves effective in generating accurate, complex and abstract conclusions and premises, and improve various commonsense reasoning tasks. Overall, our work sheds light on LLMs' limitations in grasping inferential rule and suggests ways to enhance their logical reasoning abilities~\footnote{Code and data are available at \url{https://github.com/SiyuanWangw/ULogic}.}.

The short-loading cycle is a repetitive task performed in high quantities, making it a great alternative for automation. In the short-loading cycle, an expert operator navigates towards a pile, fills the bucket with material, navigates to a dump truck, and dumps the material into the tipping body. The operator has to balance the productivity goal while minimising the fuel usage, to maximise the overall efficiency of the cycle. In addition, difficult interactions, such as the tyre-to-surface interaction further complicate the cycle. These types of hard-to-model interactions that can be difficult to address with rule-based systems, together with the efficiency requirements, motivate us to examine the potential of data-driven approaches. In this paper, the possibility of teaching an agent through reinforcement learning to approach a dump truck's tipping body and get in position to dump material in the tipping body is examined. The agent is trained in a 3D simulated environment to perform a simplified navigation task. The trained agent is directly transferred to a real vehicle, to perform the same task, with no additional training. The results indicate that the agent can successfully learn to navigate towards the dump truck with a limited amount of control signals in simulation and when transferred to a real vehicle, exhibits the correct behaviour.

In this paper, we generalize the Pearl and Neyman-Rubin methodologies in causal inference by introducing a generalized approach that incorporates fuzzy logic. Indeed, we introduce a fuzzy causal inference approach that consider both the vagueness and imprecision inherent in data, as well as the subjective human perspective characterized by fuzzy terms such as 'high', 'medium', and 'low'. To do so, we introduce two fuzzy causal effect formulas: the Fuzzy Average Treatment Effect (FATE) and the Generalized Fuzzy Average Treatment Effect (GFATE), together with their normalized versions: NFATE and NGFATE. When dealing with a binary treatment variable, our fuzzy causal effect formulas coincide with classical Average Treatment Effect (ATE) formula, that is a well-established and popular metric in causal inference. In FATE, all values of the treatment variable are considered equally important. In contrast, GFATE takes into account the rarity and frequency of these values. We show that for linear Structural Equation Models (SEMs), the normalized versions of our formulas, NFATE and NGFATE, are equivalent to ATE. Further, we provide identifiability criteria for these formulas and show their stability with respect to minor variations in the fuzzy subsets and the probability distributions involved. This ensures the robustness of our approach in handling small perturbations in the data. Finally, we provide several experimental examples to empirically validate and demonstrate the practical application of our proposed fuzzy causal inference methods.

Learning interpretable models has become a major focus of machine learning research, given the increasing prominence of machine learning in socially important decision-making. Among interpretable models, rule lists are among the best-known and easily interpretable ones. However, finding optimal rule lists is computationally challenging, and current approaches are impractical for large datasets. We present a novel and scalable approach to learn nearly optimal rule lists from large datasets. Our algorithm uses sampling to efficiently obtain an approximation of the optimal rule list with rigorous guarantees on the quality of the approximation. In particular, our algorithm guarantees to find a rule list with accuracy very close to the optimal rule list when a rule list with high accuracy exists. Our algorithm builds on the VC-dimension of rule lists, for which we prove novel upper and lower bounds. Our experimental evaluation on large datasets shows that our algorithm identifies nearly optimal rule lists with a speed-up up to two orders of magnitude over state-of-the-art exact approaches. Moreover, our algorithm is as fast as, and sometimes faster than, recent heuristic approaches, while reporting higher quality rule lists. In addition, the rules reported by our algorithm are more similar to the rules in the optimal rule list than the rules from heuristic approaches.