Related papers: Scroll nets
In this paper, we utilize Isabelle/HOL to develop a formal framework for the basic theory of double-pushout graph transformation. Our work includes defining essential concepts like graphs, morphisms, pushouts, and pullbacks, and…
The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on frameworks for reasoning about path expressions…
The biologically inspired framework of port-graphs has been successfully used to specify complex systems. It is the basis of the PORGY modelling tool. To facilitate the specification of proof normalisation procedures via graph rewriting, in…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…
In this work we present a computation paradigm based on a concurrent and incremental construction of proof nets (de-sequentialized or graphical proofs) of the pure multiplicative and additive fragment of Linear Logic, a resources conscious…
Plural (or multiple-conclusion) cuts are inferences made by applying a structural rule introduced by Gentzen for his sequent formulation of classical logic. As singular (single-conclusion) cuts yield trees, which underlie ordinary natural…
In the first part of this paper we present a theory of proof nets for full multiplicative linear logic, including the two units. It naturally extends the well-known theory of unit-free multiplicative proof nets. A linking is no longer a set…
Isomorphism between formulae is defined with respect to categories formalizing equality of deductions in classical propositional logic and in the multiplicative fragment of classical linear propositional logic caught by proof nets. This…
Document-level relation extraction (DocRE) models generally use graph networks to implicitly model the reasoning skill (i.e., pattern recognition, logical reasoning, coreference reasoning, etc.) related to the relation between one entity…
We present a new Convolutional Neural Network (CNN) model for text classification that jointly exploits labels on documents and their component sentences. Specifically, we consider scenarios in which annotators explicitly mark sentences (or…
This paper explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
Reconstructing the topology of complex networks from observational data remains a central challenge in network science. Here we propose a framework that is based on the Dempster-Shafer evidence theory to infer network structures directly…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Belief systems are rarely globally consistent, yet effective reasoning often persists locally. We propose a novel graph-theoretic framework that cleanly separates credibility--external, a priori trust in sources--from confidence--an…
We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as…
Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…
Humans excel at solving novel reasoning problems from minimal exposure, guided by inductive biases, assumptions about which entities and relationships matter. Yet the computational form of these biases and their neural implementation remain…