Related papers: Euler diagrams as an introduction to set-theoretic…
Recent research increasingly brings to question the appropriateness of using predictive tools in complex, real-world tasks. While a growing body of work has explored ways to improve value alignment in these tools, comparatively less work…
Metric graphs are often introduced based on combinatorics, upon "associating" each edge of a graph with an interval; or else, casually "gluing" a collection of intervals at their endpoints in a network-like fashion. Here we propose an…
Modern communication networks are inherently complex in nature. First of all, they have a large number of heterogeneous components. Secondly, their connectivity is extremely dynamic. Nodes can come and go, links can be removed and added…
The Euler calculus -- an integral calculus based on Euler characteristic as a valuation on constructible functions -- is shown to be an incisive tool for answering questions about injectivity and invertibility of recent transforms based on…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
We develop a graphical notation to introduce classical Lie algebras. Although this paper deals with well-known results, our pictorial point of view is slightly different to the traditional one. Our graphical notation is fairly elementary…
Euler's elastica is a classical model of flexible slender structures, relevant in many industrial applications. Static equilibrium equations can be derived via a variational principle. The accurate approximation of solutions of this problem…
Rule sets are often used in Machine Learning (ML) as a way to communicate the model logic in settings where transparency and intelligibility are necessary. Rule sets are typically presented as a text-based list of logical statements…
Defeasible reasoning is the mode of reasoning where conclusions can be overturned by taking into account new evidence. A commonly used method in cognitive science and logic literature is to handcraft argumentation supporting inference…
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
In problems such as variable selection and graph estimation, models are characterized by Boolean logical structure such as presence or absence of a variable or an edge. Consequently, false positive error or false negative error can be…
Autoformalization involves automatically translating informal math into formal theorems and proofs that are machine-verifiable. Euclidean geometry provides an interesting and controllable domain for studying autoformalization. In this…
Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…
Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…
We compute the number of equivalence classes of nonperiodic covering cycles of given length in a non oriented connected graph. A covering cycle is a closed path that traverses each edge of the graph at least once. A special case is the…
Soft set theory and rough set theory are mathematical tools to deal with uncertainties. In [3], authors combined these concepts and introduced soft rough sets. In this paper, we introduce the concepts of soft rough graphs, vertex and edge…
Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of…
After a brief presentation of Feynman diagrams, we criticizise the idea that Feynman diagrams can be considered to be pictures or depictions of actual physical processes. We then show that the best interpretation of the role they play in…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…