Related papers: Self-referential theories
We study automorphism groups of formal matrix algebras. We also consider automorphisms of ordinary matrix algebras (in particular, triangular matrix algebras).
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
It is a mystery which input features contribute to a neural network's output. Various explanation (feature attribution) methods are proposed in the literature to shed light on the problem. One peculiar observation is that these explanations…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…
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…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
We present a general framework for evaluating image counterfactuals. The power and flexibility of deep generative models make them valuable tools for learning mechanisms in structural causal models. However, their flexibility makes…
We study automorphic Lie algebras using a family of evaluation maps parametrised by the representations of the associative algebra of functions. This provides a descending chain of ideals for the automorphic Lie algebra which is used to…
A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such.…
Cluster-tilted algebras are trivial extensions of tilted algebras. This correspondence induces a surjective map from tilted algebras to cluster-tilted algebras. If B is a cluster-tilted algebra, we use the fibre of B under this map to study…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
A family of naturally reductive pseudo-Riemannian spaces is constructed out of the representations of Lie algebras with ad-invariant metrics. We exhibit peculiar examples, study their geometry and characterize the corresponding naturally…
We introduce a class of algebras that can be used as recognisers for regular tree languages. We show that it is the only such class that forms a pseudo-variety and we prove the existence of syntactic algebras. Finally, we give a more…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
A theory graph is a network of axiomatic theories connected with meaning-preserving mappings called theory morphisms. Theory graphs are well suited for organizing large bodies of mathematical knowledge. Traditional and formal proofs do not…
In the theory of programming languages, type inference is the process of inferring the type of an expression automatically, often making use of information from the context in which the expression appears. Such mechanisms turn out to be…
Pattern avoidance classes of permutations that cannot be expressed as unions of proper subclasses can be described as the set of subpermutations of a single bijection. In the case that this bijection is a permutation of the natural numbers…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…
We start with definitions of the general notions of the theory of $\Bbb Z_{2}$-graded algebras. Then we consider theory of inductive families of $\Bbb Z_{2}$-graded semisimple finite-dimensional algebras and its representations in the…
A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…