Many-Valued Coalgebraic Logic: From Boolean Algebras to Primal Varieties

We study many-valued coalgebraic logics with primal algebras of truth-degrees. We describe a way to lift algebraic semantics of classical coalgebraic logics, given by an endofunctor on the variety of Boolean algebras, to this many-valued setting, and we show that many important properties of the original logic are inherited by its lifting. Then, we deal with the problem of obtaining a concrete axiomatic presentation of the variety of algebras for this lifted logic, given that we know one for the original one. We solve this problem for a class of presentations which behaves well with respect to a lattice structure on the algebra of truth-degrees

Many-valued coalgebraic logic over semi-primal varieties

We study many-valued coalgebraic logics with semi-primal algebras of truth-degrees. We provide a systematic way to lift endofunctors defined on the variety of Boolean algebras to endofunctors on the variety generated by a semi-primal algebra. We show that this can be extended to a technique to lift classical coalgebraic logics to many-valued ones, and that (one-step) completeness and expressivity are preserved under this lifting. For specific classes of endofunctors, we also describe how to obtain an axiomatization of the lifted many-valued logic directly from an axiomatization of the original classical one. In particular, we apply all of these techniques to classical modal logic

Natural dualities for varieties generated by finite positive MV-chains

peer reviewedWe provide a simple natural duality for the varieties generated by the negation- and implication-free reduct of a finite MV-chain. We study these varieties through the dual equivalences thus obtained. For example, we fully characterize their algebraically closed, existentially closed and injective members. We also explore the relationship between this natural duality and Priestley duality in terms of distributive skeletons and Priestley powers

Algebraic and coalgebraic modal logic: From Boolean algebras to semi-primal varieties

We study many-valued variants of modal logic and, more generally, coalgebraic logic, under the assumption that the underlying algebra of truth-degrees is a semi-primal bounded lattice-expansion. Throwing light on the category theoretical relation between the variety generated by such an algebra and the variety of Boolean algebras, we describe multiple adjunctions between these varieties. In particular, we show that the Boolean skeleton functor has two adjoints, both defined by taking certain Boolean powers, and we identify properties of these adjunctions which fully characterize semi-primality of an algebra. Making use of these relations, we show how to lift endofunctors encoding classical coalgebraic logics in order to obtain many-valued counterparts of these logics. We show that one-step completeness, expressivity and finite axiomatizability are preserved under this lifting, and we show that for classical modal logic and similar cases, an axiomatization of the lifted many-valued logic can be directly obtained from an axiomatization of the original logic. Lastly, we develop the theory of natural dualities for varieties generated by finite positive MV-chains and apply this to the algebraic study of the negation-free fragment of bimodal finite Lukasiewicz logic

Rasender Fortschritt in der Arbeitswelt

In der heutigen Gesellschaft haben wir es laufend mit Beschleunigung zu tun: z.B. in der Arbeit, im Privatleben, in der Freizeit. Nachdem es in der Literatur keine eindeutige Definition von Beschleunigung gibt, hat der Soziologe Hartmut Rosa (2005) erste Versuche dahingehend unternommen. Er unterteilt Beschleunigung in drei Dimensionen: technische Beschleunigung, Beschleunigung des sozialen Wandels, Beschleunigung des Lebenstempos. Ziel der vorliegenden Untersuchung war es, einen bestehenden Fragebogen (Forstik, 2010; Pöppl, 2009) zu überarbeiten und in ein anderes Berufsfeld zu übertragen. Der Fragebogen wurde bei einer Stichprobe von 270 FlugbegleiterInnen angewendet. Es wurden Items teilweise übernommen, aber auch neu entwickelt oder umformuliert sowie aus dem Fragebogen ausgeschlossen. Itemanalysen (Reliabilitätsanalyse, CFA) wurden zur Bestimmung der Güte der Items herangezogen. Anschließend wurde überprüft, ob die dreidimensionale Struktur der Beschleunigung bestätigt werden kann. Ergebnisse der CFA zeigten, dass Beschleunigung eine dreidimensionale Struktur aufweist. Letztendlich interessierte noch, ob zwischen der Wahrnehmung von Beschleunigung und Burnout (als Folge der zunehmenden Anforderungen) ein Zusammenhang besteht. Die logistische Regression ergab, dass die Wahrnehmung von Beschleunigung keinen Beitrag zur Vorhersage von Burnout liefert

The Minor Order for Homomorphisms via Natural Dualities

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize the minor homomorphism posets of finite algebras in terms of disjoint unions of dual partition lattices and investigate reconstruction problems for homomorphisms

New perspectives on semi-primal varieties

peer reviewedWe study varieties generated by semi-primal lattice-expansions by means of category theory. We provide a new proof of the Keimel-Werner topological duality for such varieties and, using similar methods, establish its discrete version. We describe multiple adjunctions between the variety of Boolean algebras and the variety generated by a semi-primal lattice-expansion, both on the topological side and explicitly algebraic. In particular, we show that the Boolean skeleton functor has two adjoints, both defined by taking certain Boolean powers, and we identify properties of these adjunctions which fully characterize semi-primality of an algebra. Lastly, we give a new characterization of canonical extensions of algebras in semi-primal varieties in terms of their Boolean skeletons