Symbolic Graph Research Articles

Conjunctive block coding for hyperdimensional graph representation

Knowledge Graphs (KGs) have become a pivotal knowledge representation tool in machine learning, not only providing access to existing knowledge but also enabling the discovery of new knowledge through advanced applications. Among the scalable reasoning methods used for such applications, distributed graph embedding approaches, particularly GNNs, have become popular for large-scale graph-related tasks. However, many of these methods have limitations in their interpretability and fail to take into account structural similarity in their representation. Hyperdimensional Computing (HDC), also known as Vector Symbolic Architecture (VSA), addresses this issue by using well-defined cognitive operations on distributed representations of symbolic concepts. This work proposes and evaluates a new vector symbolic graph representation, CLOG, that preserves approximate structural similarity beyond edge correspondence and fundamentally differs from previous methods. The model's effectiveness in graph representation is evaluated through theoretical analysis, graph reconstruction experiments, and link prediction task, highlighting its efficiency and accuracy. This approach significantly advances the field by enhancing the capabilities of HDC in graph representation, representing a notable improvement over existing methods.

Toward Semantic Communication Protocols: A Probabilistic Logic Perspective

Classical medium access control (MAC) protocols are interpretable, yet their task-agnostic control signaling messages (CMs) are ill-suited for emerging mission-critical applications. By contrast, neural network (NN) based protocol models (NPMs) learn to generate task-specific CMs, but their rationale and impact lack interpretability. To fill this void, in this article we propose, for the first time, a semantic protocol model (SPM) constructed by transforming an NPM into an interpretable symbolic graph written in the probabilistic logic programming language (ProbLog). This transformation is viable by extracting and merging common CMs and their connections, while treating the NPM as a CM generator. By extensive simulations, we corroborate that the SPM tightly approximates its original NPM while occupying only 0.02% memory. By leveraging its interpretability and memory-efficiency, we demonstrate several SPM-enabled applications such as SPM reconfiguration for collision-avoidance, as well as comparing different SPMs via semantic entropy calculation and storing multiple SPMs to cope with non-stationary environments.

Neuro-Symbolic Word Embedding Using Textual and Knowledge Graph Information

The construction of high-quality word embeddings is essential in natural language processing. In existing approaches using a large text corpus, the word embeddings learn only sequential patterns in the context; thus, accurate learning of the syntax and semantic relationships between words is limited. Several methods have been proposed for constructing word embeddings using syntactic information. However, these methods are not trained for the semantic relationships between words in sentences or external knowledge. In this paper, we present a method for improved word embeddings using symbolic graphs for external knowledge and the relationships of the syntax and semantic role between words in sentences. The proposed model sequentially learns two symbolic graphs with different properties through a graph convolutional network (GCN) model. A new symbolic graph representation is generated to understand sentences grammatically and semantically. This graph representation includes comprehensive information that combines dependency parsing and semantic role labeling. Subsequently, word embeddings are constructed through the GCN model. The same GCN model initializes the word representations that are created in the first step and trains the relationships of ConceptNet using the relationships between words. The proposed word embeddings outperform the baselines in benchmarks and extrinsic tasks.

Exploring attractor bifurcations in Boolean networks

BackgroundBoolean networks (BNs) provide an effective modelling formalism for various complex biochemical phenomena. Their long term behaviour is represented by attractors–subsets of the state space towards which the BN eventually converges. These are then typically linked to different biological phenotypes. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a methodology for analysing bifurcations in asynchronous parametrised Boolean networks.ResultsIn this paper, we propose a computational framework employing advanced symbolic graph algorithms that enable the analysis of large networks with hundreds of Boolean variables. To visualise the results of this analysis, we developed a novel interactive presentation technique based on decision trees, allowing us to quickly uncover parameters crucial to the changes in the attractor landscape. As a whole, the methodology is implemented in our tool AEON. We evaluate the method’s applicability on a complex human cell signalling network describing the activity of type-1 interferons and related molecules interacting with SARS-COV-2 virion. In particular, the analysis focuses on explaining the potential suppressive role of the recently proposed drug molecule GRL0617 on replication of the virus.ConclusionsThe proposed method creates a working analogy to the concept of bifurcation analysis widely used in kinetic modelling to reveal the impact of parameters on the system’s stability. The important feature of our tool is its unique capability to work fast with large-scale networks with a relatively large extent of unknown information. The results obtained in the case study are in agreement with the recent biological findings.

Formal testing of timed graph transformation systems using metric temporal graph logic

Embedded real-time systems generate state sequences where time elapses between state changes. Ensuring that such systems adhere to a provided specification of admissible or desired behavior is essential. Formal model-based testing is often a suitable cost-effective approach. We introduce an extended version of the formalism of symbolic graphs, which encompasses types as well as attributes, for representing states of dynamic systems. Relying on this extension of symbolic graphs, we present a novel formalism of timed graph transformation systems (TGTSs) that supports the model-based development of dynamic real-time systems at an abstract level where possible state changes and delays are specified by graph transformation rules. We then introduce an extended form of the metric temporal graph logic (MTGL) with increased expressiveness to improve the applicability of MTGL for the specification of timed graph sequences generated by a TGTS. Based on the metric temporal operators of MTGL and its built-in graph binding mechanics, we express properties on the structure and attributes of graphs as well as on the occurrence of graphs over time that are related by their inner structure. We provide formal support for checking whether a single generated timed graph sequence adheres to a provided MTGL specification. Relying on this logical foundation, we develop a testing framework for TGTSs that are specified using MTGL. Lastly, we apply this testing framework to a running example by using our prototypical implementation in the tool AutoGraph.

Graph-Convolved Factorization Machines for Personalized Recommendation

Factorization machines (FMs) and their neural network variants (neural FMs) for modeling second-order feature interactions are effective in building modern recommendation systems. However, feature interactions are based upon pairs of features, whereas multi-features correlations commonly arise in real-world financial product recommendation scenarios. We propose an effective neural recommender system, graph-convolved factorization machine (GCFM), with the spirit of the symbolic graph reasoning principle that provides lightweight and interpretable recommendation suggestions. Given a sample for the recommendation, GCFM constructs the corresponding dense feature embeddings and computes the sample-specific feature relationship graph. Then, a multi-filter graph-convolved feature crossing (GCFC) layer for feature embeddings establishes cross features with their neighboring embeddings. GCFM thus extends the feature interactions from pairs to neighbors to capture more comprehensive and explainable information while simultaneously reaping the advantages of representation learning. To exploit these capabilities, we apply a Graph Bayesian Optimization (GBO). During training, our GBO automatically optimizes our GCFM, including training hyperparameters and architecture hyperparameters. Besides, we conduct extensive experiments on two public financial applications benchmarks, USCFC and OTC, and two real-world datasets that we collect offline. Our GCFM significantly outperforms state-of-the-art algorithms and shows its interpretability in recommendation tasks.

Predicate Extension of Symbolic Memory Graphs for the Analysis of Memory Safety Correctness

Predicate Extension of Symbolic Memory Graphs for the Analysis of Memory Safety Correctness

Unifying neural learning and symbolic reasoning for spinal medical report generation.

Automated medical report generation in spine radiology, i.e., given spinal medical images and directly create radiologist-level diagnosis reports to support clinical decision making, is a novel yet fundamental study in the domain of artificial intelligence in healthcare. However, it is incredibly challenging because it is an extremely complicated task that involves visual perception and high-level reasoning processes. In this paper, we propose the neural-symbolic learning (NSL) framework that performs human-like learning by unifying deep neural learning and symbolic logical reasoning for the spinal medical report generation. Generally speaking, the NSL framework firstly employs deep neural learning to imitate human visual perception for detecting abnormalities of target spinal structures. Concretely, we design an adversarial graph network that interpolates a symbolic graph reasoning module into a generative adversarial network through embedding prior domain knowledge, achieving semantic segmentation of spinal structures with high complexity and variability. NSL secondly conducts human-like symbolic logical reasoning that realizes unsupervised causal effect analysis of detected entities of abnormalities through meta-interpretive learning. NSL finally fills these discoveries of target diseases into a unified template, successfully achieving a comprehensive medical report generation. When employed in a real-world clinical dataset, a series of empirical studies demonstrate its capacity on spinal medical report generation and show that our algorithm remarkably exceeds existing methods in the detection of spinal structures. These indicate its potential as a clinical tool that contributes to computer-aided diagnosis.

Using the scenario approach in anti-corruption management processes (on the example of the construction industry)

This study discusses the methodological and applied problems of increasing the effectiveness of the anti-corruption management process. An analysis of the essence and forms of corruption, as well as their negative impacts on the socioeconomic development of the society is offered.
 To increase the effectiveness of anti-corruption problem-solving and assess the decision-making process pertaining to management, a scenario analysis is proposed.
 The analysis of basic multigraph models of anti-corruption management focuses on the construction industry, using functional symbolic graphs.
 According to the results, it is more effective to look more broadly at the criminological problem of combating corruption by linking its solution to developments in the fields of economics, sociology, and psychology.
 The current publication is considered a new approach to the development of specific measures to counter this type of crime.

On the essence and initiality of conflicts in [formula omitted]-adhesive transformation systems

Understanding conflicts between transformation steps and rules is an important topic in algebraic graph transformation. A conflict occurs when two transformation steps are not parallel independent, that is, when after applying one of them the other can no longer occur. A static analysis technique called Critical Pair Analysis allows the detection of all potential conflicts between pairs of rules, by enumerating Critical Pairs. Since these are often too numerous for even simple rules, finding appropriate subsets of critical pairs is the topic of ongoing research. We contribute to this thread by proposing a new characterization for root causes of conflicts, called “conflict essences”, exploiting a recently proposed characterization of parallel independence. Furthermore we show that conflict essences are at least as precise as the “conflict reasons” previously proposed, and uniquely determine the so-called “initial conflicts”, an appropriate subset of critical pairs, under relatively mild assumptions on the underlying category. Finally, we show that several M-adhesive categories of interest have the necessary properties for our results to hold, including typed, attributed and symbolic graphs. While our results are formulated for conflicts, they are directly applicable to dependencies in M-adhesive transformation systems.

Speculative Symbolic Graph Execution of Imperative Deep Learning Programs

The rapid evolution of deep neural networks is demanding deep learning (DL) frameworks not only to satisfy the requirement of quickly executing large computations, but also to support straightforward programming models for quickly implementing and experimenting with complex network structures. However, existing frameworks fail to excel in both departments simultaneously, leading to diverged efforts for optimizing performance and improving usability. This paper presents JANUS, a system that combines the advantages from both sides by transparently converting an imperative DL program written in Python, a de-facto scripting language for DL, into an efficiently executable symbolic dataflow graph. JANUS can convert various dynamic features of Python, including dynamic control flow, dynamic types, and impure functions, into elements of a symbolic dataflow graph. Our experiments show that JANUS can achieve fast DL training by exploiting the techniques imposed by symbolic graph-based DL frameworks, while maintaining the simple and flexible programmability of imperative DL frameworks at the same time.

Fault Diagnosis of Discrete-Event systems Based on the Symbolic Observation Graph

Fault diagnosis of discrete-event systems (DESs) has received a lot of attention in industry and academia during the last two decades. In DES based diagnosis, the two main discussed topics are offline diagnosability analysis and online diagnosis. A pioneering approach that led to the development of various techniques is based on the so-called diagnose. However, this approach suffers from the combinatorial explosion problem due to the exponential complexity of construction. To partially overcome this problem, an efficient approach to construct a symbolic diagnoser is proposed in this paper. The proposed approach consists in constructing a diagnoser based on the symbolic observation graph (SOG), which combines symbolic and enumarative representations. The construction of the diagnoser as well as the verification of diagnosability are performed simultaneously on the fly, which can considerably reduce the state space of the diagnoser and thus the overall running time. To evaluate the efficiency and the scalability of the approach, some experimental results are presented and discussed based on a DES benchmark.

An application of comparison criteria to fractional spectral problem having Coloumb potential

In this study, the zeros of eigen functions of spectral theory are considered in fractional Sturm-Liouville problem. The 1st and 2nd comparison theorems for fractional Sturm-Liouville equation with boundary condition and their proofs are given. In this way, our new approximation will contribute to construct fractional Sturm-Liouville theory. Also, its an application is given in case of Coulomb potential and the results are presented by a symbolic graph.

Conflict Detection for Edits on Extended Feature Models using Symbolic Graph Transformation

Feature models are used to specify variability of user-configurable systems as appearing, e.g., in software product lines. Software product lines are supposed to be long-living and, therefore, have to continuously evolve over time to meet ever-changing requirements. Evolution imposes changes to feature models in terms of edit operations. Ensuring consistency of concurrent edits requires appropriate conflict detection techniques. However, recent approaches fail to handle crucial subtleties of extended feature models, namely constraints mixing feature-tree patterns with first-order logic formulas over non-Boolean feature attributes with potentially infinite value domains. In this paper, we propose a novel conflict detection approach based on symbolic graph transformation to facilitate concurrent edits on extended feature models. We describe extended feature models formally with symbolic graphs and edit operations with symbolic graph transformation rules combining graph patterns with first-order logic formulas. The approach is implemented by combining eMoflon with an SMT solver, and evaluated with respect to applicability.

Improved Conflict Detection for Graph Transformation with Attributes

In graph transformation, a conflict describes a situation where two alternative transformations cannot be arbitrarily serialized. When enriching graphs with attributes, existing conflict detection techniques typically report a conflict whenever at least one of two transformations manipulates a shared attribute. In this paper, we propose an improved, less conservative condition for static conflict detection of graph transformation with attributes by explicitly taking the semantics of the attribute operations into account. The proposed technique is based on symbolic graphs, which extend the traditional notion of graphs by logic formulas used for attribute handling. The approach is proven complete, i.e., any potential conflict is guaranteed to be detected.

A Calculus for Concurrent Processes with Cryptographic Primitives

We introduce cryptographic primitives to the symbolic transition graph with the binary equivalence relation based on the CCS language with value-passing processes, which is designed for the description and analysis of security protocols. The STGR with cryptographic primitives, which is an extension of the STG, is applied to partition domains of conversations of security protocols that run in an infinite concurrent way, where principals possessing their relevant keys have received and transformed the message. The cryptographic primitives enable us to consider cryptographic issues on the principal conversations of security protocols in more detail. Our work results in a highly efficient solution to reduce computational complexities to prove safety properties of security protocols.

Implementing a Matrix Vector Transition Net

Aims: Classic Petri nets also known as place transition nets provide many interesting and useful features for system modeling. However they are limited by the place types that are used. An approach is presented where a matrix vector transition net is used for modeling complex system behavior. This is more expressive than a Petri net. Proposed Solution: A modified form of a traditional place transition net is used. The idea is to combine the ideas from Petri net behavior with the matrix vector approach. Implementing the Matrix Vector Transition Net: Ordinary Petri net places are replaced with matrices or vectors. The input and output arcs have a specific function matrix that determines firing. Firing and behavior remains conceptually similar to that of a petri net. Row and column vectors can also be used interchangeably. The behavior of matrix transition nets is similar to that of a place transition net. Instead of tokens, matrix elements are used. This type of structure increases the modeling power, abstraction capacity and the complexity of the net. Case Study: A toy case of an abstract network structure containing processing elements is used to illustrate the use of the matrix vector transition net structure. Results and Findings: The behavior of matrix transition nets is shown to be similar to that of a place transition net. Instead of tokens, matrix elements are used. It is possible to construct a symbolic marking graph or reachability graph for the system This type of structure definitely increases the modeling power, abstraction capacity and the complexity of the net. The matrix transition net could be useful for certain types of communication system problems and complex system interfacing.

Lazy Graph Transformation

Applying an attributed graph transformation rule to a given object graph always implies some kind of constraint solving. In many cases, the given constraints are almost trivial to solve. For instance, this is the case when a rule describes a transformation G ⇒ H, where the attributes of H are obtained by some simple computation from the attributes of G. However there are many other cases where the constraints to solve may be not so trivial and, moreover, may have several answers. This is the case, for instance, when the transformation process includes some kind of searching. In the current approaches to attributed graph transformation these constraints must be completely solved when defining the matching of the given transformation rule. This kind of early binding is well-known from other areas of Computer Science to be inadequate. For instance, the solution chosen for the constraints associated to a given transformation step may be not fully adequate, meaning that later, in the search for a better solution, we may need to backtrack this transformation step. In this paper, based on our previous work on the use of symbolic graphs to deal with different aspects related with attributed graphs, including attributed graph transformation, we present a new approach that, based on the new notion of narrowing graph transformation rule, allows us to delay constraint solving when doing attributed graph transformation, in a way that resembles lazy computation. For this reason, we have called lazy this new kind of transformation. Moreover, we show that the approach is sound and complete with respect to standard attributed graph transformation. A running example, where a graph transformation system describes some basic operations of a travel agency, shows the practical interest of the approach.

On the OBDD complexity of the most significant bit of integer multiplication

Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations. Ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for boolean functions. Among the many areas of application are verification, model checking, computer-aided design, relational algebra, and symbolic graph algorithms. In this paper it is shown that the OBDD complexity of the most significant bit of integer multiplication is exponential answering an open question posed by Wegener (2000) [18].

Synthesis of controllers for symmetric systems

This article deals with supervisory control problem for coloured Petri (CP) nets. Considering a CP-net, we build a condensed version of the ordinary state-space, namely the symbolic reachability graph (SRG). This latter graph allows to cope with state-space explosion problem for symmetric systems. The control specification can be expressed in terms of either forbidden states or forbidden sequences of transitions. According to these specifications, we derive the controller by applying the theory of regions on the basis of the SRG. Thanks to expressiveness power of CP-nets, the obtained controller to be connected to the plant model is reduced to one single place.