Related papers: Doubly F-Bounded Generics
Modeling generics in object-oriented programming languages such as Java and C# is a challenge. Recently we proposed a new order-theoretic approach to modeling generics. Given the strong relation between order theory and category theory, in…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Double Fibonacci sequences are introduced and they are related to operations with Fibonacci modules. Generalizations and examples are also discussed.
For a strongly connected category $\mathcal C$ with pair-wise coproducts, we introduce a cosimplicial object, which serves as a sort of resolution for computing higher derived functors of ${\sf lim} : \mathrm{Ab}^{\mathcal C}\to…
We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.
In this series of papers, we propose a theory of enumerative invariants counting self-dual objects in self-dual categories. Ordinary enumerative invariants in abelian categories can be seen as invariants for the structure group $\mathrm{GL}…
Maximum composite likelihood estimation is a useful alternative to maximum likelihood estimation when data arise from data generating processes (DGPs) that do not admit tractable joint specification. We demonstrate that generic composite…
We consider a generic class of log-concave, possibly random, (Gibbs) measures. We prove the concentration of an infinite family of order parameters called multioverlaps. Because they completely parametrise the quenched Gibbs measure of the…
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…
Dual feasible functions (DFFs) have been used to provide bounds for standard packing problems and valid inequalities for integer optimization problems. In this paper, the connection between general DFFs and a particular family of…
We introduce a generalized notion of inference system to support more flexible interpretations of recursive definitions. Besides axioms and inference rules with the usual meaning, we allow also coaxioms, which are, intuitively, axioms which…
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier U, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a…
The notion of "super convex spaces" generalizes the idea of convex spaces by replacing finite affine sums with countable affine sums. Using this notion permits a very elegant approach for analysis of the Giry monad on standard measurable…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
We establish results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements…
Open-ended Commonsense Reasoning is defined as solving a commonsense question without providing 1) a short list of answer candidates and 2) a pre-defined answer scope. Conventional ways of formulating the commonsense question into a…
We show that finitely generated irreducible $\mathrm{II}_1$ subfactors are generic in the following sense. Given a separable $\mathrm{II}_1$ factor $M$ and an integer $n\geq 2$, equip the set of $n$-tuples of self-adjoint operators in $M$…