Related papers: What Makes a Strong Monad?
We characterize strongly finitary monads on categories $\mathsf{Pos}$, $\mathsf{CPO}$ and $\mathsf{DCPO}$ as precisely those preserving sifted colimits. Or, equivalently, enriched finitary monads preserving reflexive coinserters. We study…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive…
Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…
Complex machine learning algorithms are used more and more often in critical tasks involving text data, leading to the development of interpretability methods. Among local methods, two families have emerged: those computing importance…
We extend a few fundamental aspects of the classical theory of non-unique factorization, as presented in Geroldinger and Halter-Koch's 2006 monograph on the subject, to a non-commutative and non-cancellative setting, in the same spirit of…
We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages…
There are different notions of computation, the most popular being monads, applicative functors, and arrows. In this article we show that these three notions can be seen as monoids in a monoidal category. We demonstrate that at this level…
Grammatical features such as number and gender serve two central functions in human languages. While they encode salient semantic attributes like numerosity and animacy, they also offload sentence processing cost by predictably linking…
Many social, technological and biological interactions involve network relationships whose outcome intimately depends on the structure of the network and on the strengths of the connections. Yet, although much information is now available…
Wadler and Thiemann unified type-and-effect systems with monadic semantics via a syntactic correspondence and soundness results with respect to an operational semantics. They conjecture that a general, "coherent" denotational semantics can…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
All natural languages exhibit a distinction between content words (like nouns and adjectives) and function words (like determiners, auxiliaries, prepositions). Yet surprisingly little has been said about the emergence of this universal…
We prove that a monoid $M$ is a group if and only if, in the category of monoids, all points over $M$ are strong. This sharpens and greatly simplifies a result of Montoli, Rodelo and Van der Linden which characterises groups amongst monoids…
In this paper, we concentrate on counting and testing dominant polynomials with integer coefficients. A polynomial is called dominant if it has a simple root whose modulus is strictly greater than the moduli of its remaining roots. In…
We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg-Moore category M^T is monoidal and the forgetful functor from M^T to M is separable Frobenius. Whenever M is also Cauchy complete, a simple…
The $abc$ conjecture is a very deep concept in number theory with wide application to many areas of number theory. In this article we introduce the conjecture and give examples of its applications. In particular we apply the $abc$…
We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…
In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…