Observações sobre geometria sintética

Pós-graduação em Matemática em Rede Nacional - IBILCE

Uma introdução à geometria esférica

Pós-graduação em Matemática em Rede Nacional - IBILCE

Introdução a ontologias e suas aplicações

Different vocabularies and contexts are barriers to the communication between people or software systems. It is necessary a common understanding in the domain that is talked about, so it can be obtained a correct interpretation of the information. An ontology formally models the structure of a domain and turn explicit the shared understanding in the form of concepts and relations that emerge from its observation. Constitutes a sort of framework used in the mapping to the meaning of the information that is talked about. The formal accuracy in which they are defined, by means of axioms, allow machine processing, implicating in systems interoperability. Structured this way, the knowledge is easily transferred between people or systems from different contexts. Ontologies present several applications nowadays. They are considered the infra-structure to the Semantic Web, which is composed by Web resources with embedded meaning. Thereby, the automatic execution of complex tasks is allowed, with the benefit from the effective communication between Web software agents. Among other applications, they also have been used to structure the knowledge generated from several areas, like Biology and Software Engineering.

Origamic design: uma nova forma de desenvolver produtos

During a long time, origami was associated with decoration and craft production of ornaments and figures. However, in the end of 20th century, it began to be studied by mathematicians who were looking for interrelationships between this art and science. Through disciplines like geometry, trigonometry, calculation and linear algebra, they generated a set of axioms and theorems that became possible specific conversion of origami in computational geometry and the development of several softwares. Thus, origami began to be applied in engineering and design studies of innovative product and the term “origamics” was created to demonstrate its interdisciplinary nature. In this article will be presented some works exploring the constructive principles of origami to contribute with the diffusion of origamics. In this way more professionals will be able to understand the scientific and technological potential of this art.

Rotações no espaço tridimensional por meio de produtos quaterniônicos

Pós-graduação em Matemática Universitária - IGCE

On universal Banach spaces of density continuum

We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a""(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a""(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C([0, c]) into a""(a)/c (0).

An architecture for scaling ontology networks

Constructing ontology networks typically occurs at design time at the hands of knowledge engineers who assemble their components statically. There are, however, use cases where ontology networks need to be assembled upon request and processed at runtime, without altering the stored ontologies and without tampering with one another. These are what we call "virtual [ontology] networks", and keeping track of how an ontology changes in each virtual network is called "multiplexing". Issues may arise from the connectivity of ontology networks. In many cases, simple flat import schemes will not work, because many ontology managers can cause property assertions to be erroneously interpreted as annotations and ignored by reasoners. Also, multiple virtual networks should optimize their cumulative memory footprint, and where they cannot, this should occur for very limited periods of time. We claim that these problems should be handled by the software that serves these ontology networks, rather than by ontology engineering methodologies. We propose a method that spreads multiple virtual networks across a 3-tier structure, and can reduce the amount of erroneously interpreted axioms, under certain raw statement distributions across the ontologies. We assumed OWL as the core language handled by semantic applications in the framework at hand, due to the greater availability of reasoners and rule engines. We also verified that, in common OWL ontology management software, OWL axiom interpretation occurs in the worst case scenario of pre-order visit. To measure the effectiveness and space-efficiency of our solution, a Java and RESTful implementation was produced within an Apache project. We verified that a 3-tier structure can accommodate reasonably complex ontology networks better, in terms of the expressivity OWL axiom interpretation, than flat-tree import schemes can. We measured both the memory overhead of the additional components we put on top of traditional ontology networks, and the framework's caching capabilities.

Interpreting Judgements using Knowledge Representation Methods and Computational Models of Argument

The goal of the present research is to define a Semantic Web framework for precedent modelling, by using knowledge extracted from text, metadata, and rules, while maintaining a strong text-to-knowledge morphism between legal text and legal concepts, in order to fill the gap between legal document and its semantics. The framework is composed of four different models that make use of standard languages from the Semantic Web stack of technologies: a document metadata structure, modelling the main parts of a judgement, and creating a bridge between a text and its semantic annotations of legal concepts; a legal core ontology, modelling abstract legal concepts and institutions contained in a rule of law; a legal domain ontology, modelling the main legal concepts in a specific domain concerned by case-law; an argumentation system, modelling the structure of argumentation. The input to the framework includes metadata associated with judicial concepts, and an ontology library representing the structure of case-law. The research relies on the previous efforts of the community in the field of legal knowledge representation and rule interchange for applications in the legal domain, in order to apply the theory to a set of real legal documents, stressing the OWL axioms definitions as much as possible in order to enable them to provide a semantically powerful representation of the legal document and a solid ground for an argumentation system using a defeasible subset of predicate logics. It appears that some new features of OWL2 unlock useful reasoning features for legal knowledge, especially if combined with defeasible rules and argumentation schemes. The main task is thus to formalize legal concepts and argumentation patterns contained in a judgement, with the following requirement: to check, validate and reuse the discourse of a judge - and the argumentation he produces - as expressed by the judicial text.

A syntactic realization theorem for justification logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms \$mathsfd\$, \$mathsft\$, \$mathsfb\$, \$mathsf4\$, and \$mathsf5\$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for \$mathsfKB5\$ and \$mathsfS5\$ by showing that the positive introspection operator is superfluous.

Bayesian Approach to Spectral Function Reconstruction for Euclidean Quantum Field Theories

We present a novel approach to the inference of spectral functions from Euclidean time correlator data that makes close contact with modern Bayesian concepts. Our method differs significantly from the maximum entropy method (MEM). A new set of axioms is postulated for the prior probability, leading to an improved expression, which is devoid of the asymptotically flat directions present in the Shanon-Jaynes entropy. Hyperparameters are integrated out explicitly, liberating us from the Gaussian approximations underlying the evidence approach of the maximum entropy method. We present a realistic test of our method in the context of the nonperturbative extraction of the heavy quark potential. Based on hard-thermal-loop correlator mock data, we establish firm requirements in the number of data points and their accuracy for a successful extraction of the potential from lattice QCD. Finally we reinvestigate quenched lattice QCD correlators from a previous study and provide an improved potential estimation at T2.33TC.