On the role of Computational Logic in Data Science: representing, learning, reasoning, and explaining knowledge

In this thesis we discuss in what ways computational logic (CL) and data science (DS) can jointly contribute to the management of knowledge within the scope of modern and future artificial intelligence (AI), and how technically-sound software technologies can be realised along the path. An agent-oriented mindset permeates the whole discussion, by stressing pivotal role of autonomous agents in exploiting both means to reach higher degrees of intelligence. Accordingly, the goals of this thesis are manifold. First, we elicit the analogies and differences among CL and DS, hence looking for possible synergies and complementarities along 4 major knowledge-related dimensions, namely representation, acquisition (a.k.a. learning), inference (a.k.a. reasoning), and explanation. In this regard, we propose a conceptual framework through which bridges these disciplines can be described and designed. We then survey the current state of the art of AI technologies, w.r.t. their capability to support bridging CL and DS in practice. After detecting lacks and opportunities, we propose the notion of logic ecosystem as the new conceptual, architectural, and technological solution supporting the incremental integration of symbolic and sub-symbolic AI. Finally, we discuss how our notion of logic ecosys- tem can be reified into actual software technology and extended towards many DS-related directions.

Sense development through non verbal signs: early infancy and clinical psychoterapy

This thesis will describe the development of a relationship which is not necessarily verbal, but which generates communication, creates sense and meaning between human beings and produces “becomings” in the body that feels, perceives and physically transforms itself. This leads to a biosemiotic understanding of both the seen and unseen figure.

Studio di ausili tecnologici compensativi di supporto all'iter di apprendimento matematico secondario e universitario degli studenti con dislessia

Data coming out from various researches carried out over the last years in Italy on the problem of school dispersion in secondary school show that difficulty in studying mathematics is one of the most frequent reasons of discomfort reported by students. Nevertheless, it is definitely unrealistic to think we can do without such knowledge in today society: mathematics is largely taught in secondary school and it is not confined within technical-scientific courses only. It is reasonable to say that, although students may choose academic courses that are, apparently, far away from mathematics, all students will have to come to terms, sooner or later in their life, with this subject. Among the reasons of discomfort given by the study of mathematics, some mention the very nature of this subject and in particular the complex symbolic language through which it is expressed. In fact, mathematics is a multimodal system composed by oral and written verbal texts, symbol expressions, such as formulae and equations, figures and graphs. For this, the study of mathematics represents a real challenge to those who suffer from dyslexia: this is a constitutional condition limiting people performances in relation to the activities of reading and writing and, in particular, to the study of mathematical contents. Here the difficulties in working with verbal and symbolic codes entail, in turn, difficulties in the comprehension of texts from which to deduce operations that, once combined together, would lead to the problem final solution. Information technologies may support this learning disorder effectively. However, these tools have some implementation limits, restricting their use in the study of scientific subjects. Vocal synthesis word processors are currently used to compensate difficulties in reading within the area of classical studies, but they are not used within the area of mathematics. This is because the vocal synthesis (or we should say the screen reader supporting it) is not able to interpret all that is not textual, such as symbols, images and graphs. The DISMATH software, which is the subject of this project, would allow dyslexic users to read technical-scientific documents with the help of a vocal synthesis, to understand the spatial structure of formulae and matrixes, to write documents with a technical-scientific content in a format that is compatible with main scientific editors. The system uses LaTex, a text mathematic language, as mediation system. It is set up as LaTex editor, whose graphic interface, in line with main commercial products, offers some additional specific functions with the capability to support the needs of users who are not able to manage verbal and symbolic codes on their own. LaTex is translated in real time into a standard symbolic language and it is read by vocal synthesis in natural language, in order to increase, through the bimodal representation, the ability to process information. The understanding of the mathematic formula through its reading is made possible by the deconstruction of the formula itself and its “tree” representation, so allowing to identify the logical elements composing it. Users, even without knowing LaTex language, are able to write whatever scientific document they need: in fact the symbolic elements are recalled by proper menus and automatically translated by the software managing the correct syntax. The final aim of the project, therefore, is to implement an editor enabling dyslexic people (but not only them) to manage mathematic formulae effectively, through the integration of different software tools, so allowing a better teacher/learner interaction too.

Reasoning with incomplete and imprecise preferences

Preferences are present in many real life situations but it is often difficult to quantify them giving a precise value. Sometimes preference values may be missing because of privacy reasons or because they are expensive to obtain or to produce. In some other situations the user of an automated system may have a vague idea of whats he wants. In this thesis we considered the general formalism of soft constraints, where preferences play a crucial role and we extended such a framework to handle both incomplete and imprecise preferences. In particular we provided new theoretical frameworks to handle such kinds of preferences. By admitting missing or imprecise preferences, solving a soft constraint problem becomes a different task. In fact, the new goal is to find solutions which are the best ones independently of the precise value the each preference may have. With this in mind we defined two notions of optimality: the possibly optimal solutions and the necessary optimal solutions, which are optimal no matter we assign a precise value to a missing or imprecise preference. We provided several algorithms, bases on both systematic and local search approaches, to find such kind of solutions. Moreover, we also studied the impact of our techniques also in a specific class of problems (the stable marriage problems) where imprecision and incompleteness have a specific meaning and up to now have been tackled with different techniques. In the context of the classical stable marriage problem we developed a fair method to randomly generate stable marriages of a given problem instance. Furthermore, we adapted our techniques to solve stable marriage problems with ties and incomplete lists, which are known to be NP-hard, obtaining good results both in terms of size of the returned marriage and in terms of steps need to find a solution.

A moment symbolic representation of Lévy processes with applications

By using a symbolic method, known in the literature as the classical umbral calculus, a symbolic representation of Lévy processes is given and a new family of time-space harmonic polynomials with respect to such processes, which includes and generalizes the exponential complete Bell polynomials, is introduced. The usefulness of time-space harmonic polynomials with respect to Lévy processes is that it is a martingale the stochastic process obtained by replacing the indeterminate x of the polynomials with a Lévy process, whereas the Lévy process does not necessarily have this property. Therefore to find such polynomials could be particularly meaningful for applications. This new family includes Hermite polynomials, time-space harmonic with respect to Brownian motion, Poisson-Charlier polynomials with respect to Poisson processes, Laguerre and actuarial polynomials with respect to Gamma processes , Meixner polynomials of the first kind with respect to Pascal processes, Euler, Bernoulli, Krawtchuk, and pseudo-Narumi polynomials with respect to suitable random walks. The role played by cumulants is stressed and brought to the light, either in the symbolic representation of Lévy processes and their infinite divisibility property, either in the generalization, via umbral Kailath-Segall formula, of the well-known formulae giving elementary symmetric polynomials in terms of power sum symmetric polynomials. The expression of the family of time-space harmonic polynomials here introduced has some connections with the so-called moment representation of various families of multivariate polynomials. Such moment representation has been studied here for the first time in connection with the time-space harmonic property with respect to suitable symbolic multivariate Lévy processes. In particular, multivariate Hermite polynomials and their properties have been studied in connection with a symbolic version of the multivariate Brownian motion, while multivariate Bernoulli and Euler polynomials are represented as powers of multivariate polynomials which are time-space harmonic with respect to suitable multivariate Lévy processes.

Cognition in context: Evidence on affordances and verbal language

This thesis investigated affordances and verbal language to demonstrate the flexibility of embodied simulation processes. Starting from the assumption that both object/action understanding and language comprehension are tied to the context in which they take place, six studies clarified the factors that modulate simulation. The studies in chapter 4 and 5 investigated affordance activation in complex scenes, revealing the strong influence of the visual context, which included either objects and actions, on compatibility effects. The study in chapter 6 compared the simulation triggered by visual objects and objects names, showing differences depending on the kind of materials processed. The study in chapter 7 tested the predictions of the WAT theory, confirming that the different contexts in which words are acquired lead to the difference typically observed in the literature between concrete and abstract words. The study in chapter 8 on the grounding of abstract concepts tested the mapping of temporal contents on the spatial frame of reference of the mental timeline, showing that metaphoric congruency effects are not automatic, but flexibly mediated by the context determined by the goals of different tasks. The study in chapter 9 investigated the role of iconicity in verbal language, showing sound-to-shape correspondences when every-day object figures, result that validated the reality of sound-symbolism in ecological contexts. On the whole, this evidence favors embodied views of cognition, and supports the hypothesis of a high flexibility of simulation processes. The reported conceptual effects confirm that the context plays a crucial role in affordances emergence, metaphoric mappings activation and language grounding. In conclusion, this thesis highlights that in an embodied perspective cognition is necessarily situated and anchored to a specific context, as it is sustained by the existence of a specific body immersed in a specific environment.

Dynamic analysis of the motorcycle chattering behaviour by means of symbolic multibody modelling

Aim of this research is the development and validation of a comprehensive multibody motorcycle model featuring rigid-ring tires, taking into account both slope and roughness of road surfaces. A novel parametrization for the general kinematics of the motorcycle is proposed, using a mixed reference-point and relative-coordinates approach. The resulting description, developed in terms of dependent coordinates, makes it possible to efficiently include rigid-ring kinematics as well as road elevation and slope. The equations of motion for the multibody system are derived symbolically and the constraint equations arising from the dependent-coordinate formulation are handled using a projection technique. Therefore the resulting system of equations can be integrated in time domain using a standard ODE algorithm. The model is validated with respect to maneuvers experimentally measured on the race track, showing consistent results and excellent computational efficiency. More in detail, it is also capable of reproducing the chatter vibration of racing motorcycles. The chatter phenomenon, appearing during high speed cornering maneuvers, consists of a self-excited vertical oscillation of both the front and rear unsprung masses in the range of frequency between 17 and 22 Hz. A critical maneuver is numerically simulated, and a self-excited vibration appears, consistent with the experimentally measured chatter vibration. Finally, the driving mechanism for the self-excitation is highlighted and a physical interpretation is proposed.

Symbolic Dynamics Analysis: a new methodology for foetal heart rate variability analysis

Cardiotocography (CTG) is a widespread foetal diagnostic methods. However, it lacks of objectivity and reproducibility since its dependence on observer's expertise. To overcome these limitations, more objective methods for CTG interpretation have been proposed. In particular, many developed techniques aim to assess the foetal heart rate variability (FHRV). Among them, some methodologies from nonlinear systems theory have been applied to the study of FHRV. All the techniques have proved to be helpful in specific cases. Nevertheless, none of them is more reliable than the others. Therefore, an in-depth study is necessary. The aim of this work is to deepen the FHRV analysis through the Symbolic Dynamics Analysis (SDA), a nonlinear technique already successfully employed for HRV analysis. Thanks to its simplicity of interpretation, it could be a useful tool for clinicians. We performed a literature study involving about 200 references on HRV and FHRV analysis; approximately 100 works were focused on non-linear techniques. Then, in order to compare linear and non-linear methods, we carried out a multiparametric study. 580 antepartum recordings of healthy fetuses were examined. Signals were processed using an updated software for CTG analysis and a new developed software for generating simulated CTG traces. Finally, statistical tests and regression analyses were carried out for estimating relationships among extracted indexes and other clinical information. Results confirm that none of the employed techniques is more reliable than the others. Moreover, in agreement with the literature, each analysis should take into account two relevant parameters, the foetal status and the week of gestation. Regarding the SDA, results show its promising capabilities in FHRV analysis. It allows recognizing foetal status, gestation week and global variability of FHR signals, even better than other methods. Nevertheless, further studies, which should involve even pathological cases, are necessary to establish its reliability.