Related papers: Shallow Embedding of Type Theory is Morally Correc…
We investigate the extent to which the weak equivalences in a model category can be equipped with algebraic structure. We prove, for instance, that there exists a monad T such that a morphism of topological spaces admits T-algebra structure…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
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…
Word embeddings represent a transformative technology for analyzing text data in social work research, offering sophisticated tools for understanding case notes, policy documents, research literature, and other text-based materials. This…
We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or…
Liquid Haskell is an extension to the Haskell programming language that adds support for refinement types: data types augmented with SMT-decidable logical predicates that refine the set of values that can inhabit a type. Furthermore, Liquid…
We study methods for learning sentence embeddings with syntactic structure. We focus on methods of learning syntactic sentence-embeddings by using a multilingual parallel-corpus augmented by Universal Parts-of-Speech tags. We evaluate the…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
Recent work has shown that a model's input word embeddings can serve as effective control variables for steering its behavior toward outputs that satisfy desired properties. However, this has only been demonstrated for pretrained…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
This study provides some results about two-level type-theoretic notions in a way that the proofs are fully formalizable in a proof assistant implementing two-level type theory such as Agda. The difference from prior works is that these…
Ontologies are widely used for representing domain knowledge and meta data, playing an increasingly important role in Information Systems, the Semantic Web, Bioinformatics and many other domains. However, logical reasoning that ontologies…
Besides the text content, documents and their associated words usually come with rich sets of meta informa- tion, such as categories of documents and semantic/syntactic features of words, like those encoded in word embeddings. Incorporating…
Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
We present techniques for reasoning about constructor classes that (like the monad class) fix polymorphic operations and assert polymorphic axioms. We do not require a logic with first-class type constructors, first-class polymorphism, or…
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the…
Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of $\alpha$-equivalence, capture-avoiding substitution, typing contexts, runtime environments,…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
Higher inductive types are inductive types that include nontrivial higher-dimensional structure, represented as identifications that are not reflexivity. While work proceeds on type theories with a computational interpretation of univalence…