Related papers: Stratified Type Theory
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
Sequential decision making significantly speeds up research and is more cost-effective compared to fixed-n methods. We present a method for sequential decision making for stratified count data that retains Type-I error guarantee or false…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
Hierarchical classification aims to sort the object into a hierarchical structure of categories. For example, a bird can be categorized according to a three-level hierarchy of order, family, and species. Existing methods commonly address…
Scala's type system unifies ML modules, object-oriented, and functional programming. The Dependent Object Types (DOT) family of calculi has been proposed as a new foundation for Scala and similar languages. Unfortunately, it is not clear…
We introduce stratified labelings as a novel semantical approach to abstract argumentation frameworks. Compared to standard labelings, stratified labelings provide a more fine-grained assessment of the controversiality of arguments using…
Many object-oriented dynamic languages allow programmers to _extract methods_ from objects and treat them as functions. This allows for flexible programming patterns, but presents challenges for type systems. In particular, a simple…
One important assumption underlying common classification models is the stationarity of the data. However, in real-world streaming applications, the data concept indicated by the joint distribution of feature and label is not stationary but…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of…
This paper concerns the construction of tests for universal hypothesis testing problems, in which the alternate hypothesis is poorly modeled and the observation space is large. The mismatched universal test is a feature-based technique for…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
Riehl and Shulman introduced simplicial type theory (STT), a variant of homotopy type theory which aimed to study not just homotopy theory, but its fusion with category theory: $(\infty,1)$-category theory. While notoriously technical,…
Large teams of heterogeneous agents have the potential to solve complex multi-task problems that are intractable for a single agent working independently. However, solving complex multi-task problems requires leveraging the relative…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
We argue that locally Cartesian closed categories form a suitable doctrine for defining dependent type theories, including non-extensional ones. Using the theory of sketches, one may define syntactic categories for type theories in a style…
Subtyping, also known as subtype polymorphism, is a concept extensively studied in programming language theory, delineating the substitutability relation among datatypes. This property ensures that programs designed for supertype objects…
We introduce the Generalized Turing Test (GTT), a formal framework for comparing the capabilities of arbitrary agents via indistinguishability. For agents A and B, we define the Turing comparator A $\geq$ B to hold if B, acting as a…