We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
Cognitive functions like perception, memory, language, or consciousness are based on highly parallel and distributed information processing by the brain. One of the major unresolved questions is how information can be integrated and how coherent representational states can be established in the distributed neuronal systems subserving these functions. It has been suggested that this so-called ''binding problem'' may be solved in the temporal domain. The hypothesis is that synchronization of neuronal discharges can serve for the integration of distributed neurons into (...) cell assemblies and that this process may underlie the selection of perceptually and behaviorally relevant information. As we intend to show here, this temporal binding hypothesis has implications for the search of the neural correlate of consciousness. We review experimental results, mainly obtained in the visual system, which support the notion of temporal binding. In particular, we discuss recent experiments on the neural mechanisms of binocular rivalry which suggest that appropriate synchronization among cortical neurons may be one of the necessary conditions for the buildup of perceptual states and awareness of sensory stimuli. (shrink)
We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly -game-closed forcings. PFA can be destroyed by a strongly -game-closed forcing but not by an ω2-closed.
We show that strongly compact cardinals and MM are sensitive to $\lambda$-closed forcings for arbitrarily large $\lambda$. This is done by adding ‘regressive' $\lambda$-Kurepa trees in either case. We argue that the destruction of regressive Kurepa trees requires a non-standard application of MM. As a corollary, we find a consistent example of an $\omega_2$-closed poset that is not forcing equivalent to any $\omega_2$-directed-closed poset.
We argue that brains generate predictions only within the constraints of the action repertoire. This makes the computational complexity tractable and fosters a step-by-step parallel development of sensory and motor systems. Hence, it is more of a benefit than a literal constraint and may serve as a universal normative principle to understand sensorimotor coupling and interactions with the world.
Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Lévy collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to א₁. Later we give applications, among them the consistency of MM with אω not being Jónsson which answers a question raised in the set theory meeting at Oberwolfach in 2005.
This paper gives a simple method for providing categorial brands of feature-based unification grammars with a model-theoretic semantics. The key idea is to apply the paradigm of fibred semantics (or layered logics, see Gabbay (1990)) in order to combine the two components of a feature-based grammar logic. We demonstrate the method for the augmentation of Lambek categorial grammar with Kasper/Rounds-style feature logic. These are combined by replacing (or annotating) atomic formulas of the first logic, i.e. the basic syntactic types, by (...) formulas of the second. Modelling such a combined logic is less trivial than one might expect. The direct application of the fibred semantics method where a combined atomic formula like np (num: sg & pers: 3rd) denotes those strings which have the indicated property and the categorial operators denote the usual left- and right-residuals of these string sets, does not match the intuitive, unification-based proof theory. Unification implements a global bookkeeping with respect to a proof whereas the direct fibring method restricts its view to the atoms of the grammar logic. The solution is to interpret the (embedded) feature terms as global feature constraints while maintaining the same kind of fibred structures. For this adjusted semantics, the anticipated proof system is sound and complete. (shrink)
The neuroscientific naturalism poses a challenge to any philosophical attempt to determine human nature. Although the neurosciences describe the cognitive capacities of human beings as something that is socially acquired, they lack adequate reflection on the social forms in which these capacities emerge and thereby tend to naturalize not only human beings, but society as a whole. In an attempt to find alternatives to the neuroscientific naturalism, the authors refer to the traditions of Critical Theory and psychoanalysis, which enable a (...) different understanding of human nature. This is followed by the debate between Honneth and Whitebook on the question of an anti- or pre-social self, and in reference to Adorno and Lorenzer, the authors develop a concept of second nature that allows them to adhere to the dynamics of the material nature and sociality within the human subject. (shrink)
We characterize the tree of functions with finite support in terms of definability. This turns out to have various applications: a new kind of tree dichotomy for ω1 on the one hand. On the other hand, we prove a reflection principle for trees on ω2 under SPFA. This reflection of trees implies stationary reflection.