Paul and the schismata in I corinthians

This thesis sets out to reconstruct the situation at Corinth, with particular emphasis upon the divisions, at the time of Paul’s writing of I Corinthians (Introduction). An essential component of such a reconstruction, which is presupposed to be necessary for the interpretation of the epistle, is the sociological dimension of the community (Chapter I). Difficulties involved in the reconstruction of the divisions are discussed (largely from a review of proposed interpretations), and a methodology is adopted which lays the principal emphasis upon Chapters 1-4 as the source of information (Chapter II).In the second part, statements of a basically factual nature in I Cor. 1-4 are examined, leading to the preliminary conclusion that a plurality of divisions, centred upon rival leaders, existed, but was possibly not taken seriously at Corinth (Chapter III). The overall development of argument (in I-4) relates the divisions to the theme of human .wisdom, opposed to God's power. Paul views divisions as proof of 'fleshly' dependence on human wisdom, expressed in 'puffed up' behaviour, denying dependence upon God (Chapter IV). Corroborative evidence of Paul's strategy of attacking false wisdom at the root of all divisiveness, rather than particular parties, is provided by stylistically prominent indications of purpose (e.g. imperatives, purpose clauses). Paul's claim to unique authority and responsibility is an attempt to transcend divisions (Chapter V).In the third part (Chapter VI), the conclusions from I Cor. 1-4 are tested against relevant sections of I Cor. 5-16. The evidence confirms the overall conclusion of a diversity of tensions within the community, producing, within a vacuum of authority, divisions centred upon leaders. Paul appeals for a voluntary surrender of rights and freedom, in consideration for others, and for the building up of the community (Conclusion)

Set-valued mapping and Rough Probability

In 1982, the theory of rough sets proposed by Pawlak and in 2013, Luay concerned a rough probability by using the notion of Topology. In this paper, we study the rough probability in the stochastic approximation spaces by using set-valued mapping and obtain results on rough expectation, and rough variance.Comment: 9 page

Rough matroids based on coverings

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algorithm design and combinatorial optimization. An excellent introduction to the topic of rough matroids is due to Zhu and Wang. On the basis of their work, we study the rough matroids based on coverings in this paper. First, we investigate some properties of the definable sets with respect to a covering. Specifically, it is interesting that the set of all definable sets with respect to a covering, equipped with the binary relation of inclusion $\subseteq$, constructs a lattice. Second, we propose the rough matroids based on coverings, which are a generalization of the rough matroids based on relations. Finally, some properties of rough matroids based on coverings are explored. Moreover, an equivalent formulation of rough matroids based on coverings is presented. These interesting and important results exhibit many potential connections between rough sets and matroids.Comment: 15page