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)

In this paper, we intend to discuss if and in what sense semiosis (meaning process, cf. C. S. Peirce) can be regarded as an "emergent" process in semiotic systems. It is not our problem here to answer when or how semiosis emerged in nature. As a prerequisite for the very formulation of these problems, we are rather interested in discussing the conditions which should be fulfilled for semiosis to be characterized as an emergent process. The first step in this work (...) is to summarize a systematic analysis of the variety of emergence theories and concepts, elaborated by Achim Stephan. Along the summary of this analysis, we pose fundamental questions that have to be answered in order to ascribe a precise meaning to the term "emergence" in the context of an understanding of semiosis. After discussing a model for explaining emergence based on Salthe's hierarchical structuralism, which considers three levels at a time in a semiotic system, we present some tentative answers to those questions. (shrink)