User interaction widgets for interactive theorem proving

Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using a script for storing textual commands for the system. In the tradition of LCF, the proof language of Matita is procedural and relies on tactic and tacticals to proceed toward proof completion. The interaction paradigm offered to the user is based on the script management technique at the basis of the popularity of the Proof General generic interface for interactive theorem provers: while editing a script the user can move forth the execution point to deliver commands to the system, or back to retract (or “undo”) past commands. Matita has been developed from scratch in the past 8 years by several members of the Helm research group, this thesis author is one of such members. Matita is now a full-fledged proof assistant with a library of about 1.000 concepts. Several innovative solutions spun-off from this development effort. This thesis is about the design and implementation of some of those solutions, in particular those relevant for the topic of user interaction with theorem provers, and of which this thesis author was a major contributor. Joint work with other members of the research group is pointed out where needed. The main topics discussed in this thesis are briefly summarized below. Disambiguation. Most activities connected with interactive proving require the user to input mathematical formulae. Being mathematical notation ambiguous, parsing formulae typeset as mathematicians like to write down on paper is a challenging task; a challenge neglected by several theorem provers which usually prefer to fix an unambiguous input syntax. Exploiting features of the underlying calculus, Matita offers an efficient disambiguation engine which permit to type formulae in the familiar mathematical notation. Step-by-step tacticals. Tacticals are higher-order constructs used in proof scripts to combine tactics together. With tacticals scripts can be made shorter, readable, and more resilient to changes. Unfortunately they are de facto incompatible with state-of-the-art user interfaces based on script management. Such interfaces indeed do not permit to position the execution point inside complex tacticals, thus introducing a trade-off between the usefulness of structuring scripts and a tedious big step execution behavior during script replaying. In Matita we break this trade-off with tinycals: an alternative to a subset of LCF tacticals which can be evaluated in a more fine-grained manner. Extensible yet meaningful notation. Proof assistant users often face the need of creating new mathematical notation in order to ease the use of new concepts. The framework used in Matita for dealing with extensible notation both accounts for high quality bidimensional rendering of formulae (with the expressivity of MathMLPresentation) and provides meaningful notation, where presentational fragments are kept synchronized with semantic representation of terms. Using our approach interoperability with other systems can be achieved at the content level, and direct manipulation of formulae acting on their rendered forms is possible too. Publish/subscribe hints. Automation plays an important role in interactive proving as users like to delegate tedious proving sub-tasks to decision procedures or external reasoners. Exploiting the Web-friendliness of Matita we experimented with a broker and a network of web services (called tutors) which can try independently to complete open sub-goals of a proof, currently being authored in Matita. The user receives hints from the tutors on how to complete sub-goals and can interactively or automatically apply them to the current proof. Another innovative aspect of Matita, only marginally touched by this thesis, is the embedded content-based search engine Whelp which is exploited to various ends, from automatic theorem proving to avoiding duplicate work for the user. We also discuss the (potential) reusability in other systems of the widgets presented in this thesis and how we envisage the evolution of user interfaces for interactive theorem provers in the Web 2.0 era.

Designing and Programming Organizational Infrastructures for Agents situated in Artifact-based Environments

Actual trends in software development are pushing the need to face a multiplicity of diverse activities and interaction styles characterizing complex and distributed application domains, in such a way that the resulting dynamics exhibits some grade of order, i.e. in terms of evolution of the system and desired equilibrium. Autonomous agents and Multiagent Systems are argued in literature as one of the most immediate approaches for describing such a kind of challenges. Actually, agent research seems to converge towards the definition of renewed abstraction tools aimed at better capturing the new demands of open systems. Besides agents, which are assumed as autonomous entities purposing a series of design objectives, Multiagent Systems account new notions as first-class entities, aimed, above all, at modeling institutional/organizational entities, placed for normative regulation, interaction and teamwork management, as well as environmental entities, placed as resources to further support and regulate agent work. The starting point of this thesis is recognizing that both organizations and environments can be rooted in a unifying perspective. Whereas recent research in agent systems seems to account a set of diverse approaches to specifically face with at least one aspect within the above mentioned, this work aims at proposing a unifying approach where both agents and their organizations can be straightforwardly situated in properly designed working environments. In this line, this work pursues reconciliation of environments with sociality, social interaction with environment based interaction, environmental resources with organizational functionalities with the aim to smoothly integrate the various aspects of complex and situated organizations in a coherent programming approach. Rooted in Agents and Artifacts (A&A) meta-model, which has been recently introduced both in the context of agent oriented software engineering and programming, the thesis promotes the notion of Embodied Organizations, characterized by computational infrastructures attaining a seamless integration between agents, organizations and environmental entities.

Functional Genomics and Cell Biology of the Dolphin (Tursiops runcatus): Establishment of Novel Molecular Tools to Study Marine Mammals in Changing Environments

The dolphin (Tursiops truncatus) is a mammal that is adapted to life in a totally aquatic environment. Despite the popularity and even iconic status of the dolphin, our knowledge of its physiology, its unique adaptations and the effects on it of environmental stressors are limited. One approach to improve this limited understanding is the implementation of established cellular and molecular methods to provide sensitive and insightful information for dolphin biology. We initiated our studies with the analysis of wild dolphin peripheral blood leukocytes, which have the potential to be informative of the animal’s global immune status. Transcriptomic profiles from almost 200 individual samples were analyzed using a newly developed species-specific microarray to assess its value as a prognostic and diagnostic tool. Functional genomics analyses were informative of stress-induced gene expression profiles and also of geographical location specific transcriptomic signatures, determined by the interaction of genetic, disease and environmental factors. We have developed quantitative metrics to unambiguously characterize the phenotypic properties of dolphin cells in culture. These quantitative metrics can provide identifiable characteristics and baseline data which will enable identification of changes in the cells due to time in culture. We have also developed a novel protocol to isolate primary cultures from cryopreserved tissue of stranded marine mammals, establishing a tissue (and cell) biorepository, a new approach that can provide a solution to the limited availability of samples. The work presented represents the development and application of tools for the study of the biology, health and physiology of the dolphin, and establishes their relevance for future studies of the impact on the dolphin of environmental infection and stress.

Semantic Service Architectures for Smart Environments

Many industries and academic institutions share the vision that an appropriate use of information originated from the environment may add value to services in multiple domains and may help humans in dealing with the growing information overload which often seems to jeopardize our life. It is also clear that information sharing and mutual understanding between software agents may impact complex processes where many actors (humans and machines) are involved, leading to relevant socioeconomic benefits. Starting from these two input, architectural and technological solutions to enable “environment-related cooperative digital services” are here explored. The proposed analysis starts from the consideration that our environment is physical space and here diversity is a major value. On the other side diversity is detrimental to common technological solutions, and it is an obstacle to mutual understanding. An appropriate environment abstraction and a shared information model are needed to provide the required levels of interoperability in our heterogeneous habitat. This thesis reviews several approaches to support environment related applications and intends to demonstrate that smart-space-based, ontology-driven, information-sharing platforms may become a flexible and powerful solution to support interoperable services in virtually any domain and even in cross-domain scenarios. It also shows that semantic technologies can be fruitfully applied not only to represent application domain knowledge. For example semantic modeling of Human-Computer Interaction may support interaction interoperability and transformation of interaction primitives into actions, and the thesis shows how smart-space-based platforms driven by an interaction ontology may enable natural ad flexible ways of accessing resources and services, e.g, with gestures. An ontology for computational flow execution has also been built to represent abstract computation, with the goal of exploring new ways of scheduling computation flows with smart-space-based semantic platforms.

Applicability of Process Mining Techniques in Business Environments

This thesis analyses problems related to the applicability, in business environments, of Process Mining tools and techniques. The first contribution is a presentation of the state of the art of Process Mining and a characterization of companies, in terms of their "process awareness". The work continues identifying circumstance where problems can emerge: data preparation; actual mining; and results interpretation. Other problems are the configuration of parameters by not-expert users and computational complexity. We concentrate on two possible scenarios: "batch" and "on-line" Process Mining. Concerning the batch Process Mining, we first investigated the data preparation problem and we proposed a solution for the identification of the "case-ids" whenever this field is not explicitly indicated. After that, we concentrated on problems at mining time and we propose the generalization of a well-known control-flow discovery algorithm in order to exploit non instantaneous events. The usage of interval-based recording leads to an important improvement of performance. Later on, we report our work on the parameters configuration for not-expert users. We present two approaches to select the "best" parameters configuration: one is completely autonomous; the other requires human interaction to navigate a hierarchy of candidate models. Concerning the data interpretation and results evaluation, we propose two metrics: a model-to-model and a model-to-log. Finally, we present an automatic approach for the extension of a control-flow model with social information, in order to simplify the analysis of these perspectives. The second part of this thesis deals with control-flow discovery algorithms in on-line settings. We propose a formal definition of the problem, and two baseline approaches. The actual mining algorithms proposed are two: the first is the adaptation, to the control-flow discovery problem, of a frequency counting algorithm; the second constitutes a framework of models which can be used for different kinds of streams (stationary versus evolving).