A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added

A Case Study on Computational Hermeneutics: E. J. Lowe’s Modal Ontological Argument

Computers may help us to better understand (not just verify) arguments. In this article we defend this claim by showcasing the application of a new, computer-assisted interpretive method to an exemplary natural-language ar- gument with strong ties to metaphysics and religion: E. J. Lowe’s modern variant of St. Anselm’s ontological argument for the existence of God. Our new method, which we call computational hermeneutics, has been particularly conceived for use in interactive-automated proof assistants. It aims at shedding light on the meanings of words and sentences by framing their inferential role in a given argument. By employing automated theorem reasoning technology within interactive proof assistants, we are able to drastically reduce (by several orders of magnitude) the time needed to test the logical validity of an argu- ment’s formalization. As a result, a new approach to logical analysis, inspired by Donald Davidson’s account of radical interpretation, has been enabled. In computational hermeneutics, the utilization of automated reasoning tools ef- fectively boosts our capacity to expose the assumptions we indirectly commit ourselves to every time we engage in rational argumentation and it fosters the explicitation and revision of our concepts and commitments

Explainable Deep Learning

Il grande successo che il Deep Learning ha ottenuto in ambiti strategici per la nostra società quali l'industria, la difesa, la medicina etc., ha portanto sempre più realtà a investire ed esplorare l'utilizzo di questa tecnologia. Ormai si possono trovare algoritmi di Machine Learning e Deep Learning quasi in ogni ambito della nostra vita. Dai telefoni, agli elettrodomestici intelligenti fino ai veicoli che guidiamo. Quindi si può dire che questa tecnologia pervarsiva è ormai a contatto con le nostre vite e quindi dobbiamo confrontarci con essa. Da questo nasce l’eXplainable Artificial Intelligence o XAI, uno degli ambiti di ricerca che vanno per la maggiore al giorno d'oggi in ambito di Deep Learning e di Intelligenza Artificiale. Il concetto alla base di questo filone di ricerca è quello di rendere e/o progettare i nuovi algoritmi di Deep Learning in modo che siano affidabili, interpretabili e comprensibili all'uomo. Questa necessità è dovuta proprio al fatto che le reti neurali, modello matematico che sta alla base del Deep Learning, agiscono come una scatola nera, rendendo incomprensibile all'uomo il ragionamento interno che compiono per giungere ad una decisione. Dato che stiamo delegando a questi modelli matematici decisioni sempre più importanti, integrandole nei processi più delicati della nostra società quali, ad esempio, la diagnosi medica, la guida autonoma o i processi di legge, è molto importante riuscire a comprendere le motivazioni che portano questi modelli a produrre determinati risultati. Il lavoro presentato in questa tesi consiste proprio nello studio e nella sperimentazione di algoritmi di Deep Learning integrati con tecniche di Intelligenza Artificiale simbolica. Questa integrazione ha un duplice scopo: rendere i modelli più potenti, consentendogli di compiere ragionamenti o vincolandone il comportamento in situazioni complesse, e renderli interpretabili. La tesi affronta due macro argomenti: le spiegazioni ottenute grazie all'integrazione neuro-simbolica e lo sfruttamento delle spiegazione per rendere gli algoritmi di Deep Learning più capaci o intelligenti. Il primo macro argomento si concentra maggiormente sui lavori svolti nello sperimentare l'integrazione di algoritmi simbolici con le reti neurali. Un approccio è stato quelli di creare un sistema per guidare gli addestramenti delle reti stesse in modo da trovare la migliore combinazione di iper-parametri per automatizzare la progettazione stessa di queste reti. Questo è fatto tramite l'integrazione di reti neurali con la Programmazione Logica Probabilistica (PLP) che consente di sfruttare delle regole probabilistiche indotte dal comportamento delle reti durante la fase di addestramento o ereditate dall'esperienza maturata dagli esperti del settore. Queste regole si innescano allo scatenarsi di un problema che il sistema rileva durate l'addestramento della rete. Questo ci consente di ottenere una spiegazione di cosa è stato fatto per migliorare l'addestramento una volta identificato un determinato problema. Un secondo approccio è stato quello di far cooperare sistemi logico-probabilistici con reti neurali per la diagnosi medica da fonti di dati eterogenee. La seconda tematica affrontata in questa tesi tratta lo sfruttamento delle spiegazioni che possiamo ottenere dalle rete neurali. In particolare, queste spiegazioni sono usate per creare moduli di attenzione che aiutano a vincolare o a guidare le reti neurali portandone ad avere prestazioni migliorate. Tutti i lavori sviluppati durante il dottorato e descritti in questa tesi hanno portato alle pubblicazioni elencate nel Capitolo 14.2.The great success that Machine and Deep Learning has achieved in areas that are strategic for our society such as industry, defence, medicine, etc., has led more and more realities to invest and explore the use of this technology. Machine Learning and Deep Learning algorithms and learned models can now be found in almost every area of our lives. From phones to smart home appliances, to the cars we drive. So it can be said that this pervasive technology is now in touch with our lives, and therefore we have to deal with it. This is why eXplainable Artificial Intelligence or XAI was born, one of the research trends that are currently in vogue in the field of Deep Learning and Artificial Intelligence. The idea behind this line of research is to make and/or design the new Deep Learning algorithms so that they are interpretable and comprehensible to humans. This necessity is due precisely to the fact that neural networks, the mathematical model underlying Deep Learning, act like a black box, making the internal reasoning they carry out to reach a decision incomprehensible and untrustable to humans. As we are delegating more and more important decisions to these mathematical models, it is very important to be able to understand the motivations that lead these models to make certain decisions. This is because we have integrated them into the most delicate processes of our society, such as medical diagnosis, autonomous driving or legal processes. The work presented in this thesis consists in studying and testing Deep Learning algorithms integrated with symbolic Artificial Intelligence techniques. This integration has a twofold purpose: to make the models more powerful, enabling them to carry out reasoning or constraining their behaviour in complex situations, and to make them interpretable. The thesis focuses on two macro topics: the explanations obtained through neuro-symbolic integration and the exploitation of explanations to make the Deep Learning algorithms more capable or intelligent. The neuro-symbolic integration was addressed twice, by experimenting with the integration of symbolic algorithms with neural networks. A first approach was to create a system to guide the training of the networks themselves in order to find the best combination of hyper-parameters to automate the design of these networks. This is done by integrating neural networks with Probabilistic Logic Programming (PLP). This integration makes it possible to exploit probabilistic rules tuned by the behaviour of the networks during the training phase or inherited from the experience of experts in the field. These rules are triggered when a problem occurs during network training. This generates an explanation of what was done to improve the training once a particular issue was identified. A second approach was to make probabilistic logic systems cooperate with neural networks for medical diagnosis on heterogeneous data sources. The second topic addressed in this thesis concerns the exploitation of explanations. In particular, the explanations one can obtain from neural networks are used in order to create attention modules that help in constraining and improving the performance of neural networks. All works developed during the PhD and described in this thesis have led to the publications listed in Chapter 14.2

Integrating Human-Provided Information Into Belief State Representation Using Dynamic Factorization

In partially observed environments, it can be useful for a human to provide the robot with declarative information that represents probabilistic relational constraints on properties of objects in the world, augmenting the robot's sensory observations. For instance, a robot tasked with a search-and-rescue mission may be informed by the human that two victims are probably in the same room. An important question arises: how should we represent the robot's internal knowledge so that this information is correctly processed and combined with raw sensory information? In this paper, we provide an efficient belief state representation that dynamically selects an appropriate factoring, combining aspects of the belief when they are correlated through information and separating them when they are not. This strategy works in open domains, in which the set of possible objects is not known in advance, and provides significant improvements in inference time over a static factoring, leading to more efficient planning for complex partially observed tasks. We validate our approach experimentally in two open-domain planning problems: a 2D discrete gridworld task and a 3D continuous cooking task. A supplementary video can be found at http://tinyurl.com/chitnis-iros-18.Comment: IROS 2018 final versio