Related papers: Equality, Quasi-Implicit Products, and Large Elimi…

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…

The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…

We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…

Training data influence estimation methods quantify the contribution of training documents to a model's output, making them a promising source of information for example-based explanations. As humans cannot interpret thousands of documents,…

We develop a qualitative model of decision making with two aims: to describe how people make simple decisions and to enable computer programs to do the same. Current approaches based on Planning or Decisions Theory either ignore uncertainty…

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…

Classification with abstention has gained a lot of attention in recent years as it allows to incorporate human decision-makers in the process. Yet, abstention can potentially amplify disparities and lead to discriminatory predictions. The…

Providing explanations along with predictions is crucial in some text processing tasks. Therefore, we propose a new self-interpretable model that performs output prediction and simultaneously provides an explanation in terms of the presence…

Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…

We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…

This paper considers the problem of testing whether there exists a non-negative solution to a possibly under-determined system of linear equations with known coefficients. This hypothesis testing problem arises naturally in a number of…

We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…

We present a convenient notation for positive/negative-conditional equations. The idea is to merge rules specifying the same function by using case-, if-, match-, and let-expressions. Based on the presented macro-rule-construct,…

Classical Decision Theory provides a normative framework for representing and reasoning about complex preferences. Straightforward application of this theory to automate decision making is difficult due to high elicitation cost. In response…

We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…

We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…

Currently, there is a significant amount of research being conducted in the field of artificial intelligence to improve the explainability and interpretability of deep learning models. It is found that if end-users understand the reason for…

Scoring rules evaluate probabilistic forecasts of an unknown state against the realized state and are a fundamental building block in the incentivized elicitation of information. This paper develops mechanisms for scoring elicited text…

In argumentative discourse, persuasion is often achieved by refuting or attacking others arguments. Attacking is not always straightforward and often comprise complex rhetorical moves such that arguers might agree with a logic of an…

We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…