The study of nonmonotonic logics is one mayor field of Artificial Intelligence (AI). The reason why such kind of formalisms are so attractive to model human reasoning is that they allow to withdraw former conclusion. At the end of the 1980s the novel idea of using argumentation to model nonmonotonic reasoning emerged in AI. Nowadays argumentation theory is a vibrant research area in AI, covering aspects of knowledge representation, multi-agent systems, and also philosophical questions. Phan Minh Dung’s abstract argumentation frameworks (AFs) play a dominant role in the field of argumentation. In AFs arguments and attacks between them are treated as primitives, i.e. the internal structure of arguments is not considered. The major focus is on resolving conflicts. To this end a variety of semantics have been defined, each of them specifying acceptable sets of arguments, so-called extensions, in a particular way. Although, Dung-style AFs are among the simplest argumentation systems one can think of, this approach is still powerful. It can be seen as a general theory capturing several nonmonotonic formalisms as well as a tool for solving well-known problems as the stable-marriage problem. This thesis is mainly concerned with the investigation of metalogical properties of Dung’s abstract theory. In particular, we provide cardinality, monotonicity and splitting results as well as characterization theorems for equivalence notions. The established results have theoretical and practical gains. On the one hand, they yield deeper theoretical insights into how this nonmonotonic theory works, and on the other the obtained results can be used to refine existing algorithms or even give rise to new computational procedures. A further main part is the study of problems regarding dynamic aspects of abstract argumentation. Most noteworthy we solve the so-called enforcing and the more general minimal change problem for a huge number of semantics.

The study of nonmonotonic logics is one mayor field of Artificial Intelligence (AI). The reason why such kind of formalisms are so attractive to model human reasoning is that they allow to withdraw former conclusion. At the end of the 1980s the novel idea of using argumentation to model nonmonotonic reasoning emerged in AI. Nowadays argumentation theory is a vibrant research area in AI, covering aspects of knowledge representation, multi-agent systems, and also philosophical questions. Phan Minh Dung’s abstract argumentation frameworks (AFs) play a dominant role in the field of argumentation. In AFs arguments and attacks between them are treated as primitives, i.e. the internal structure of arguments is not considered. The major focus is on resolving conflicts. To this end a variety of semantics have been defined, each of them specifying acceptable sets of arguments, so-called extensions, in a particular way. Although, Dung-style AFs are among the simplest argumentation systems one can think of, this approach is still powerful. It can be seen as a general theory capturing several nonmonotonic formalisms as well as a tool for solving well-known problems as the stable-marriage problem. This thesis is mainly concerned with the investigation of metalogical properties of Dung’s abstract theory. In particular, we provide cardinality, monotonicity and splitting results as well as characterization theorems for equivalence notions. The established results have theoretical and practical gains. On the one hand, they yield deeper theoretical insights into how this nonmonotonic theory works, and on the other the obtained results can be used to refine existing algorithms or even give rise to new computational procedures. A further main part is the study of problems regarding dynamic aspects of abstract argumentation. Most noteworthy we solve the so-called enforcing and the more general minimal change problem for a huge number of semantics.

Magistrinio darbo problematikos formulavimas vadovaujasi prielaida, jog dalis moderniosios filosofijos projektų formavosi kaip reakcija į Vakarų Europos mąstymo tradiciją, kurios formuojantį pagrindą sudarė filosofija. Dėl šios priežasties neatsiejamu šių projektų egzistavimo požymiu laikytina nuosekli filosofijos istorijos kritika, tuo pačiu pateikianti alternatyvius filosofijos supratimo orientyrus. Tokiu radikaliu filosofijos sąjūdžiu, XX a. laikomas egzistencializmas. Magistriniam darbui pasirinktos dvi filosofų figūros: Rosenzweigas ir Heideggeris. Abu filosofai kritiškai reflektavo filosofijos istoriją bei abu pateikė alternatyvius mąstymo projektus. Pagrindiniu Vakarų tradicijos kritikos bei naujo mąstymo suformulavimo svarbiausiu aspektu laikome fundamentalų „pirminių mąstymo prielaidų” perklausimą. Atlikęs tokį perklausimą bei taip atsiribojęs nuo „mąstymo metafizikos”, Rosenzweigas susikuria naujas prieigas prie tikėjimo problematikos. Panaudodamas Johano Wolfgango Geothes profenomeno sampratos bei savo mokytojo – Hermanno Coheno diferencialinės matematikos teorijos idėjas, jis pateikia trijų (metafizinio Dievo, metaloginio pasaulio ir metaetinio žmogaus) profenomenų aprašymą. Metaetinio žmogaus sąmonės struktūros gretinimas su „naujojo mąstymo” (tokį pavadinimą Rosenzweigas pats prisiskiria savo filosofijai) pirminėmis prielaidomis, atveda prie dialoginės (Zwiesprache) apreiškimo (Offenbarung) sąmonės struktūros aprašymo. Tik apreiškimo sąmonei atsiveria pirmapradė... [toliau žr. visą tekstą] / The formulation of theme in this paper is followed the assumption that a part of projects of modern philosophy were generated as a reaction to the tradition of Western Europe thinking, which was influenced by philosophy. That is the reason why coherent criticism of history of philosophy, in the same time giving the perception guides of philosophy, is considered as a concurrent attribute of that project existence. Existentialism of the 20th century is considered as such radical movement of philosophy. Two philosophical figures were chosen from this general context: Rosenzweig and Heidegger. Both thinkers made critical reflections on history of philosophy and both give the alternative projects of thinking. The fundamental reasking of „prime thought assumptions” is considered as an important aspect of main criticism of Western tradition and the formulation of new thinking. After this performed reasking and disassociation from “metaphysics of thought”, Rosenzweig creates new approaches to the faith theme. Using the prophenomenon perception of Johan Wolfgang Geothe and his teachers, Herman Cohen’s ideas about diferencial mathematics theory, he presents description of three prophenomenon (metaphysical God, metalogical world and metaethical man). The comparison of consequence’s structure of metaethical man with prime assumptions of “new thought” (this definition Rosenzweig attributes to his own philosophy) leads to description of dialogical (Zwiesprache) revelational (Offenbarung)... [to full text]