Related papers: Leveraging the Information Contained in Theory Pre…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
We endow the category of bialgebras over a pair of operads in distribution with a cofibrantly generated model category structure. We work in the category of chain complexes over a field of characteristic zero. We split our construction in…
Although they exist since more than ten years already, have attracted diverse implementations, and have been used successfully in a significant number of applications, declarative mapping languages for constructing knowledge graphs from…
Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical…
We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the…
Algebraic effects are computational effects that can be represented by an equational theory whose operations produce the effects at hand. The free model of this theory induces the expected computational monad for the corresponding effect.…
We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to…
When using existing ACL2 datatype frameworks, many theorems require type hypotheses. These hypotheses slow down the theorem prover, are tedious to write, and are easy to forget. We describe a principled approach to types that provides…
We show that a class of algebras is closed under the taking of homomorphic images and direct products if and only if the class consists of all algebras that satisfy a set of (generally simultaneous) equations. For classes of regular…
We present the Theorem Prover Museum, and initiative to conserve -- and make publicly available -- the sources and source-related artefacts of automated reasoning systems. Theorem provers have been at the forefront of Artificial…
If $\A$ is an algebra over a field $\F$ and $\s$ is a generating set of $\A$, the length of $\s$ indicates the maximal length needed to express an arbitrary element of $\A$ as a linear combination of words in the elements of $\s$. The…
The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also…
We assume that every element of a matrix has a small, individual error, and model it by an external number, which is the sum of a nonstandard real number and a neutrix, the latter being a convex (external) set having the group property. The…
Nowadays, represented by Deep Learning techniques, the field of machine learning is experiencing unprecedented prosperity and its influence is demonstrated in academia, industry and civil society. "Intelligent" has become a label which…
Information algebra is algebraic structure for local computation and inference. Given an initial universe set and a parameter set, we show that a soft set system over them is an information algebra. Moreover, in a soft set system, the…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
Large language models (LLMs) can support scientific literature synthesis, but remain prone to hallucinated references, uneven coverage, and weakly grounded thematic organization. We evaluate whether bibliometric structure improves…
Programming languages tend to evolve over time to use more and more concepts from theoretical computer science. Still, there is a gap between programming and pure mathematics. Not all theoretical results have realized their promising…
In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…