Theoretical and implementation aspects in the mechanization of the metatheory of programming languages

Interactive theorem provers are tools designed for the certification of formal proofs developed by means of man-machine collaboration. Formal proofs obtained in this way cover a large variety of logical theories, ranging from the branches of mainstream mathematics, to the field of software verification. The border between these two worlds is marked by results in theoretical computer science and proofs related to the metatheory of programming languages. This last field, which is an obvious application of interactive theorem proving, poses nonetheless a serious challenge to the users of such tools, due both to the particularly structured way in which these proofs are constructed, and to difficulties related to the management of notions typical of programming languages like variable binding. This thesis is composed of two parts, discussing our experience in the development of the Matita interactive theorem prover and its use in the mechanization of the metatheory of programming languages. More specifically, part I covers: - the results of our effort in providing a better framework for the development of tactics for Matita, in order to make their implementation and debugging easier, also resulting in a much clearer code; - a discussion of the implementation of two tactics, providing infrastructure for the unification of constructor forms and the inversion of inductive predicates; we point out interactions between induction and inversion and provide an advancement over the state of the art. In the second part of the thesis, we focus on aspects related to the formalization of programming languages. We describe two works of ours: - a discussion of basic issues we encountered in our formalizations of part 1A of the Poplmark challenge, where we apply the extended inversion principles we implemented for Matita; - a formalization of an algebraic logical framework, posing more complex challenges, including multiple binding and a form of hereditary substitution; this work adopts, for the encoding of binding, an extension of Masahiko Sato's canonical locally named representation we designed during our visit to the Laboratory for Foundations of Computer Science at the University of Edinburgh, under the supervision of Randy Pollack.

Innovation and economic performance of the firms in the service sector: relevant issues and open problems

This thesis is a collection of essays related to the topic of innovation in the service sector. The choice of this structure is functional to the purpose of single out some of the relevant issues and try to tackle them, revising first the state of the literature and then proposing a way forward. Three relevant issues has been therefore selected: (i) the definition of innovation in the service sector and the connected question of measurement of innovation; (ii) the issue of productivity in services; (iii) the classification of innovative firms in the service sector. Facing the first issue, chapter II shows how the initial width of the original Schumpeterian definition of innovation has been narrowed and then passed to the service sector form the manufacturing one in a reduce technological form. Chapter III tackle the issue of productivity in services, discussing the difficulties for measuring productivity in a context where the output is often immaterial. We reconstruct the dispute on the Baumol’s cost disease argument and propose two different ways to go forward in the research on productivity in services: redefining the output along the line of a characteristic approach; and redefining the inputs, particularly analysing which kind of input it’s worth saving. Chapter IV derives an integrated taxonomy of innovative service and manufacturing firms, using data coming from the 2008 CIS survey for Italy. This taxonomy is based on the enlarged definition of “innovative firm” deriving from the Schumpeterian definition of innovation and classify firms using a cluster analysis techniques. The result is the emergence of a four cluster solution, where firms are differentiated by the breadth of the innovation activities in which they are involved. Chapter 5 reports some of the main conclusions of each singular previous chapter and the points worth of further research in the future.

Coding of reaching in 3-D space

Many psychophysical studies suggest that target depth and direction during reaches are processed independently, but the neurophysiological support to this view is so far limited. Here, we investigated the representation of reach depth and direction by single neurons in an area of the medial posterior parietal cortex (V6A). Single-unit activity was recorded from V6A in two Macaca fascicularis monkeys performing a fixation-to-reach task to targets at different depths and directions. We found that in a substantial percentage of V6A neurons depth and direction signals jointly influenced fixation, planning and arm movement-related activity in 3D space. While target depth and direction were equally encoded during fixation, depth tuning became stronger during arm movement planning, execution and target holding. The spatial tuning of fixation activity was often maintained across epochs, and this occurred more frequently in depth. These findings support for the first time the existence of a common neural substrate for the encoding of target depth and direction during reaching movements in the posterior parietal cortex. Present results also highlight the presence in V6A of several types of cells that process independently or jointly eye position and arm movement planning and execution signals in order to control reaches in 3D space. It is possible that depth and direction influence also the metrics of the reach action and that this effect on the reach kinematic variables can account for the spatial tuning we found in V6A neural activity. For this reason, we recorded and analyzed behavioral data when one monkey performed reaching movements in 3-D space. We evaluated how the target spatial position, in particular target depth and target direction, affected the kinematic parameters and trajectories describing the motor action properties.

Quality of Service in Distributed Stream Processing for large scale Smart Pervasive Environments

The wide diffusion of cheap, small, and portable sensors integrated in an unprecedented large variety of devices and the availability of almost ubiquitous Internet connectivity make it possible to collect an unprecedented amount of real time information about the environment we live in. These data streams, if properly and timely analyzed, can be exploited to build new intelligent and pervasive services that have the potential of improving people's quality of life in a variety of cross concerning domains such as entertainment, health-care, or energy management. The large heterogeneity of application domains, however, calls for a middleware-level infrastructure that can effectively support their different quality requirements. In this thesis we study the challenges related to the provisioning of differentiated quality-of-service (QoS) during the processing of data streams produced in pervasive environments. We analyze the trade-offs between guaranteed quality, cost, and scalability in streams distribution and processing by surveying existing state-of-the-art solutions and identifying and exploring their weaknesses. We propose an original model for QoS-centric distributed stream processing in data centers and we present Quasit, its prototype implementation offering a scalable and extensible platform that can be used by researchers to implement and validate novel QoS-enforcement mechanisms. To support our study, we also explore an original class of weaker quality guarantees that can reduce costs when application semantics do not require strict quality enforcement. We validate the effectiveness of this idea in a practical use-case scenario that investigates partial fault-tolerance policies in stream processing by performing a large experimental study on the prototype of our novel LAAR dynamic replication technique. Our modeling, prototyping, and experimental work demonstrates that, by providing data distribution and processing middleware with application-level knowledge of the different quality requirements associated to different pervasive data flows, it is possible to improve system scalability while reducing costs.

Relative influence of gaze and static arm position in the Superior Parietal Lobule of the macaque monkey during reaching

The superior parietal lobule (SPL) of macaques is classically described as an associative cortex implicated in visuospatial perception, planning and control of reaching and grasping movements (De Vitis et al., 2019; Galletti et al., 2003, 2018, 2022; Fattori et al., 2017; Hadjidimitrakis et al., 2015). These processes are the result of the integration of signals related to different sensory modalities. During a goal-directed action, eye and limb information are combined to ensure that the hand is transported at the gazed target location and the arm is maintained steady in the final position. The SPL areas V6A, PEc and PE contain cells sensitive to the direction of gaze and limb position but less is known about the degree of independent encoding of these signals. In this thesis, we evaluated the influence of eye and arm position information upon single neuron activity of areas V6A, PEc and PE during the holding period after the execution of arm reaching movement, when the gaze and hand are both still at the reach target. Two male macaques (Macaca fascicularis) performed a reaching task while single unit activity was recorded from areas V6A, PEc and PE. We found that neurons in all these areas were modulated by eye and static arm positions with a joint encoding of gaze and somatosensory signals in V6A and PEc and a mostly separate processing of the two signals in PE. The elaboration of this information reflects the functional gradient found in the SPL with the caudal sector characterized by visuo-somatic properties in comparison to the rostral sector dominated by somatosensory signals. This evidence well agree also with the recent reallocation of areas V6A and PEc in Brodmann’s area 7 depending on their similar structural and functional features with respect to PE belonging to Brodmann’s area 5 (Gamberini et al., 2020).

Interactive theorem provers: issues faced as a user and tackled as a developer

Interactive theorem provers (ITP for short) are tools whose final aim is to certify proofs written by human beings. To reach that objective they have to fill the gap between the high level language used by humans for communicating and reasoning about mathematics and the lower level language that a machine is able to “understand” and process. The user perceives this gap in terms of missing features or inefficiencies. The developer tries to accommodate the user requests without increasing the already high complexity of these applications. We believe that satisfactory solutions can only come from a strong synergy between users and developers. We devoted most part of our PHD designing and developing the Matita interactive theorem prover. The software was born in the computer science department of the University of Bologna as the result of composing together all the technologies developed by the HELM team (to which we belong) for the MoWGLI project. The MoWGLI project aimed at giving accessibility through the web to the libraries of formalised mathematics of various interactive theorem provers, taking Coq as the main test case. The motivations for giving life to a new ITP are: • study the architecture of these tools, with the aim of understanding the source of their complexity • exploit such a knowledge to experiment new solutions that, for backward compatibility reasons, would be hard (if not impossible) to test on a widely used system like Coq. Matita is based on the Curry-Howard isomorphism, adopting the Calculus of Inductive Constructions (CIC) as its logical foundation. Proof objects are thus, at some extent, compatible with the ones produced with the Coq ITP, that is itself able to import and process the ones generated using Matita. Although the systems have a lot in common, they share no code at all, and even most of the algorithmic solutions are different. The thesis is composed of two parts where we respectively describe our experience as a user and a developer of interactive provers. In particular, the first part is based on two different formalisation experiences: • our internship in the Mathematical Components team (INRIA), that is formalising the finite group theory required to attack the Feit Thompson Theorem. To tackle this result, giving an effective classification of finite groups of odd order, the team adopts the SSReflect Coq extension, developed by Georges Gonthier for the proof of the four colours theorem. • our collaboration at the D.A.M.A. Project, whose goal is the formalisation of abstract measure theory in Matita leading to a constructive proof of Lebesgue’s Dominated Convergence Theorem. The most notable issues we faced, analysed in this part of the thesis, are the following: the difficulties arising when using “black box” automation in large formalisations; the impossibility for a user (especially a newcomer) to master the context of a library of already formalised results; the uncomfortable big step execution of proof commands historically adopted in ITPs; the difficult encoding of mathematical structures with a notion of inheritance in a type theory without subtyping like CIC. In the second part of the manuscript many of these issues will be analysed with the looking glasses of an ITP developer, describing the solutions we adopted in the implementation of Matita to solve these problems: integrated searching facilities to assist the user in handling large libraries of formalised results; a small step execution semantic for proof commands; a flexible implementation of coercive subtyping allowing multiple inheritance with shared substructures; automatic tactics, integrated with the searching facilities, that generates proof commands (and not only proof objects, usually kept hidden to the user) one of which specifically designed to be user driven.

The uncertainty in standardised sound power measurements: complying with ISO 17025

In the context of “testing laboratory” one of the most important aspect to deal with is the measurement result. Whenever decisions are based on measurement results, it is important to have some indication of the quality of the results. In every area concerning with noise measurement many standards are available but without an expression of uncertainty, it is impossible to judge whether two results are in compliance or not. ISO/IEC 17025 is an international standard related with the competence of calibration and testing laboratories. It contains the requirements that testing and calibration laboratories have to meet if they wish to demonstrate that they operate to a quality system, are technically competent and are able to generate technically valid results. ISO/IEC 17025 deals specifically with the requirements for the competence of laboratories performing testing and calibration and for the reporting of the results, which may or may not contain opinions and interpretations of the results. The standard requires appropriate methods of analysis to be used for estimating uncertainty of measurement. In this point of view, for a testing laboratory performing sound power measurement according to specific ISO standards and European Directives, the measurement of uncertainties is the most important factor to deal with. Sound power level measurement, according to ISO 3744:1994 , performed with a limited number of microphones distributed over a surface enveloping a source is affected by a certain systematic error and a related standard deviation. Making a comparison of measurement carried out with different microphone arrays is difficult because results are affected by systematic errors and standard deviation that are peculiarities of the number of microphones disposed on the surface, their spatial position and the complexity of the sound field. A statistical approach could give an overview of the difference between sound power level evaluated with different microphone arrays and an evaluation of errors that afflict this kind of measurement. Despite the classical approach that tend to follow the ISO GUM this thesis present a different point of view of the problem related to the comparison of result obtained from different microphone arrays.

Letteratura postmoderna e comunicazione pubblicitaria, problemi teorici e analisi testuali

Premise: In the literary works of our anthropological and cultural imagination, the various languages and the different discursive practices are not necessarily quoted, expressly alluded to or declared through clear expressive mechanisms; instead, they rather constitute a substratum, a background, now consolidated, which with irony and intertextuality shines through the thematic and formal elements of each text. The various contaminations, hybridizations and promptings that we find in the expressive forms, the rhetorical procedures and the linguistic and thematic choices of post-modern literary texts are shaped as fluid and familiar categories. Exchanges and passages are no longer only allowed but also inevitable; the post-modern imagination is made up of an agglomeration of discourses that are no longer really separable, built up from texts that blend and quote one another, composing, each with its own specificities, the great family of the cultural products of our social scenario. A literary work, therefore, is not only a whole phenomenon, delimited hic et nunc by a beginning and an ending, but is a fragment of that complex, dense and boundless network that is given by the continual interrelations between human forms of communication and symbolization. The research hypothesis: A vision is delineated of comparative literature as a discipline attentive to the social contexts in which texts take shape and move and to the media-type consistency that literary phenomena inevitably take on. Hence literature is seen as an open systematicity that chooses to be contaminated by other languages and other discursive practices of an imagination that is more than ever polymorphic and irregular. Inside this interpretative framework the aim is to focus the analysis on the relationship that postmodern literature establishes with advertising discourse. On one side post-modern literature is inserted in the world of communication, loudly asserting the blending and reciprocal contamination of literary modes with media ones, absorbing their languages and signification practices, translating them now into thematic nuclei, motifs and sub-motifs and now into formal expedients and new narrative choices; on the other side advertising is chosen as a signification practice of the media universe, which since the 1960s has actively contributed to shaping the dynamics of our socio-cultural scenarios, in terms which are just as important as those of other discursive practices. Advertising has always been a form of communication and symbolization that draws on the collective imagination – myths, actors and values – turning them into specific narrative programs for its own texts. Hence the aim is to interpret and analyze this relationship both from a strictly thematic perspective – and therefore trying to understand what literature speaks about when it speaks about advertising, and seeking advertising quotations in post-modern fiction – and from a formal perspective, with a search for parallels and discordances between the rhetorical procedures, the languages and the verifiable stylistic choices in the texts of the two different signification practices. The analysis method chosen, for the purpose of constructive multiplication of the perspectives, aims to approach the analytical processes of semiotics, applying, when possible, the instruments of the latter, in order to highlight the thematic and formal relationships between literature and advertising. The corpus: The corpus of the literary texts is made up of various novels and, although attention is focused on the post-modern period, there will also be ineludible quotations from essential authors that with their works prompted various reflections: H. De Balzac, Zola, Fitzgerald, Joyce, Calvino, etc… However, the analysis focuses the corpus on three authors: Don DeLillo, Martin Amis and Aldo Nove, and in particular the followings novels: “Americana” (1971) and “Underworld” (1999) by Don DeLillo, “Money” (1984) by Martin Amis and “Woobinda and other stories without a happy ending” (1996) and “Superwoobinda” (1998) by Aldo Nove. The corpus selection is restricted to these novels for two fundamental reasons: 1. assuming parameters of spatio-temporal evaluation, the texts are representative of different socio-cultural contexts and collective imaginations (from the masterly glimpses of American life by DeLillo, to the examples of contemporary Italian life by Nove, down to the English imagination of Amis) and of different historical moments (the 1970s of DeLillo’s Americana, the 1980s of Amis, down to the 1990s of Nove, decades often used as criteria of division of postmodernism into phases); 2. adopting a perspective of strictly thematic analysis, as mentioned in the research hypothesis, the variations and the constants in the novels (thematic nuclei, topoi, images and narrative developments) frequently speak of advertising and inside the narrative plot they affirm various expressions and realizations of it: value ones, thematic ones, textual ones, urban ones, etc… In these novels the themes and the processes of signification of advertising discourse pervade time, space and the relationships that the narrator character builds around him. We are looking at “particle-characters” whose endless facets attest the influence and contamination of advertising in a large part of the narrative developments of the plot: on everyday life, on the processes of acquisition and encoding of the reality, on ideological and cultural baggage, on the relationships and interchanges with the other characters, etc… Often the characters are victims of the implacable consequentiality of the advertising mechanism, since the latter gets the upper hand over the usual processes of communication, which are overwhelmed by it, wittingly or unwittingly (for example: disturbing openings in which the protagonist kills his or her parents on the basis of a spot, former advertisers that live life codifying it through the commercial mechanisms of products, sons and daughters of advertisers that as children instead of playing outside for whole nights saw tapes of spots.) Hence the analysis arises from the text and aims to show how much the developments and the narrative plots of the novels encode, elaborate and recount the myths, the values and the narrative programs of advertising discourse, transforming them into novel components in their own right. And also starting from the text a socio-cultural reference context is delineated, a collective imagination that is different, now geographically, now historically, and from comparison between them the aim is to deduce the constants, the similarities and the variations in the relationship between literature and advertising.

Expressiveness in biologically inspired languages

A very recent and exciting new area of research is the application of Concurrency Theory tools to formalize and analyze biological systems and one of the most promising approach comes from the process algebras (process calculi). A process calculus is a formal language that allows to describe concurrent systems and comes with well-established techniques for quantitative and qualitative analysis. Biological systems can be regarded as concurrent systems and therefore modeled by means of process calculi. In this thesis we focus on the process calculi approach to the modeling of biological systems and investigate, mostly from a theoretical point of view, several promising bio-inspired formalisms: Brane Calculi and k-calculus family. We provide several expressiveness results mostly by means of comparisons between calculi. We provide a lower bound to the computational power of the non Turing complete MDB Brane Calculi by showing an encoding of a simple P-System into MDB. We address the issue of local implementation within the k-calculus family: whether n-way rewrites can be simulated by binary interactions only. A solution introducing divergence is provided and we prove a deterministic solution preserving the termination property is not possible. We use the symmetric leader election problem to test synchronization capabilities within the k-calculus family. Several fragments of the original k-calculus are considered and we prove an impossibility result about encoding n-way synchronization into (n-1)-way synchronization. A similar impossibility result is obtained in a pure computer science context. We introduce CCSn, an extension of CCS with multiple input prefixes and show, using the dining philosophers problem, that there is no reasonable encoding of CCS(n+1) into CCSn.

Fonti cartografiche di Toscana e Catalogna di Età Moderna e Contemporanea. Ricostruire con il GIS, comunicare con WebGIS

The aim of this study is the creation of a Historical GIS that spatially reference data retrieved from Italian and Catalan historical sources and records. The generation of locates these metasource was achieved through the integral acquisition of source-oriented records and the insertion of mark-up fields, yet maintaining, where possible, the original encoding of the source documents. In order to standardize the set of information contained in the original documents and thus allow queries to the database, additional fields were introduced. Once the initial phase of data research and analysis was concluded the new virtual source was published online within an open WebGIS source. As a conclusion we have created a dynamic and spatially referenced database of geo-historical information. The configuration of this new source is such to guarantee the best possible accessibility.

Sviluppo di metodologie per la Stima in Tempo Reale delle Grandezze Indicate in Motori a Combustione Interna

Modern Internal Combustion Engines are becoming increasingly complex in terms of their control systems and strategies. The growth of the algorithms’ complexity results in a rise of the number of on-board quantities for control purposes. In order to improve combustion efficiency and, simultaneously, limit the amount of pollutant emissions, the on-board evaluation of two quantities in particular has become essential; namely indicated torque produced by the engine and the angular position where 50% of fuel mass injected over an engine cycle is burned (MFB50). The above mentioned quantities can be evaluated through the measurement of in-cylinder pressure. Nonetheless, at the time being, the installation of in-cylinder pressure sensors on vehicles is extremely uncommon mainly because of measurement reliability and costs. This work illustrates a methodological approach for the estimation of indicated torque and MFB50 that is based on the engine speed fluctuation measurement. This methodology is compatible with the typical on-board application restraints. Moreover, it requires no additional costs since speed can be measured using the system already mounted on the vehicle, which is made of a magnetic pick-up faced to a toothed wheel. The estimation algorithm consists of two main parts: first, the evaluation of indicated torque fluctuation based on speed measurement and secondly, the evaluation of the mean value of the indicated torque (over an engine cycle) and MFB50 by using the relationship with the indicated torque harmonic and other engine quantities. The procedure has been successfully applied to an L4 turbocharged Diesel engine mounted on-board a vehicle.

I beni immateriali nella valutazione d'azienda

In seguito ad una disamina del materiale presente in letteratura, ci siamo chiesti se i numerosi investimenti pubblicitari, promozionali, di marketing e, per dirla in una parola sola “intangibili”, generassero un aumento del valore dell’impresa nel contesto valutativo oppure se dessero origine esclusivamente ad aumenti di fatturato. L’obiettivo più ambito consiste nel capitalizzare gli investimenti su attività intangibili come la costruzione del marchio, l’utilizzo di brevetti, le operazioni rivolte alla soddisfazione del cliente e tutto quanto si possa definire immateriale. Eppure coesistono nel mare magnum della stessa azienda. Fino a quando non si potrà inserire criteri di valutazione d’azienda delle performance di marketing non ci potrà essere crescita in quanto, le risorse, sono utilizzate senza un criterio di ritorno di investimento.

Type Systems for Distributed Programs: Components and Sessions

Modern software systems, in particular distributed ones, are everywhere around us and are at the basis of our everyday activities. Hence, guaranteeing their cor- rectness, consistency and safety is of paramount importance. Their complexity makes the verification of such properties a very challenging task. It is natural to expect that these systems are reliable and above all usable. i) In order to be reliable, compositional models of software systems need to account for consistent dynamic reconfiguration, i.e., changing at runtime the communication patterns of a program. ii) In order to be useful, compositional models of software systems need to account for interaction, which can be seen as communication patterns among components which collaborate together to achieve a common task. The aim of the Ph.D. was to develop powerful techniques based on formal methods for the verification of correctness, consistency and safety properties related to dynamic reconfiguration and communication in complex distributed systems. In particular, static analysis techniques based on types and type systems appeared to be an adequate methodology, considering their success in guaranteeing not only basic safety properties, but also more sophisticated ones like, deadlock or livelock freedom in a concurrent setting. The main contributions of this dissertation are twofold. i) On the components side: we design types and a type system for a concurrent object-oriented calculus to statically ensure consistency of dynamic reconfigurations related to modifications of communication patterns in a program during execution time. ii) On the communication side: we study advanced safety properties related to communication in complex distributed systems like deadlock-freedom, livelock- freedom and progress. Most importantly, we exploit an encoding of types and terms of a typical distributed language, session π-calculus, into the standard typed π- calculus, in order to understand their expressive power.

The posterior parietal cortex: a bridge between vision and action

The present work takes into account three posterior parietal areas, V6, V6A, and PEc, all operating on different subsets of signals (visual, somatic, motor). The work focuses on the study of their functional properties, to better understand their respective contribution in the neuronal circuits that make possible the interactions between subject and external environment. In the caudalmost pole of parietal lobe there is area V6. Functional data suggest that this area is related to the encoding of both objects motion and ego-motion. However, the sensitivity of V6 neurons to optic flow stimulations has been tested only in human fMRI experiments. Here we addressed this issue by applying on monkey the same experimental protocol used in human studies. The visual stimulation obtained with the Flow Fields stimulus was the most effective and powerful to activate area V6 in monkey, further strengthening this homology between the two primates. The neighboring areas, V6A and PEc, show different cytoarchitecture and connectivity profiles, but are both involved in the control of reaches. We studied the sensory responses present in these areas, and directly compared these.. We also studied the motor related discharges of PEc neurons during reaching movements in 3D space comparing also the direction and depth tuning of PEc cells with those of V6A. The results show that area PEc and V6A share several functional properties. Area PEc, unlike V6A, contains a richer and more complex somatosensory input, and a poorer, although complex visual one. Differences emerged also comparing the motor-related properties for reaches in depth: the incidence of depth modulations in PEc and the temporal pattern of modulation for depth and direction allow to delineate a trend among the two parietal visuomotor areas.

Deficit in the Emotional Embodiment in Alexithymia

Alexithymia refers to difficulties in recognizing one’s own emotions and others emotions. Theories of emotional embodiment suggest that, in order to understand other peoples’ feelings, observers re-experience, or simulate, the relevant component (i.e. somatic, motor, visceral) of emotion’s expressed by others in one’s self. In this way, the emotions are “embodied”. Critically, to date, there are no studies investigating the ability of alexithymic individuals in embodying the emotions conveyed by faces. In the present dissertation different implicit paradigms and techniques falling within the field of affective neuroscience have been employed in order to test a possible deficit in the embodiment of emotions in alexithymia while subjects were requested to observe faces manifesting different expression: fear, disgust, happiness and neutral. The level of the perceptual encoding of emotional faces and the embodiment of emotions in the somato-sensory and sensory-motor system have been investigated. Moreover, non-communicative motor reaction to emotional stimuli (i.e. visceral reactions) and interoceptive abilities of alexithymic subjects have been explored. The present dissertation provided convergent evidences in support of a deficit in the processing of fearful expression in subjects with high alexithymic personality traits. Indeed, the pattern of fear induced changes in the perceptual encoding, in the somato-sensory and in the somato-motor system (both the communicative and non communicative one) is widely and consistently altered in alexithymia. This support the hypothesis of a diminished responses to fearful stimuli in alexithymia. In addition, the overall results on happiness and disgust, although preliminary, provided interesting results. Indeed, the results on happiness revealed a defective perceptual encoding, coupled with a slight difficulty (i.e. delayed responses) at the level of the communicative somato-motor system, and the emotion of disgust has been found to be abnormally embodied at the level of the somato-sensory system.