Related papers: Constructible motivic functions and motivic integr…

We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…

We propose a new definition of actual causes, using structural equations to model counterfactuals.We show that the definitions yield a plausible and elegant account ofcausation that handles well examples which have caused problems forother…

The analytic implicit function theorem is extended. The function f of the theorem is integrated with respect to the dependent variable of the implicit function. A geometrical interpretation is given for the sub-geometry of the integral…

We provide a formal, simple and intuitive theory of rational decision making including sequential decisions that affect the environment. The theory has a geometric flavor, which makes the arguments easy to visualize and understand. Our…

In model-driven development, an ordered model transformation is a nested set of transformations between source and target classes, in which each transformation is governed by its own pre and post- conditions, but structurally dependent on…

Psychosocial constructs can only be assessed indirectly, and measures are typically formed by a combination of indicators that are thought to relate to the construct. Reflective and formative measurement models offer different…

We present constructive provability logic, an intuitionstic modal logic that validates the L\"ob rule of G\"odel and L\"ob's provability logic by permitting logical reflection over provability. Two distinct variants of this logic, CPL and…

We study a new notion of reduction between structures called enumerable functors related to the recently investigated notion of computable functors. Our main result shows that enumerable functors and effective interpretability with the…

Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…

In this paper, we construct some maps related to the motivic Galois action on depth-graded motivic multiple zeta values. And from these maps we give some short exact sequences about depth-graded motivic multiple zeta values in depth two and…

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…

We develop a power structure over the Grothendieck ring of varieties relative to an abelian monoid, which allows us to compute the motivic class of the generalized Kummer scheme. We obtain a generalized version of Cheah's formula for the…

As a pivotal component to attaining generalizable solutions in human intelligence, reasoning provides great potential for reinforcement learning (RL) agents' generalization towards varied goals by summarizing part-to-whole arguments and…

We present a one-fits-all programmatic approach to reason about a plethora of objectives on probabilistic programs. The first ingredient is to add a reward-statement to the language. We then define a program transformation applying a…

Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.

We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type…

This is the final version of the 2007 preprint titled "On the derived category of 1-motives, I". It has been substantially expanded to contain a motivic proof of (two thirds of) Deligne's conjecture on 1-motives with rational coefficients,…

Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…

Formal verification has been successfully developed in computer science for verifying combinatorial classes of models and specifications. In like manner, formal verification methods have been developed for dynamical systems. However, the…

We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…