Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations. Explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all the known results on definable functions of certain such theories can be reobtained in a uniform way.

Consider the following restriction of the polymorphically typed lambda calculus . All quantifications are parameter free. In other words, in every universal type α.τ, the quantified variable α is the only free variable in the scope τ of the quantification. This fragment can be locally proven terminating in a system of intuitionistic second-order arithmetic known to have strength of finitely iterated inductive definitions.

Defining a composition operation on sets of formulas one obtains a many-sorted algebra which satisfies the superassociative law and one more identity. This algebra is called the clone of formulas of the given type. The interpretations of formulas on an algebraic system of the same type form a many-sorted algebra with similar properties. The satisfaction of a formula by an algebraic system defines a Galois connection between classes of algebraic systems of the same type and collections of formulas. Hypersubstitutions are (...) mappings sending pairs of operation symbols to pairs of terms of the corresponding arities and relation symbols to formulas of the same arities. Using hypersubstitutions we define hyperformulas. Satisfaction of a hyperformula by an algebraic system defines a second Galois connection between classes of algebraic systems of the same type and collections of formulas. A class of algebraic systems is said to be solid if every formula which is satisfied is also satisfied as a hyperformula. On the basis of these two Galois connections we construct a conjugate pair of additive closure operators and are able to characterize solid classes of algebraic systems. (shrink)

The article argues that the ‘crisis of Europe’, triggered by market and governance dysfunctionalities (summarized as the Euro crisis), represents a ‘critical moment’ in the evolution of a European society. This society so far does not offer much resistance to such critical moments which is due to its incapacity to form a demos capable of acting together. The existing European society – and this is the basic claim – is nothing but the sum of individuals living in ‘sub-European’ (mainly national) (...) groups. The evolution triggered by this critical situation opens pathways to turn these peoples of Europe into something more than being a sum of peoples governed by supranational bureaucracies. To decipher such processes a model is presented using Hirschman’s idea of exit, voice and loyalty as mechanisms to generate social ties. Two points arise as crucial. The first is the observation that national societies which continue to provide foundational claims for people have turned into interest groups in the context of the European Union. This undermines not only the ontological nationalism still dominating the self-presentation of national societies in Europe, but it also offers evolutionary paths towards a society beyond national foundational claims in Europe. Yet it also provokes reactive processes such as the return to the self-contained nation (or even ethnic group). This is the core of the crisis of Europe. The systemic crises of the state and the market in Europe are speeding up an evolutionary process of people-making, the outcome of which could be either the regression to a people with foundational identities or to a people without foundational identities. The latter will be described as a postnational society, which would make an emerging European society the first really modern society. (shrink)

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order (...) to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely. (shrink)

Eusociality is the form of animal social organization with a reproductive division of labor, most prominently known from ants and bees. Here I ask the question why this enormously successful form of social organization is missing in the largest and most diverse group of vertebrates, the teleost fishes. I first briefly review the phylogenetic distribution and likely evolutionary origins of eusociality. Then, after an equally very brief review of the diverse life history strategies of teleosts, I conclude that it is (...) not the lack of evolutionary pre-adaptations which is keeping teleosts from becoming eusocial. Rather, I argue, that the absence of eusocial fish is caused by a number of differences between aquatic (chiefly marine) and terrestrial ecosystems: (1) Greater offspring dispersal in aquatic ecosystems reduces the role of kin-selection. (2) Lesser predictability of the environment at larger timescales in marine ecosystems disfavors eusociality. (3) A briefer impact of resource pulses in aquatic ecosystems will cause less evolutionary pressure towards cooperation, and eventually eusociality. Finally, I conclude by predicting that the most likely places to find eusocial fishes will be the deep-water regions of the ocean and the African rift lakes. (shrink)

Child psychologist Mallory James returns to Moonglade, the Australian plantation where she was raised, to care for her beloved uncle Robert, who has had a heart attack. Having left the area years earlier after being betrayed by her fiancâe, Jason Cartwright, Mallory is shocked and dismayed to find that Jason and his decidedly disturbed twin sister, Jessica, have been hired on at her uncle's estate. Her longtime friend and occasional adversary, Blaine Forrester, is also nearby. As Mallory settles back into (...) her old home, she can't help but begin to love Jason's feisty young daughter, Ivy. She and Blaine begin to wander down the path of romance, but it's obvious that their happiness won't come easily. (shrink)