Related papers: Revisiting Decidable Bounded Quantification, via D…
A classifier is considered interpretable if each of its decisions has an explanation which is small enough to be easily understood by a human user. A DNF formula can be seen as a binary classifier $\kappa$ over boolean domains. The size of…
System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…
We adapt arguments concerning entropy-theoretic convergence from the independent case to the case of FKG random variables. FKG systems are chosen since their dependence structure is controlled through covariance alone, though in the sequel…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
Recently it was shown that it is undecidable whether a term rewrite system can be proved terminating by a polynomial interpretation in the natural numbers. In this paper we show that this is also the case when restricting the…
Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification,…
Explainability of Deep Neural Networks (DNNs) has been garnering increasing attention in recent years. Of the various explainability approaches, concept-based techniques stand out for their ability to utilize human-meaningful concepts…
In this communication, we resolve a longstanding open question in the probabilistic verification of infinite-state systems. We show that model checking {\it stateless probabilistic pushdown systems (pBPA)} against {\it probabilistic…
We investigate an original family of quantum distinguishability problems, where the goal is to perfectly distinguish between $M$ quantum states that become identical under a completely decohering map. Similarly, we study distinguishability…
The problem of attempting to learn the mapping between data and labels is the crux of any machine learning task. It is, therefore, of interest to the machine learning community on practical as well as theoretical counts to consider the…
Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…
Systems of decision rules and decision trees are widely used as a means for knowledge representation, as classifiers, and as algorithms. They are among the most interpretable models for classifying and representing knowledge. The study of…
Despite the success of deep learning in dermoscopy image analysis, its inherent black-box nature hinders clinical trust, motivating the use of prototypical networks for case-based visual transparency. However, inevitable selection bias in…
The emptiness and containment problems for probabilistic automata are natural quantitative generalisations of the classical language emptiness and inclusion problems for Boolean automata. It is well known that both problems are undecidable.…
Since Val Tannen's pioneer work on the combination of simply-typed lambda-calculus and first-order rewriting (LICS'88), many authors have contributed to this subject by extending it to richer typed lambda-calculi and rewriting paradigms,…
For each Turing machine T, we construct an algebra A'(T) such that the variety generated by A'(T) has definable principal subcongruences if and only if T halts, thus proving that the property of having definable principal subcongruences is…
We consider probabilistic automata on infinite words with acceptance defined by safety, reachability, B\"uchi, coB\"uchi, and limit-average conditions. We consider quantitative and qualitative decision problems. We present extensions and…
We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…
Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…