37 research outputs found
Explaining deep neural networks through knowledge extraction and graph analysis
Explainable Artificial Intelligence (XAI) has recently become an active research
field due to the need for transparency and accountability when deploying AI models for high-stake decision making. Despite the success of Deep Neural Networks
(DNNs), understanding their decision processes is still a known challenge. The research direction presented in this thesis stems from the idea that combining knowledge with deep representations can be the key to more transparent decision making.
Specifically, we have focused on Computer Vision tasks and Convolutional Neural
Networks (CNNs) and we have proposed a graph representation, called co-activation
graph, that serves as an intermediate representation between knowledge encoded
within a CNN and the semantics contained in external knowledge bases. Given a
trained CNN, we first show how a co-activation graph can be created and exploited
to generate global insights for the model’s inner-workings. Then, we propose a
taxonomy extraction method that captures how symbolic class concepts and their
hypernyms in a given domain are hierarchically organised in the model’s subsymbolic
representation. We then illustrate how background knowledge can be connected to
the graph in order to generate textual local factual and counterfactual explanations.
Our results indicate that graph analysis approaches applied to co-activation graphs
can reveal important insights into how CNNs work and enable both global and local
semantic explanations. Despite focusing on CNN architectures, we believe that our
approach can be adapted to other architectures which would make it possible to apply the same methodology in other domains such as Natural Language Processing.
At the end of the thesis we will discuss interesting research directions that are being
investigated in the area of using knowledge graphs and graph analysis for explainability of deep learning models, and we outline opportunities for the development
of this research are
Intermediate forms and technological change: Exploring the links between technology and topology
The study of technology and technological change is a dynamic field where diverse disciplines from the social sciences and the humanities converge. It is possible to find several ontologies that incorporate topological referents as heuristic metaphors and simple methodological devices in technological studies. The paper examines two related topological concepts, continuity and convergence, based on the notions of accumulation of knowledge and a combination of pre-existing technologies to arrive at the notions of convergence and inflation. The paper concludes with some future research guidelines that formally explore the potential of topology in technology and technological change studies
Dualities in modal logic
Categorical dualities are an important tool in the study of (modal) logics. They offer conceptual understanding and enable the transfer of results between the different semantics of a logic. As such, they play a central role in the proofs of completeness theorems, Sahlqvist theorems and Goldblatt-Thomason theorems. A common way to obtain dualities is by extending existing ones. For example, Jonsson-Tarski duality is an extension of Stone duality. A convenient formalism to carry out such extensions is given by the dual categorical notions of algebras and coalgebras. Intuitively, these allow one to isolate the new part of a duality from the existing part. In this thesis we will derive both existing and new dualities via this route, and we show how to use the dualities to investigate logics. However, not all (modal logical) paradigms fit the (co)algebraic perspective. In particular, modal intuitionistic logics do not enjoy a coalgebraic treatment, and there is a general lack of duality results for them. To remedy this, we use a generalisation of both algebras and coalgebras called dialgebras. Guided by the research field of coalgebraic logic, we introduce the framework of dialgebraic logic. We show how a large class of modal intuitionistic logics can be modelled as dialgebraic logics and we prove dualities for them. We use the dialgebraic framework to prove general completeness, Hennessy-Milner, representation and Goldblatt-Thomason theorems, and instantiate this to a wide variety of modal intuitionistic logics. Additionally, we use the dialgebraic perspective to investigate modal extensions of the meet-implication fragment of intuitionistic logic. We instantiate general dialgebraic results, and describe how modal meet-implication logics relate to modal intuitionistic logics
Topological Relations.
A family of constructs is proposed that generalizes the notion of closure operator associated to a partial order. The constructs of the family (and some of its sub constructs) hold adjoint relations with Gconv which ensure a topological resemblance; furthermore, it is shown that the constructs are topological categories.Se propone una familia de constructos que generaliza la noción de operador clausura asociado a un orden parcial. Los constructos de la familia (y algunos de sus subconstructos) cumplen relaciones de adjunción con Gconv lo que nos asegura un símil topológico; aún más, se demuestra que los constructos son categorías topológicas
Finite Models for a Spatial Logic with Discrete and Topological Path Operators
This paper analyses models of a spatial logic with path operators based on the class of neighbourhood spaces, also called pretopological or closure spaces, a generalisation of topological spaces. For this purpose, we distinguish two dimensions: the type of spaces on which models are built, and the type of allowed paths. For the spaces, we investigate general neighbourhood spaces and the subclass of quasi-discrete spaces, which closely resemble graphs. For the paths, we analyse the cases of quasi-discrete paths, which consist of an enumeration of points, and topological paths, based on the unit interval. We show that the logic admits finite models over quasi-discrete spaces, both with quasi-discrete and topological paths. Finally, we prove that for general neighbourhood spaces, the logic does not have the finite model property, either for quasi-discrete or topological paths
Closure Hyperdoctrines
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems.
In this paper we present an abstract theoretical framework for the systematic investigation of the logical aspects of closure spaces. To this end, we introduce the notion of closure (hyper)doctrines, i.e. doctrines endowed with inflationary operators (and subject to suitable conditions). The generality and effectiveness of this concept is witnessed by many examples arising naturally from topological spaces, fuzzy sets, algebraic structures, coalgebras, and covering at once also known cases such as Kripke frames and probabilistic frames (i.e., Markov chains). By leveraging general categorical constructions, we provide axiomatisations and sound and complete semantics for various fragments of logics for closure operators. Hence, closure hyperdoctrines are useful both for refining and improving the theory of existing spatial logics, and for the definition of new spatial logics for new applications
A new pretopological way of identifying spreaders in propagation diffusion phenomena
In a world that's increasingly connected, many crises are related to propagation phenomena where we need to either repress the spreading (e.g. epidemics, computer viruses, fake news...) or try to accelerate it (e.g. the diffusion of a new anti-virus patch). A good understanding of such phenomena involves a knowledge of both the structure of the whole system and the specifics of the transmission process. The standard way to deal with the former has been through a characterization of the structure by the use of networks, where nodes are the components of the system where the propagation occurs, and links exist between them if there's a possibility of transmission from one component to the other. This allows to identify the super-spreaders (i.e. components that diffuse in a disproportionally large amount) as nodes with certain particular network properties. Here we propose the use of pretopology as a framework to characterize the structure of a system, as well as a new pretopological metric for the identification of super-spreaders. Since the metric can easily be transformed into an equivalent network metric, it is easy to compare its performance with some of the classical network indices of node importance. The relevance of the metric is tested by the use of some standard agent-based models of epidemics and opinion dynamics. Finally, a pretopological model of opinion diffusion is also proposed and studied
Fuzzy Sets, Fuzzy Logic and Their Applications
The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity
The Principle of Stability
How can inferences from models to the phenomena they represent be justified when those models represent only imperfectly? Pierre Duhem considered just this problem, arguing that inferences from mathematical models of phenomena to real physical applications must also be demonstrated to be approximately correct when the assumptions of the model are only approximately true. Despite being little discussed among philosophers, this challenge was taken up (if only sometimes implicitly) by mathematicians and physicists both contemporaneous with and subsequent to Duhem, yielding a novel and rich mathematical theory of stability with epistemological consequences