Formal XAI (explainable AI) is a growing area that focuses on computing explanations with mathematical guarantees for the decisions made by ML models. Inside formal XAI, one of the most studied cases is that of explaining the choices taken by decision trees, as they are traditionally deemed as one of the most interpretable classes of models. Recent work has focused on studying the computation of sufficient reasons, a kind of explanation in which given a decision tree and an instance , one explains the decision ( ) by providing a subset of the features of such that for any other instance compatible with , it holds that ( ) = ( ), intuitively meaning that the features in are already enough to fully justify the classification of by . It has been argued, however, that sufficient reasons constitute a restrictive notion of explanation. For such a reason, the community has started to study their probabilistic counterpart, in which one requires that the probability of ( ) = ( ) must be at least some value ∈ (0, 1], where is a random instance that is compatible with . Our paper settles the computational complexity of -sufficient-reasons over decision trees, showing that both (1) finding -sufficient-reasons that are minimal in size, and (2) finding -sufficient-reasons that are minimal inclusion-wise, do not admit polynomial-time algorithms (unless PTIME = NP). This is in stark contrast with the deterministic case ( = 1) where inclusion-wise minimal sufficient-reasons are easy to compute. By doing this, we answer two open problems originally raised by Izza et al., and extend the hardness of explanations for Boolean circuits presented by Wäldchen et al. to the more restricted case of decision trees. On the positive side, we identify structural restrictions of decision trees that make the problem tractable, and show how SAT solvers might be able to tackle these problems in practical settings.Preprint. Under review.

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RESUMENEl artículo se propone relevar las representaciones e imaginarios perrunos, distinguiendo distintas modalidades en las literaturas hispánicas, europea y norteamericana. Plantea que en el capitalismo tardío y la masificación de las mascotas, se ha producido una osmosis entre la sociedad humana y la perruna, interacción que tiene su correlato en la literatura. Una osmosis que paradojalmente revela la humanidad de los animales y la insociabilidad y soledad espiritual del ser humano. Reafirmando el carácter específico del lenguaje literario como desocultamiento y revelación, el artículo plantea distintas variables -filosófica, científica e histórico-social-para abordar el corpus, e indagar los imaginarios perrunos en la literatura, sobre todo respecto a la condición humana vis a vis la condición animal, y también viceversa.Palabras clave: Perros, imaginarios, condición humana, condición animal, especies, antropocentrismo, humanismo, posthumanismo. ABSTRACTThis article explores canine representations and imaginaries in modern literature and culture, distinguishing different modes in Hispanic, American and European narratives. It is suggested that with the proliferation of mascots in late capitalism, osmosis has been produced between human and canine society, creating an interaction that has a correlation in literature. It is an osmosis that paradoxically reveals the humanity of animals and the unsociability and spiritual isolation of human beings. Reaffirming the * El presente artículo se realiza en el marco del Proyecto Fondecyt 1100148 "Representaciones e imaginarios perrunos".

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