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### Reasoning with Graphs

Renata P. de Freitas, Paulo A.S. Veloso, Sheila R.M. Veloso, Petrucio Viana
2006 Electronical Notes in Theoretical Computer Science
The graph calculus, however, has a playful aspect, with rules easier to grasp and use.  ...  Here, we give a formal presentation of the system, with precise formulation of syntax, semantics, and derivation rules.  ...  Introduction In this paper we study +RG, the (positive) relational calculus with graphs. The basis for the graph relational calculus was introduced by S. Curtis and G. Lowe [5] .  ...

### Reasoning with !-Graphs [article]

Alexander Merry
2014 arXiv   pre-print
This notation greatly eases reasoning with CFAs, but string graphs are inadequate to properly encode this reasoning.  ...  It then demonstrates how we can reason directly about !-graphs, viewed as (typically infinite) families of string graphs.  ...  -graphs and !-graph equations can be used in conjunction with double-pushout graph rewriting to do equational reasoning both with and on infinite families of morphisms in these categories.  ...

### Reasoning with graph constraints

Fernando Orejas, Hartmut Ehrig, Ulrike Prange
2009 Formal Aspects of Computing
The work that we present is not the first logic to reason about graphs.  ...  With respect to the second issue, we think that there are two main reasons that justify our work in this direction.  ...  This means that, implicitly, in this case subsumption coincides with equality. There are two reasons for this.  ...

### REASONING WITH GRAPH OPERATIONS [chapter]

Roger T. Hartley, Michael J. Coombs
1991 Principles of Semantic Networks
Model Generative Reasoning implements this cycle through a family of operations on representations based on conceptual graphs.  ...  Fragment removes potential incoherences from hypotheses, while preserving coherence with the observations.  ...  The reason why we can work with the simplified graph is that specialize and its dual, fragment only work on the concept nodes of the conceptual graph, through the operation join.  ...

### Reasoning with contextual graphs

Patrick Brézillon, Laurent Pasquier, Jean-Charles Pomerol
2002 European Journal of Operational Research
We introduce the notion of contextual graph to take into account temporal and context-based reasoning.  ...  Decision trees allow the modeling of event-dependent reasoning, but do not consider the dynamics of contextual changes in reasoning.  ...  This is the reason why we introduced the notion of contextual graph.  ...

### Knowledge Graph Reasoning with Relational Directed Graph [article]

Yongqi Zhang, Quanming Yao
2021 arXiv   pre-print
Reasoning on the knowledge graph (KG) aims to infer new facts from existing ones.  ...  Here, we propose a variant of graph neural network, i.e., RED-GNN, to address the above challenges by learning the RElational Digraph with a variant of GNN.  ...  Definition 2 (Layered st-graph [2] ). The layered st-graph is a directed graph with exactly one source node (s) and one sink node (t).  ...

### Concurrent Reasoning with Inference Graphs [chapter]

Daniel R. Schlegel, Stuart C. Shapiro
2014 Lecture Notes in Computer Science
The use of scheduling heuristics within a prioritized message passing architecture allows inference graphs to perform very well in forward, backward, bi-directional, and focused reasoning.  ...  propositional graph representation.  ...  Inference Graphs Inference graphs are an extension of propositional graphs to allow deductive reasoning to be performed in a concurrent processing system.  ...

### Reasoning with discrete factor graph

Indar Sugiarto, Paul Maier, Jorg Conradt
2013 2013 International Conference on Robotics, Biomimetics, Intelligent Computational Systems
This paper describes conceptual methods in working with factor graph especially with discrete random variables, how to learn its parameter and how to perform inference for making a reasoning task with  ...  We provide several illustrative examples to highlight important aspects when developing a model for factor graphs.  ...  Factor graph for kinematics control in robotics One final example of reasoning with factor graph is for computing kinematics control of a robot.  ...

### Variational Reasoning for Question Answering with Knowledge Graph [article]

Yuyu Zhang, Hanjun Dai, Zornitsa Kozareva, Alexander J. Smola, Le Song
2017 arXiv   pre-print
Second, many questions require multi-hop logic reasoning over the knowledge graph to retrieve the answers.  ...  However, it is challenging to build QA systems which can learn to reason over knowledge graphs based on question-answer pairs alone.  ...  E.2 Visualization of the learned reasoning rule To check what the reasoning graph have learned, we visualize the inference path with highest score in the reasoning-graph.  ...

### Knowledge Aware Conversation Generation with Explainable Reasoning over Augmented Graphs [article]

Zhibin Liu, Zheng-Yu Niu, Hua Wu, Haifeng Wang
2019 arXiv   pre-print
For knowledge selection on the graph, we formulate it as a problem of multi-hop graph reasoning to effectively capture conversation flow, which is more explainable and flexible in comparison with previous  ...  To fully leverage long text information that differentiates our graph from others, we improve a state of the art reasoning algorithm with machine reading comprehension technology.  ...  Conclusion In this paper, we propose to augment a knowledge graph with texts and integrate it into an opendomain chatting machine with both graph reasoning based knowledge selector and knowledge aware  ...

### Question Answering by Reasoning Across Documents with Graph Convolutional Networks [article]

Nicola De Cao, Wilker Aziz, Ivan Titov
2019 arXiv   pre-print
Graph convolutional networks (GCNs) are applied to these graphs and trained to perform multi-step reasoning.  ...  We introduce a neural model which integrates and reasons relying on information spread within documents and across multiple documents. We frame it as an inference problem on a graph.  ...  Reasoning on an entity graph Entity graph In an offline step, we organize the content of each training instance in a graph connecting mentions of candidate answers within and across supporting documents  ...

### Multi-Hop Knowledge Graph Reasoning with Reward Shaping [article]

Xi Victoria Lin and Richard Socher and Caiming Xiong
2018 arXiv   pre-print
Multi-hop reasoning is an effective approach for query answering (QA) over incomplete knowledge graphs (KGs).  ...  KG Setup Following previous work, we treat every KG link as bidirectional and augment the graph with the reversed (e o , r −1 , e s ) links.  ...  A possible reason for this is that embedding based methods map every link in the KG into the same embedding space, which implicitly encodes the connectivity of the whole graph.  ...

### Learning and Reasoning with the Graph Structure Representation in Robotic Surgery [article]

Mobarakol Islam, Lalithkumar Seenivasan, Lim Chwee Ming, Hongliang Ren
2020 arXiv   pre-print
Learning to infer graph representations and performing spatial reasoning in a complex surgical environment can play a vital role in surgical scene understanding in robotic surgery.  ...  We design an attention link function and integrate with a graph parsing network to recognize the surgical interactions.  ...  Utilizing these features, an enhanced graph-based deep reasoning model then infers a parse graph, g * = argmax g p(Y g |V g , E g , F) p(V g , E g |F, G) [15] to deduce interactions between the defective  ...

### Combinatorial optimization and reasoning with graph neural networks [article]

Quentin Cappart, Didier Chételat, Elias Khalil, Andrea Lodi, Christopher Morris, Petar Veličković
2021 arXiv   pre-print
However, recent years have seen a surge of interest in using machine learning, especially graph neural networks (GNNs), as a key building block for combinatorial tasks, either directly as solvers or by  ...  Figure 6 : The utility of dynamically choosing the graph to reason over for incremental connectivity.  ...  Powered by the rapid development of GNNs, algorithmic reasoning experienced a strong resurgence, tackling combinatorial algorithms of superlinear complexity with graph-structured processing at the core  ...

### Cross Chest Graph for Disease Diagnosis with Structural Relational Reasoning [article]

Gangming Zhao, Baolian Qi, Jinpeng Li
2021 arXiv   pre-print
Meanwhile, the relationship between any pair of images is modeled by a knowledge-reasoning module to simulate the doctor's habit of comparing multiple images.  ...  We therefore propose the Cross-chest Graph (CCG), which improves the performance of automatic lesion detection by imitating doctor's training and decision-making process.  ...  relation module (IR), the model with the knowledge reasoning (KR), the model combining Table 4 .  ...
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