Title from title page of PDF (University of Missouri--St. Louis, viewed March 22, 2010). Includes bibliographical references.

A filosofia, para Hegel, é o saber conceitual que se pensa e pensa sua época, sendo esse saber resultado do processo de desenvolvimento histórico e cultural do mundo. Nesse sentido, a Fenomenologia do Espírito é a apresentação necessária do movimento de formação do saber que surgiu na época de Hegel, o qual ele denomina de saber absoluto. Esse é o resultado do percurso que culminou na Revolução Francesa, na religião protestante e na filosofia do idealismo transcendental, e a Fenomenologia apresenta esse encadeamento através de suas figuras, isto é, momentos da história, da cultura e da filosofia tomados a partir de sua perspectiva conceitual e conectados de forma a demonstrar as transformações do saber ele mesmo. A partir disso, Hegel denomina o saber absoluto como última figura do espírito, que, como ele aponta no final da obra, também é a nova figura, a filosofia como ciência, e se propõe a desenvolvê-la naquilo que ele chama de Ciência da Lógica. Desse modo, o objetivo desse ou, em outras palavras, se é possível, a partir do próprio sistema hegeliano, considerar o surgimento de novas figuras do espírito depois da figura do saber absoluto ou da filosofia do idealismo absoluto. Para isso, busca-se esclarecer a noção de figura na Fenomenologia, bem como suas condições de possibilidade e aquilo que Hegel utiliza como o seu método científico, a saber, o processo dialético, explicitado na noção de suprassunção (Aufhebung). A fim de esclarecer essas noções de modo mais preciso, recorre-se a noções da Ciência da Lógica e retorna-se à Fenomenologia a partir deles, de modo a compreendê-los de maneira concreta e de salientar os aspectos lógicos já presentes nessa obra. Para isso, procurase demonstrar aqui que a Lógica hegeliana não é apenas uma ciência formal, como a metafísica tradicional usualmente considera, mas também uma ontologia, um estudo de como o ser é. Para Hegel, o ser é o conceito e por isso se pode ter um saber conceitual, como o saber absoluto, acerca da realidade e ele ser um saber efetivo, isto é, um conhecimento das coisas como elas são nelas mesmas, e não apenas como elas aparecem para nós segundo nossas condições de possibilidade da experiência, como tenta mostrar o idealismo transcendental de Kant. Por isso, este trabalho defende que a ontologia hegeliana não é nem um retorno à metafísica tradicional, nem uma radicalização dessa, mas uma apropriação de seus conceitos revistos sob a óptica das novas lentes do saber absoluto, um saber qualitativamente diferente dos saberes anteriores e que, precisamente por isso, permitiria a continuação e atualização desse saber de acordo com novos momentos históricos e culturais. / For Hegel, philosophy is the conceptual knowing that is thought about and thinks about its time. This knowing derives from the process of historical and cultural development of the world. Thus, the Phenomenology of Spirit is the necessary presentation of the movement of knowledge acquisition that arose in Hegel's time, which he calls absolute knowing. This is the result of the path that climaxed in the French Revolution, in the Protestant religion and in the philosophy of transcendental idealism. The Phenomenology presents this chaining through its figures, that is, moments of history, of culture and of philosophy taken from their conceptual perspective and connected in order to demonstrate the transformations of knowing itself. Based on this, Hegel considers absolute knowing the last figure of spirit, which, as he points out at the end of the work, is also the new figure, philosophy as science, and proposes to develop it in what he calls the Science of Logic. Therefore, this study aims to investigate in what sense one can understand the determination of figure of or, in other words, if it is possible, based on the Hegelian system itself, to consider the emergence of new figures of spirit after the figure of absolute knowing or of the philosophy of absolute idealism. In order to do so, it seeks to clarify the notion of figure in the Phenomenology, as well as its conditions of possibility and what Hegel uses as his scientific method, namely, the dialectical process, explicit in the notion of sublation. In order to more precisely clarify these notions, notions from the Science of Logic are used and a return to the Phenomenology is made based on them, so as to understand them in a concrete way and to emphasize the logical aspects already present in this work. To this end, here we try to demonstrate that the Hegelian Logic is not only a formal science, as traditional metaphysics usually considers it to be, but also an ontology, a study of how the being is. For Hegel, the being is the concept and therefore it is possible to have a conceptual knowing, such as the absolute knowing, about reality, and it can be an actual knowing, that is, a knowledge of things as they are in themselves and not only as they appear to us according to our conditions of possibility of experience, as transcendental idealism attempts to show us. Therefore, this study argues that the Hegelian ontology is neither a return to traditional metaphysics nor a radicalization of this metaphysics, but an appropriation of its concepts revised under the new lenses of absolute knowing, a knowing that is qualitatively different from previous types of knowing and that, precisely for this reason, would allow the continuation and updating of this knowing according to new historical and cultural moments.

Unification in Description Logics has been introduced as a means to detect redundancies in ontologies. We try to extend the known decidability results for unification in the Description Logic EL to disunification since negative constraints on unifiers can be used to avoid unwanted unifiers. While decidability of the solvability of general EL-disunification problems remains an open problem, we obtain NP-completeness results for two interesting special cases: dismatching problems, where one side of each negative constraint must be ground, and local solvability of disunification problems, where we restrict the attention to solutions that are built from so-called atoms occurring in the input problem. More precisely, we first show that dismatching can be reduced to local disunification, and then provide two complementary NP-algorithms for finding local solutions of (general) disunification problems.

Unification in Description Logics has been proposed as a novel inference service that can, for example, be used to detect redundancies in ontologies. The inexpressive Description Logic EL is of particular interest in this context since, on the one hand, several large biomedical ontologies are defined using EL. On the other hand, unification in EL has recently been shown to be NP-complete, and thus of considerably lower complexity than unification in other DLs of similarly restricted expressive power. However, EL allows the use of the top concept (>), which represents the whole interpretation domain, whereas the large medical ontology SNOMEDCT makes no use of this feature. Surprisingly, removing the top concept from EL makes the unification problem considerably harder. More precisely, we will show that unification in EL without the top concept is PSpace-complete. / This is an updated version of the original report that includes Appendix A on locality of unifiers.

Ontology-based access to large data-sets has recently gained a lot of attention. To access data e_ciently, one approach is to rewrite the ontology into Datalog, and then use powerful Datalog engines to compute implicit entailments. Existing rewriting techniques support Description Logics (DLs) from ELH to Horn-SHIQ. We go one step further and present one such data-independent rewriting technique for Horn-SRIQ⊓, the extension of Horn-SHIQ that supports role chain axioms, an expressive feature prominently used in many real-world ontologies. We evaluated our rewriting technique on a large known corpus of ontologies. Our experiments show that the resulting rewritings are of moderate size, and that our approach is more efficient than state-of-the-art DL reasoners when reasoning with data-intensive ontologies. / This is an extended version of the article to appear in the proceedings of AAAI 2019.