Multi-level Contextual Type Theory

Contextual type theory distinguishes between bound variables and meta-variables to write potentially incomplete terms in the presence of binders. It has found good use as a framework for concise explanations of higher-order unification, characterize holes in proofs, and in developing a foundation for programming with higher-order abstract syntax, as embodied by the programming and reasoning environment Beluga. However, to reason about these applications, we need to introduce meta^2-variables to characterize the dependency on meta-variables and bound variables. In other words, we must go beyond a two-level system granting only bound variables and meta-variables. In this paper we generalize contextual type theory to n levels for arbitrary n, so as to obtain a formal system offering bound variables, meta-variables and so on all the way to meta^n-variables. We obtain a uniform account by collapsing all these different kinds of variables into a single notion of variabe indexed by some level k. We give a decidable bi-directional type system which characterizes beta-eta-normal forms together with a generalized substitution operation.Comment: In Proceedings LFMTP 2011, arXiv:1110.668

Cross-National Differences in Victimization : Disentangling the Impact of Composition and Context

Varying rates of criminal victimization across countries are assumed to be the outcome of countrylevel structural constraints that determine the supply ofmotivated o¡enders, as well as the differential composition within countries of suitable targets and capable guardianship. However, previous empirical tests of these ‘compositional’ and ‘contextual’ explanations of cross-national di¡erences have been performed upon macro-level crime data due to the unavailability of comparable individual-level data across countries. This limitation has had two important consequences for cross-national crime research. First, micro-/meso-level mechanisms underlying cross-national differences cannot be truly inferred from macro-level data. Secondly, the e¡ects of contextual measures (e.g. income inequality) on crime are uncontrolled for compositional heterogeneity. In this paper, these limitations are overcome by analysing individual-level victimization data across 18 countries from the International CrimeVictims Survey. Results from multi-level analyses on theft and violent victimization indicate that the national level of income inequality is positively related to risk, independent of compositional (i.e. micro- and meso-level) di¡erences. Furthermore, crossnational variation in victimization rates is not only shaped by di¡erences in national context, but also by varying composition. More speci¢cally, countries had higher crime rates the more they consisted of urban residents and regions with lowaverage social cohesion.

Offline and online data: on upgrading functional information to knowledge

This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories

Optimal No-regret Learning in Repeated First-price Auctions

We study online learning in repeated first-price auctions with censored feedback, where a bidder, only observing the winning bid at the end of each auction, learns to adaptively bid in order to maximize her cumulative payoff. To achieve this goal, the bidder faces a challenging dilemma: if she wins the bid--the only way to achieve positive payoffs--then she is not able to observe the highest bid of the other bidders, which we assume is iid drawn from an unknown distribution. This dilemma, despite being reminiscent of the exploration-exploitation trade-off in contextual bandits, cannot directly be addressed by the existing UCB or Thompson sampling algorithms in that literature, mainly because contrary to the standard bandits setting, when a positive reward is obtained here, nothing about the environment can be learned. In this paper, by exploiting the structural properties of first-price auctions, we develop the first learning algorithm that achieves $O(\sqrt{T}\log^2 T)$ regret bound when the bidder's private values are stochastically generated. We do so by providing an algorithm on a general class of problems, which we call monotone group contextual bandits, where the same regret bound is established under stochastically generated contexts. Further, by a novel lower bound argument, we characterize an $\Omega(T^{2/3})$ lower bound for the case where the contexts are adversarially generated, thus highlighting the impact of the contexts generation mechanism on the fundamental learning limit. Despite this, we further exploit the structure of first-price auctions and develop a learning algorithm that operates sample-efficiently (and computationally efficiently) in the presence of adversarially generated private values. We establish an $O(\sqrt{T}\log^3 T)$ regret bound for this algorithm, hence providing a complete characterization of optimal learning guarantees for this problem

Two-letter words and a fundamental homomorphism ruling geometric contextuality

It has recently been recognized by the author that the quantum contextuality paradigm may be formulated in terms of the properties of some subgroups of the two-letter free group $G$ and their corresponding point-line incidence geometry $\mathcal{G}$. I introduce a fundamental homomorphism $f$ mapping the (infinitely many) words of G to the permutations ruling the symmetries of $\mathcal{G}$. The substructure of $f$ is revealing the essence of geometric contextuality in a straightforward way.Comment: 18 pages, 11 figures, 2 tables to appear in "Symmetry: Culture and Science

Dialectics and difference: against Harvey's dialectical post-Marxism

David Harvey`s recent book, Justice, nature and the geography of difference (JNGD), engages with a central philosophical debate that continues to dominate human geography: the tension between the radical Marxist project of recent decades and the apparently disempowering relativism and `play of difference' of postmodern thought. In this book, Harvey continues to argue for a revised `post-Marxist' approach in human geography which remains based on Hegelian-Marxian principles of dialectical thought. This article develops a critique of that stance, drawing on the work of Jacques Derrida, Gilles Deleuze and Felix Guattari. I argue that dialectical thinking, as well as Harvey's version of `post-Marxism', has been undermined by the wide-ranging `post-' critique. I suggest that Harvey has failed to appreciate the full force of this critique and the implications it has for `post-Marxist' ontology and epistemology. I argue that `post-Marxism', along with much contemporary human geography, is constrained by an inflexible ontology which excessively prioritizes space in the theory produced, and which implements inflexible concepts. Instead, using the insights of several `post-' writers, I contend there is a need to develop an ontology of `context' leading to the production of `contextual theories'. Such theories utilize flexible concepts in a multilayered understanding of ontology and epistemology. I compare how an approach which produces a `contextual theory' might lead to more politically empowering theory than `post-Marxism' with reference to one of Harvey's case studies in JNGD