Related papers: Scroll nets
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…
Besides the better-known Nelson's Logic and Paraconsistent Nelson's Logic, in "Negation and separation of concepts in constructive systems" (1959), David Nelson introduced a logic called S with the aim of analyzing the constructive content…
Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…
We introduce the graphlet decomposition of a weighted network, which encodes a notion of social information based on social structure. We develop a scalable inference algorithm, which combines EM with Bron-Kerbosch in a novel fashion, for…
In many complex networks the vertices are ordered in time, and edges represent causal connections. We propose methods of analysing such directed acyclic graphs taking into account the constraints of causality and highlighting the causal…
We introduce an architecture based on deep hierarchical decompositions to learn effective representations of large graphs. Our framework extends classic R-decompositions used in kernel methods, enabling nested part-of-part relations. Unlike…
Whilst mathematicians assume classical reasoning principles by default they often context switch when working, restricting themselves to various forms of subclassical reasoning. This pattern is especially common amongst logicians and set…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
The proof theory and semantics of intuitionistic modal logics have been studied by Simpson in terms of Prawitz-style labelled natural deduction systems and Kripke models. An alternative to model-theoretic semantics is provided by…
Parsing Expression Grammars (PEGs) are a recognition-based formalism which allows to describe the syntactical and the lexical elements of a language. The main difference between Context-Free Grammars (CFGs) and PEGs relies on the…
Petri nets are a well-known model of concurrency and provide an ideal setting for the study of fundamental aspects in concurrent systems. Despite their simplicity, they still lack a satisfactory causally reversible semantics. We develop…
Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…
Graph aggregation is the process of computing a single output graph that constitutes a good compromise between several input graphs, each provided by a different source. One needs to perform graph aggregation in a wide variety of…
We continue work of our earlier paper (Lewitzka and Brunner: Minimally generated abstract logics, Logica Universalis 3(2), 2009), where abstract logics and particularly intuitionistic abstract logics are studied. Abstract logics can be…
Graph learning is crucial in the fields of bioinformatics, social networks, and chemicals. Although high-order graphlets, such as cycles, are critical to achieving an informative graph representation for node classification, edge…
In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent…
Referring to a conception put forward by Stuart Kauffman in his "Investigations", it is shown how the onset of classicity can be visualized in terms of an emergent process originating in entangled ensemble states of knotted spin networks.…
We consider congruences of straight lines in a plane with the combinatorics of the square grid, with all elementary quadrilaterals possessing an incircle. It is shown that all the vertices of such nets (we call them incircular or IC-nets)…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…