This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning.

In online social media systems users are not only posting, consuming, and sharing content, but also creating new and destroying existing connections in the underlying social network. This behavior lead us to investigate how user structural position reacts with the evolution of the underlying social network structure. While centrality metrics have been studied in the past, much less is known about their temporal behaviors and processing, mainly when analyzing not just networks snapshots, but interval graphs. Here, we study Twitter follower/followee network and how users centralities evolve over time. Our analysis is founded on temporal graphs theory. First, we model Twitter as a temporal network and revisit the concept of shortest path considering the time dimension. We show how to compute closeness and betweenness centralities using fastest paths. Then, we propose a baseline algorithm for mining streams of temporal networks. The task is to find all pairs fastest paths inside an observation window. We find that Twitter users are fairly dynamic and from one moment to the next, they can assume (or leave) central roles in the network.

When integrating data coming from multiple different sources we are faced with the possibility of inconsistency in databases. In this paper, we use one of the paraconsistent logics introduced in [9, 7] (LFI1) as a logical framework to model possibly inconsistent database instances obtained by integrating different sources. We propose a method based on the sound and complete tableau proof system of LFI1 to treat both the integration process and the evolution of the integrated database submitted to users updates. In order to treat the integrated database evolution, we introduce a kind of generalized database context, the evolutionary databases, which are databases having the capability of storing and manipulating inconsistent information and, at the same time, allowing integrity constraints to change in time. We argue that our approach is sufficiently general and can be applied in most circumstances where inconsistency may arise in databases.

The preferences adopted by individuals are constantly modified as these are driven by new experiences, natural life evolution and, mainly, influence from friends. Studying these temporal dynamics of user preferences has become increasingly important for personalization tasks in information retrieval and recommendation systems domains. However, existing models are too constrained for capturing the complexity of the underlying phenomenon. Online social networks contain rich information about social interactions and relations. Thus, these become an essential source of knowledge for the understanding of user preferences evolution. In this work, we investigate the interplay between user preferences and social networks over time. First, we propose a temporal preference model able to detect preference change events of a given user. Following this, we use temporal networks concepts to analyze the evolution of social relationships and propose strategies to detect changes in the network structure based on node centrality. Finally, we look for a correlation between preference change events and node centrality change events over Twitter and Jam social music datasets. Our findings show that there is a strong correlation between both change events, specially when modeling social interactions by means of a temporal network. Example 3 As example, let us suppose that J ohn posts 4 times about corruption (c), 3 times about sports (s), 2 times about politics ( p) and 1 time about international (i) on time 3. The temporal preferences of John on 3 are: J ohn 3 = {c J ohn 3 s, s J ohn 3 p, p J ohn 3 i, i J ohn 3 securit y, i J ohn 3 education, i J ohn 3 entertainment, i J ohn 3 economy, i J ohn 3

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