This paper focuses on the methods that explain what neurons learn during the training process.

Let q(Y;Θ) and cK(Y,X) be two smooth, decomposable circuits that are compatible overY then computing their product as a circuit rΘ,K(X,Y) = q(Y;Θ) cK(Y,X) that is decomposable overY can be done inO(|q||c|). Letr(X,Y)beacircuitthat is smooth and decomposable and deterministic overY then for a configurationx its MAP state argmaxyr(x,y)canbecomputedintimeO(|r|). For our experiments we use standard compilation tools toobtain aconstraint circuit starting from a propositional logical formula in conjunctive normal form. We now illustrate step-by-step one example of such a compilation for a simple logical formula. Deterministic sum units representdisjoint solutions to the logical formula, meaning there exists distinct assignments, characterized by the children, that satisfy the logical constraint e.g.

In the road traffic example, the network predicts probabilities for each agent's identity, action and position. At inference, logical rules are evaluated using these predictions. The resulting satisfaction degree is then used to update the network so that future predictions better align with the knowledge constraints, as illustrated in Figure 2.

This paper focuses on the methods that explain what neurons learn during the training process.

We present the Mind the Gap Model (MGM), an approach for interpretable feature extraction and selection. By placing interpretability criteria directly into the model, we allow for the model to both optimize parameters related to interpretabil-ity and to directly report a global set of distinguishable dimensions to assist with further data exploration and hypothesis generation.

This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row Decomposition. These representations anchor the system in well-known semantics while facilitating the computation using a powerful algebraic engine. A key aspect of State Algebra is its flexibility in representation. We show that although the default reduction of a state vector is not canonical, a unique canonical form can be obtained by applying a fixed variable order during the reduction process. This highlights a trade-off: by foregoing guaranteed canonicity, the framework gains increased flexibility, potentially leading to more compact representations of certain classes of problems. We explore how this framework provides tools to articulate both search-based and knowledge compilation algorithms and discuss its natural extension to probabilistic logic and Weighted Model Counting.

The proof directly follows from Theorem 3.2 from V ergari et al. [75]. Note that O ( |q ||c|) is a loose upperbound and the size of r is in practice smaller [75]. Analogously, the second statement of Theorem 3.1 follows from Proposition A.1 and by recalling For our experiments we use standard compilation tools to obtain a constraint circuit starting from a propositional logical formula in conjunctive normal form. We now illustrate step-by-step one example of such a compilation for a simple logical formula. Deterministic sum units represent disjoint solutions to the logical formula, meaning there exists distinct assignments, characterized by the children, that satisfy the logical constraint e.g.

Explainable Artificial Intelligence (XAI) plays a crucial role in fostering transparency and trust in AI systems, where traditional XAI approaches typically offer one level of abstraction for explanations, often in the form of heatmaps highlighting single or multiple input features. However, we ask whether abstract reasoning or problem-solving strategies of a model may also be relevant, as these align more closely with how humans approach solutions to problems. We propose a framework, called Symbolic XAI, that attributes relevance to symbolic queries expressing logical relationships between input features, thereby capturing the abstract reasoning behind a model's predictions. The methodology is built upon a simple yet general multi-order decomposition of model predictions. This decomposition can be specified using higher-order propagation-based relevance methods, such as GNN-LRP, or perturbation-based explanation methods commonly used in XAI. The effectiveness of our framework is demonstrated in the domains of natural language processing (NLP), vision, and quantum chemistry (QC), where abstract symbolic domain knowledge is abundant and of significant interest to users. The Symbolic XAI framework provides an understanding of the model's decision-making process that is both flexible for customization by the user and human-readable through logical formulas.

Logical fallacies are common errors in reasoning that undermine the logic of an argument. Automatically detecting logical fallacies has important applications in tracking misinformation and validating claims. In this paper, we design a process to reliably detect logical fallacies by translating natural language to First-order Logic (FOL) step-by-step using Large Language Models (LLMs). We then utilize Satisfiability Modulo Theory (SMT) solvers to reason about the validity of the formula and classify inputs as either a fallacy or valid statement. Our model also provides a novel means of utilizing LLMs to interpret the output of the SMT solver, offering insights into the counter-examples that illustrate why a given sentence is considered a logical fallacy. Our approach is robust, interpretable and does not require training data or fine-tuning. We evaluate our model on a mixed dataset of fallacies and valid sentences. The results demonstrate improved performance compared to end-to-end LLMs, with our classifier achieving an F1-score of 71\% on the Logic dataset. The approach is able to generalize effectively, achieving an F1-score of 73% on the challenge set, LogicClimate, outperforming state-of-the-art models by 21% despite its much smaller size.

We present the Mind the Gap Model (MGM), an approach for interpretable feature extraction and selection. By placing interpretability criteria directly into the model, we allow for the model to both optimize parameters related to interpretability and to directly report a global set of distinguishable dimensions to assist with further data exploration and hypothesis generation.