Related papers: Predicative toposes
Identifying and categorizing specific robot tasks, behaviors, and resources is an essential precursor to reproducing and evaluating robotics experiments across laboratories and platforms. Without some means of capturing how one environment,…
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
Prediction is a complex notion, and different predictors (such as people, computer programs, and probabilistic theories) can pursue very different goals. In this paper I will review some popular kinds of prediction and argue that the theory…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
We give a systematic treatment to the concept of hypoellipticity, putting it into an abstract form which allows us to deal with several different notions within the same framework. We then investigate when a notion of hypoellipticity…
A quick overview of category theory and topos theory including slice categories, monics, epics, isos, diagrams, cones, cocones, limits, colimits, products and coproducts, pushouts and pullbacks, equalizers and coequalizers, initial and…
We regard a geometric theory classified by a topos as a syntactic presentation for the topos and develop tools for finding such presentations. Extensions of geometric theories, which can add axioms, symbols and sorts, are treated as objects…
A duality between general partially ordered sets and certain topolgical spaces with two closures is established.
An introduction and survey of homotopy type theory in honor of W.W. Tait.
In this talk I will focus on theoretical issues related to high precision determinations of the top mass. Several mass definitions are reviewed and their respective advantages and disadvantages are discussed. Precision determinations of the…
We define a notion on preadditive categories which plays a role similar to the notion of a Grothendieck pretopology on an unenriched category. Each such additive pretopology defines an additive Grothendieck topology and suffices to define…
The predicate complementary to the well-known Godel's provability predicate is defined. From its recursiveness new consequences concerning the incompleteness argumentation are drawn and extended to new results of consistency, completeness…
Textual explanations have proved to help improve user satisfaction on machine-made recommendations. However, current mainstream solutions loosely connect the learning of explanation with the learning of recommendation: for example, they are…
The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist.
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
We define a notion which contains numerous basic notions of Analysis as special cases, for example limit, continuity, differential, Riemann and Lebesgue integral, root and exponential functions. Properties like additivity or linearity of…
This paper presents \proverb\, a text planner for argumentative texts. \proverb\'s main feature is that it combines global hierarchical planning and unplanned organization of text with respect to local derivation relations in a…
In this paper, we define the notion of a preventative expression and discuss a corpus study of such expressions in instructional text. We discuss our coding schema, which takes into account both form and function features, and present…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
This article describes the cocompletion of a category $C$ with finite limits as the homotopy category of some equivalence 2-groupoids in coproducts of elements of $C$. This yields a simple link between several definitions of an infinitary…