Related papers: Impossibility Theorems and the Universal Algebraic…
This is the first draft of a set of lecture notes developed for one-half of a seminar on two approaches to the notion of "Abelian", namely those of universal algebra, and of category theory. The half pertaining to the universal-algebraic…
Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q=1, the algebra reduces to the one proposed by Uglov-Ivanov. In the general case and $q\neq 1$, an explicit algebra homomorphism…
Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy…
We provide a foundation for working with homological and homotopical methods in categorical algebra. This involves two mutually complementary components, namely (a) the strategic selection of suitable axiomatic frameworks, some well known…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
We develop some basic results about full amalgamation classes with intrinsic trascendentals. These classes have generics whose models may have finite subsets whose intrinsic closure is not contained in its algebraic closure. We will show…
Learning algorithms that aggregate predictions from an ensemble of diverse base classifiers consistently outperform individual methods. Many of these strategies have been developed in a supervised setting, where the accuracy of each base…
Metabelian algebras are introduced and it is shown that an algebra $A$ is metabelian if and only if $A$ is a nilpotent algebra having the index of nilpotency at most $3$, i.e. $x y z t = 0$, for all $x$, $y$, $z$, $t \in A$. We prove that…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical,…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Most classical results in circuit complexity theory concern circuits over the Boolean domain. Besides their simplicity and the ease of comparing different languages, the actual architecture of computers is also an important motivating…
With the aim of studying social properties of belief merging and having a better understanding of impossibility, we extend in three ways the framework of logic-based merging introduced by Konieczny and Pino P\'erez. First, at the level of…
Mittag-Leffler modules occur naturally in algebra, algebraic geometry, and model theory, [18], [12], [17]. If $R$ is a non-right perfect ring, then it is known that in contrast with the classes of all projective and flat modules, the class…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
In this paper, we first present a classification theorem of infinite-dimensional simple Novikov algebras over an algebraically closed field with characteristic 0. Then we classify all the irreducible modules of a certain…
A recent paper (van Rooij et al. 2024) claims to have proved that achieving human-like intelligence using learning from data is intractable in a complexity-theoretic sense. We point out that the proof relies on an unjustified assumption…
These lecture notes survey the emerging area of Universal Proof Theory, which investigates general questions about the existence, equivalence, and characterization of good proof systems for broad classes of logics. In particular, the notes…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…