For such a reason, the community has started tostudy their probabilistic counterpart, inwhich one requires that the probability ofT(z) = T(x)must beatleast some valueδ (0,1],wherez isa random instance that is compatible withy.

Formal explainable artificial intelligence (XAI) offers unique theoretical guarantees of rigor when compared to other non-formal methods of explainability. However, little attention has been given to the validation of practical implementations of formal explainers. This paper develops a novel methodology for validating formal explainers and reports on the assessment of the publicly available formal explainer PyXAI. The paper documents the existence of incorrect explanations computed by PyXAI on most of the datasets analyzed in the experiments, thereby confirming the importance of the proposed novel methodology for the validation of formal explainers.

"Didn't know you were famous," the rapper Juliani, an old friend and musical collaborator, texted me from his studio in Nairobi. I didn't have a clue what he was referring to, but then he forwarded me the link to a tweet by Elon Musk that included a screenshot of a 2019 Al Jazeera column of mine, " Abolishing whiteness has never been more urgent ." The original post was circulating on Twitter/X, courtesy of a white nationalist poster who obviously wasn't too happy with the headline. Neither was Elon, who retweeted it with the comment, "It's not okay to say this about any group!" Although the post was only a few hours old, it already had five million views.

Formal XAI (explainable AI) is a growing area that focuses on computing explanations with mathematical guarantees for the decisions made by ML models.

Automated reasoning is a key technology in the young but rapidly growing field of Explainable Artificial Intelligence (XAI). Explanability helps build trust in artificial intelligence systems beyond their mere predictive accuracy and robustness. In this paper, we propose a cycle of scientific discovery that combines machine learning with automated reasoning for the generation and the selection of explanations. We present a taxonomy of explanation selection problems that draws on insights from sociology and cognitive science. These selection criteria subsume existing notions and extend them with new properties.

In recent years, the impact of machine learning (ML) and artificial intelligence (AI) in society has been absolutely remarkable. This impact is expected to continue in the foreseeable future. However,the adoption of AI/ML is also a cause of grave concern. The operation of the most advances AI/ML models is often beyond the grasp of human decision makers. As a result, decisions that impact humans may not be understood and may lack rigorous validation. Explainable AI (XAI) is concerned with providing human decision-makers with understandable explanations for the predictions made by ML models. As a result, XAI is a cornerstone of trustworthy AI. Despite its strategic importance, most work on XAI lacks rigor, and so its use in high-risk or safety-critical domains serves to foster distrust instead of contributing to build much-needed trust. Logic-based XAI has recently emerged as a rigorous alternative to those other non-rigorous methods of XAI. This paper provides a technical survey of logic-based XAI, its origins, the current topics of research, and emerging future topics of research. The paper also highlights the many myths that pervade non-rigorous approaches for XAI.

A central goal of eXplainable Artificial Intelligence (XAI) is to assign relative importance to the features of a Machine Learning (ML) model given some prediction. The importance of this task of explainability by feature attribution is illustrated by the ubiquitous recent use of tools such as SHAP and LIME. Unfortunately, the exact computation of feature attributions, using the game-theoretical foundation underlying SHAP and LIME, can yield manifestly unsatisfactory results, that tantamount to reporting misleading relative feature importance. Recent work targeted rigorous feature attribution, by studying axiomatic aggregations of features based on logic-based definitions of explanations by feature selection. This paper shows that there is an essential relationship between feature attribution and a priori voting power, and that those recently proposed axiomatic aggregations represent a few instantiations of the range of power indices studied in the past. Furthermore, it remains unclear how some of the most widely used power indices might be exploited as feature importance scores (FISs), i.e. the use of power indices in XAI, and which of these indices would be the best suited for the purposes of XAI by feature attribution, namely in terms of not producing results that could be deemed as unsatisfactory. This paper proposes novel desirable properties that FISs should exhibit. In addition, the paper also proposes novel FISs exhibiting the proposed properties. Finally, the paper conducts a rigorous analysis of the best-known power indices in terms of the proposed properties.

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.

Formal abductive explanations offer crucial guarantees of rigor and so are of interest in high-stakes uses of machine learning (ML). One drawback of abductive explanations is explanation size, justified by the cognitive limits of human decision-makers. Probabilistic abductive explanations (PAXps) address this limitation, but their theoretical and practical complexity makes their exact computation most often unrealistic. This paper proposes novel efficient algorithms for the computation of locally-minimal PXAps, which offer high-quality approximations of PXAps in practice. The experimental results demonstrate the practical efficiency of the proposed algorithms.

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.