Feature attribution methods based on game theory are ubiquitous in the field of eXplainable Artificial Intelligence (XAI). Recent works proposed rigorous feature attribution using logic-based explanations, specifically targeting high-stakes uses of machine learning (ML) models. Typically, such works exploit weak abductive explanation (WAXp) as the characteristic function to assign importance to features. However, one possible downside is that the contribution of non-WAXp sets is neglected. In fact, non-WAXp sets can also convey important information, because of the relationship between formal explanations (XPs) and adversarial examples (AExs). Accordingly, this paper leverages Shapley value and Banzhaf index to devise two novel feature importance scores. We take into account non-WAXp sets when computing feature contribution, and the novel scores quantify how effective each feature is at excluding AExs. Furthermore, the paper identifies properties and studies the computational complexity of the proposed scores.

Explainable Artificial Intelligence (XAI) is critical for attaining trust in the operation of AI systems. A key question of an AI system is ``why was this decision made this way''. Formal approaches to XAI use a formal model of the AI system to identify abductive explanations. While abductive explanations may be applicable to a large number of inputs sharing the same concrete values, more general explanations may be preferred for numeric inputs. So-called inflated abductive explanations give intervals for each feature ensuring that any input whose values fall withing these intervals is still guaranteed to make the same prediction. Inflated explanations cover a larger portion of the input space, and hence are deemed more general explanations. But there can be many (inflated) abductive explanations for an instance. Which is the best? In this paper, we show how to find a most general abductive explanation for an AI decision. This explanation covers as much of the input space as possible, while still being a correct formal explanation of the model's behaviour. Given that we only want to give a human one explanation for a decision, the most general explanation gives us the explanation with the broadest applicability, and hence the one most likely to seem sensible. (The paper has been accepted at IJCAI2025 conference.)

We view voting rules as classifiers that assign a winner (a class) to a profile of voters' preferences (an instance). We propose to apply techniques from formal explainability, most notably abductive and contrastive explanations, to identify minimal subsets of a preference profile that either imply the current winner or explain why a different candidate was not elected. Formal explanations turn out to have strong connections with classical problems studied in computational social choice such as bribery, possible and necessary winner identification, and preference learning. We design algorithms for computing abductive and contrastive explanations for scoring rules. For the Borda rule, we find a lower bound on the size of the smallest abductive explanations, and we conduct simulations to identify correlations between properties of preference profiles and the size of their smallest abductive explanations.

The uses of machine learning (ML) have snowballed in recent years. In many cases, ML models are highly complex, and their operation is beyond the understanding of human decision-makers. Nevertheless, some uses of ML models involve high-stakes and safety-critical applications. Explainable artificial intelligence (XAI) aims to help human decision-makers in understanding the operation of such complex ML models, thus eliciting trust in their operation. Unfortunately, the majority of past XAI work is based on informal approaches, that offer no guarantees of rigor. Unsurprisingly, there exists comprehensive experimental and theoretical evidence confirming that informal methods of XAI can provide human-decision makers with erroneous information. Logic-based XAI represents a rigorous approach to explainability; it is model-based and offers the strongest guarantees of rigor of computed explanations. However, a well-known drawback of logic-based XAI is the complexity of logic reasoning, especially for highly complex ML models. Recent work proposed distance-restricted explanations, i.e. explanations that are rigorous provided the distance to a given input is small enough. Distance-restricted explainability is tightly related with adversarial robustness, and it has been shown to scale for moderately complex ML models, but the number of inputs still represents a key limiting factor. This paper investigates novel algorithms for scaling up the performance of logic-based explainers when computing and enumerating ML model explanations with a large number of inputs.

Robustness is widely regarded as a fundamental problem in the analysis of machine learning (ML) models. Most often robustness equates with deciding the non-existence of adversarial examples, where adversarial examples denote situations where small changes on some inputs cause a change in the prediction. The perceived importance of ML model robustness explains the continued progress observed for most of the last decade. Whereas robustness is often assessed locally, i.e. given some target point in feature space, robustness can also be defined globally, i.e. where any point in feature space can be considered. The importance of ML model robustness is illustrated for example by the existence of competitions evaluating the progress of robustness tools, namely in the case of neural networks (NNs) but also by efforts towards robustness certification. More recently, robustness tools have also been used for computing rigorous explanations of ML models. In contrast with the observed successes of robustness, this paper uncovers some limitations with existing definitions of robustness, both global and local, but also with efforts towards robustness certification. The paper also investigates uses of adversarial examples besides those related with robustness.

Widespread use of artificial intelligence (AI) algorithms and machine learning (ML) models on the one hand and a number of crucial issues pertaining to them warrant the need for explainable artificial intelligence (XAI). A key explainability question is: given this decision was made, what are the input features which contributed to the decision? Although a range of XAI approaches exist to tackle this problem, most of them have significant limitations. Heuristic XAI approaches suffer from the lack of quality guarantees, and often try to approximate Shapley values, which is not the same as explaining which features contribute to a decision. A recent alternative is so-called formal feature attribution (FFA), which defines feature importance as the fraction of formal abductive explanations (AXp's) containing the given feature. This measures feature importance from the view of formally reasoning about the model's behavior. It is challenging to compute FFA using its definition because that involves counting AXp's, although one can approximate it. Based on these results, this paper makes several contributions. First, it gives compelling evidence that computing FFA is intractable, even if the set of contrastive formal explanations (CXp's) is provided, by proving that the problem is #P-hard. Second, by using the duality between AXp's and CXp's, it proposes an efficient heuristic to switch from CXp enumeration to AXp enumeration on-the-fly resulting in an adaptive explanation enumeration algorithm effectively approximating FFA in an anytime fashion. Finally, experimental results obtained on a range of widely used datasets demonstrate the effectiveness of the proposed FFA approximation approach in terms of the error of FFA approximation as well as the number of explanations computed and their diversity given a fixed time limit.

In contrast with ad-hoc methods for eXplainable Artificial Intelligence (XAI), formal explainability offers important guarantees of rigor. However, formal explainability is hindered by poor scalability for some families of classifiers, the most significant being neural networks. As a result, there are concerns as to whether formal explainability might serve to complement other approaches in delivering trustworthy AI. This paper addresses the limitation of scalability of formal explainability, and proposes novel algorithms for computing formal explanations. The novel algorithm computes explanations by answering instead a number of robustness queries, and such that the number of such queries is at most linear on the number of features. Consequently, the proposed algorithm establishes a direct relationship between the practical complexity of formal explainability and that of robustness. More importantly, the paper generalizes the definition of formal explanation, thereby allowing the use of robustness tools that are based on different distance norms, and also by reasoning in terms of some target degree of robustness. The experiments validate the practical efficiency of the proposed approach.

Among the existing informal approaches to XAI, the use of Shapley values as a mechanism for feature attribution is arguably the Explainable artificial intelligence (XAI) aims to help human best-known. Shapley values [Shapley 1953] were originally proposed decision-makers in understanding complex machine learning (ML) in the context of game theory, but have found a wealth of models. One of the hallmarks of XAI are measures of relative feature application domains [Roth 1988]. More importantly, for more than importance, which are theoretically justified through the use two decades Shapley values have been proposed in the context of of Shapley values. This paper builds on recent work and offers a explaining the decisions of complex ML models [Lipovetsky and simple argument for why Shapley values can provide misleading Conklin 2001; Lundberg and Lee 2017; Strumbelj and Kononenko measures of relative feature importance, by assigning more importance 2010, 2014]. The importance of Shapley values for explainability is to features that are irrelevant for a prediction, and assigning illustrated by the massive impact of tools like SHAP [Lundberg and less importance to features that are relevant for a prediction. The Lee 2017], including many recent uses that have a direct influence significance of these results is that they effectively challenge the on human beings (see [Huang and Marques-Silva 2023] for some many proposed uses of measures of relative feature importance in recent references).

In the practical deployment of machine learning (ML) models, missing data represents a recurring challenge. Missing data is often addressed when training ML models. But missing data also needs to be addressed when deciding predictions and when explaining those predictions. Missing data represents an opportunity to partially specify the inputs of the prediction to be explained. This paper studies the computation of logic-based explanations in the presence of partially specified inputs. The paper shows that most of the algorithms proposed in recent years for computing logic-based explanations can be generalized for computing explanations given the partially specified inputs. One related result is that the complexity of computing logic-based explanations remains unchanged. A similar result is proved in the case of logic-based explainability subject to input constraints. Furthermore, the proposed solution for computing explanations given partially specified inputs is applied to classifiers obtained from well-known public datasets, thereby illustrating a number of novel explainability use cases.

In the quest for Explainable Artificial Intelligence (XAI) one of the questions that frequently arises given a decision made by an AI system is, ``why was the decision made in this way?'' Formal approaches to explainability build a formal model of the AI system and use this to reason about the properties of the system. Given a set of feature values for an instance to be explained, and a resulting decision, a formal abductive explanation is a set of features, such that if they take the given value will always lead to the same decision. This explanation is useful, it shows that only some features were used in making the final decision. But it is narrow, it only shows that if the selected features take their given values the decision is unchanged. It's possible that some features may change values and still lead to the same decision. In this paper we formally define inflated explanations which is a set of features, and for each feature of set of values (always including the value of the instance being explained), such that the decision will remain unchanged. Inflated explanations are more informative than abductive explanations since e.g they allow us to see if the exact value of a feature is important, or it could be any nearby value. Overall they allow us to better understand the role of each feature in the decision. We show that we can compute inflated explanations for not that much greater cost than abductive explanations, and that we can extend duality results for abductive explanations also to inflated explanations.