Related papers: Integration motivique sur les schemas formels
Recent advances in automated theorem proving use Large Language Models (LLMs) to translate informal mathematical statements into formal proofs. However, informal cues are often ambiguous or lack strict logical structure, making it hard for…
In this study, we define interaction components of different orders between two input variables based on game theory. We further prove that interaction components of different orders satisfy several desirable properties.
In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically…
We prove a recognition principle for motivic infinite P1-loop spaces over a perfect field. This is achieved by developing a theory of framed motivic spaces, which is a motivic analogue of the theory of E-infinity-spaces. A framed motivic…
We present a formalization of the OSGi component framework. Our formalization is intended to be used as a basis for describing behavior of OSGi based systems. Furthermore, we describe specification formalisms for describing properties of…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
In this note we prove the geometrical origin of pairings of abelian schemes. According to Deligne's philosophy of motives, this means that these pairings are motivic. We make also explicit the link between pairings and linear morphisms. We…
We present a framework for formal software development with UML. In contrast to previous approaches that equip UML with a formal semantics, we follow an institution based heterogeneous approach. This can express suitable formal semantics of…
LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's…
We continue our study on infinitesimal lifting properties of maps between locally noetherian formal schemes started in math.AG/0604241. In this paper, we focus on some properties which arise specifically in the formal context. In this vein,…
This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It…
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…
With representation-theoretic applications in mind, we construct a formalism of reduced motives with integral coefficients. These are motivic sheaves from which the higher motivic cohomology of the base scheme has been removed. We show that…
In this paper we propose a research programme for getting structural characterisations for 2-dimensional languages generated by self-assembling tiles. This is part of a larger programme on getting a formal foundation of parallel,…
We propose a framework for building graphical causal model that is based on the concept of causal mechanisms. Causal models are intuitive for human users and, more importantly, support the prediction of the effect of manipulation. We…
We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.
We construct a model of the comprehension schema in the logic LP=>.
By associating a `motivic integral' to every complex projective variety X with at worst canonical, Gorenstein singularities, Kontsevich proved that, when there exists a crepant resolution of singularities Y of X, the Hodge numbers of Y do…
The given paper considered a generalized model representation of the software system "Instrumental complex for ontological engineering purpose". Represented complete software system development process. Developed relevant formal models of…