Related papers: Multiple-inheritance hazards in dependently-typed …

Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity…

In this paper, we present an alternative approach to multiple inheritance for typed feature structures. In our approach, a feature structure can be associated with several types coming from different hierarchies (dimensions). In case of…

Despite the wide variety of input types in machine learning, this diversity is often not fully reflected in their representations or model architectures, leading to inefficiencies throughout a model's lifecycle. This paper introduces an…

Sharing of notations and theories across an inheritance hierarchy of mathematical structures, e.g., groups and rings, is important for productivity when formalizing mathematics in proof assistants. The packed classes methodology is a…

In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that traditional homological algebra is…

Binary idempotent semirings govern classical path algebras. Their multiplicative structure is dyadic. We examine whether this restriction is structural or accidental. We define ternary idempotent $\Gamma$-semirings as higher-arity ordered…

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…

Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…

We investigate multi-label classification involving large sets of labels, where the output labels may be known to satisfy some logical constraints. We look at an architecture in which classifiers for individual labels are fed into an…

We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…

We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…

A new approach to the construction of general persistent polyhierarchical classifications is proposed. It is based on implicit description of category polyhierarchy by a generating polyhierarchy of classification criteria. Similarly to…

For a given hereditary abelian category satisfying some finiteness conditions, in certain twisted cases it is shown that the modified Ringel-Hall algebra is isomorphic to the naive lattice algebra and there exists an epimorphism from the…

In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…

This paper studies the form and complexity of inference in graphical models using the abstraction offered by algebraic structures. In particular, we broadly formalize inference problems in graphical models by viewing them as a sequence of…

Competitive methods for multi-label classification typically invest in learning labels together. To do so in a beneficial way, analysis of label dependence is often seen as a fundamental step, separate and prior to constructing a…

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…

The mind-brain problem is to bridge relations between in higher-level mental events and in lower-level neural events. To address this, some mathematical models have been proposed to explain how the brain can represent the discriminative…