Related papers: Some remarks on one-basedness
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We classify the unipotent character sheaves on a fixed connected component of a reductive algebraic group under a mild hypothesis on the characteristic of the ground field.
Let $T$ be a (first order complete) dependent theory, ${\mathfrak{C}}$ a $\bar\kappa$-saturated model of $T$ and $G$ a definable subgroup which is abelian. Among subgroups of bounded index which are the union of $<\bar\kappa$ type definable…
All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of…
Due to the emergence of the semantic Web and the increasing need to formalize human knowledge, ontologie engineering is now an important activity. But is this activity very different from other ones like software engineering, for example ?…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
We introduce the notion of "type" of a tableau, that allows us to define new families of tableaux including both balanced and standard Young tableaux. We use these new objects to describe the set of reduced decompositions of any…
We show that certain diagrams of $\infty$-logoses are reconstructed in homotopy type theory extended with some lex, accessible modalities, which enables us to use plain homotopy type theory to reason about not only a single $\infty$-logos…
This paper characterizes the single-peaked domain on a tree via the strategy-proofness of extreme rules defined on that tree. For any tree, these rules are unanimous and anonymous on any preference domain. In particular, we show that they…
The class of generic structures among those consisting of the measure algebra of a probability space equipped with an automorphism is axiomatizable by positive sentences interpreted using an approximate semantics. The separable generic…
It is discussed a practical possibility of a provable programming of mathematics basing on intuitionism and the dependent types feature of a programming language.The principles of constructive mathematics and provable programming are…
We study the homotopy type of the simplicial set of continuous semi-algebraic simplexes of an algebraic variety defined over a real closed field, which we will call the real homotopy type. We prove an analogue of the theorem of Artin-Mazur…
In this note we show that Voevodsky's univalence axiom holds in the model of type theory based on symmetric cubical sets. We will also discuss Swan's construction of the identity type in this variation of cubical sets. This proves that we…
Algebraic varieties which are locally isomorphic to open subsets of affine space will be called {\em plain}. Plain varieties are smooth and rational. The converse is true for curves and surfaces, and unknown in general. It is shown that…
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
Massive single-cell profiling efforts have accelerated our discovery of the cellular composition of the human body, while at the same time raising the need to formalise this new knowledge. Here, we review current cell ontology efforts to…
We describe the first results of a project of analyzing in which theories formal proofs can be ex- pressed. We use this analysis as the basis of interoperability between proof systems.