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We construct a univalent universe in the sense of Voevodsky in some suitable model categories for homotopy types (obtained from Grothendieck's theory of test categories). In practice, this means for instance that, appart from the homotopy…
Response-free item difficulty modelling promises to reduce reliance on response-based calibration but is intrinsically difficult on reading-comprehension multiple-choice items, where difficulty depends on inferential demands across wording…
Automatic verification of concurrent programs faces state explosion due to the exponential possible interleavings of its sequential components coupled with large or infinite state spaces. An alternative is deductive verification, where…
In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated by locally correct, bottom-up application of inference rules. We propose an extension of the Curry-Howard…
Region-based type systems are a powerful tool for various kinds of program analysis. We introduce a new inference algorithm for region types based on an abstract notion of environment transformation. It analyzes the code of a method only…
Recent works by Asada, Ong and Tsukada have championed a rigid description of resources. Whereas in non-rigid paradigms (e.g., standard Taylor expansion or non-idempotent intersection types), bags of resources are multisets and invariant…
Non-deductive reasoning systems are often {\em representation dependent}: representing the same situation in two different ways may cause such a system to return two different answers. Some have viewed this as a significant problem. For…
The aim of this paper is to refine and extend proposals by Sozeau and Tabareau and by Voevodsky for universe polymorphism in type theory. In those systems judgments can depend on explicit constraints between universe levels. We here present…
Composite indicators are widely used to score or classify units evaluated on multiple criteria. Their construction typically involves aggregating criteria evaluations, a common practice in Multiple Criteria Decision Aiding (MCDA). Beyond…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
In this thesis, we try to build a connection between the two schools by introducing syntactic inductive biases for deep learning models. We propose two families of inductive biases, one for constituency structure and another one for…
We define a type system with intersection types for an extension of lambda-calculus with unbind and rebind operators. In this calculus, a term with free variables, representing open code, can be packed into an "unbound" term, and passed…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
We combine the theory of inductive data types with the theory of universal measurings. By doing so, we find that many categories of algebras of endofunctors are actually enriched in the corresponding category of coalgebras of the same…
Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the "gros" semantics in the category of lcc categories: Instead of constructing an interpretation in a…
We report on a recent conjecture by Gisin on a restriction of physical processes in sets of finite information numbers (FIN) and further analyze the entropic constraint associated with the proposed algorithm. In the course, we provide a…
Tandem duplication is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain et al. (2017) proposed the study of codes that correct tandem…
By extending type theory with a universe of definitionally associative and unital polynomial monads, we show how to arrive at a definition of opetopic type which is able to encode a number of fully coherent algebraic structures. In…
We compare Friedlander's definition of the etale topological type for simplicial schemes to another definition involving realizations of pro-simplicial sets. This can be expressed as a notion of hypercover descent for etale homotopy. We use…