A recent paper by Jakl, Jung and Pultr succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We (...) provide product representation theorems for these algebras, as well as completeness, algebraizability results for the corresponding logics. (shrink)

We develop a Priestley-style duality theory for different classes of algebras having a bilattice reduct. A similar investigation has already been realized by B. Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis, but only from an abstract category-theoretic point of view. In the present work we are instead interested in a concrete study of the topological spaces that correspond to bilattices and some related algebras that are obtained through expansions of the algebraic language.

As false information may spread rapidly on social media, a profound understanding of how it can be debunked is required. This study offers empirical insights into the development of rumors after they are debunked, the various user groups who are involved in the process, and their network structures. As crisis situations are highly sensitive to the spread of rumors, Twitter posts from during the 2017 G20 summit are examined. Tweets regarding five rumors that were debunked during this event were manually (...) coded into the following categories: rumor, debunking message, uncertainty about rumor, uncertainty about debunking message, and others. Our findings show that rumors which are debunked early and vehemently by official sources are the most likely to be stopped. When individuals participate in the process, they typically do so by sharing uncommented media content, as opposed to contributing user-generated content. Depending on the conditions in which a rumor arises, different network structures can be found. Since some rumors are easier for individuals to verify than others, our results have implications for the priorities of journalists and official sources. (shrink)