A Theological Challenge: Coordinating Biological, Social, and Religious Visions of Humanity

This paper attempts two tasks. First, it sketches how the natural sciences (including especially the biological sciences), the social sciences, and the scientific study of religion can be understood to furnish complementary, consonant perspectives on human beings and human groups. This suggests that it is possible to speak of a modern secular interpretation of humanity (MSIH) to which these perspectives contribute (though not without tensions). MSIH is not a comprehensive interpretation of human beings, if only because it adopts a posture of neutrality with regard to the reality of religious objects and the truth of theological claims about them. MSIH is certainly an impressively forceful interpretation, however, and it needs to be reckoned with by any perspective on human life that seeks to insert its truth claims into the arena of public debate. Second, the paper considers two challenges that MSIH poses to specifically theological interpretations of human beings. On the one hand, in spite of its posture of religious neutrality, MSIH is a key element in a class of wider, seemingly antireligious interpretations of humanity, including especially projectionist and illusionist critiques of religion. It is consonance with MSIH that makes these critiques such formidable competitors for traditional theological interpretations of human beings. On the other hand, and taking the religiously neutral posture of MSIH at face value, theological accounts of humanity that seek to coordinate the insights of MSIH with positive religious visions of human life must find ways to overcome or manage such dissonance as arises. The goal of synthesis is defended as important, and strategies for managing these challenges, especially in light of the pluralism of extant philosophical and theological interpretations of human beings, are advocated.

Fixed Point vs. First-Order Logic on Finite Ordered Structures with Unary Relations

We prove that first order logic is strictly weaker than fixed point logic over every infinite classes of finite ordered structures with unary relations: Over these classes there is always an inductive unary relation which cannot be defined by a first-order formula, even when every inductive sentence (i.e., closed formula) can be expressed in first-order over this particular class. Our proof first establishes a property valid for every unary relation definable by first-order logic over these classes which is peculiar to classes of ordered structures with unary relations. In a second step we show that this property itself can be expressed in fixed point logic and can be used to construct a non-elementary unary relation.

Scalable Peer-to-Peer Indexing with Constant State

We present a distributed indexing scheme for peer to peer networks. Past work on distributed indexing traded off fast search times with non-constant degree topologies or network-unfriendly behavior such as flooding. In contrast, the scheme we present optimizes all three of these performance measures. That is, we provide logarithmic round searches while maintaining connections to a fixed number of peers and avoiding network flooding. In comparison to the well known scheme Chord, we provide competitive constant factors. Finally, we observe that arbitrary linear speedups are possible and discuss both a general brute force approach and specific economical optimizations.

Seed Scheduling for Peer-to-Peer Networks

The initial phase in a content distribution (file sharing) scenario is a delicate phase due to the lack of global knowledge and the dynamics of the overlay. An unwise distribution of the pieces in this phase can cause delays in reaching steady state, thus increasing file download times. We devise a scheduling algorithm at the seed (source peer with full content), based on a proportional fair approach, and we implement it on a real file sharing client [1]. In dynamic overlays, our solution improves up to 25% the average downloading time of a standard protocol ala BitTorrent.

Efficient Support for Common Relations in Lightweight Formal Reasoning Systems

In work that involves mathematical rigor, there are numerous benefits to adopting a representation of models and arguments that can be supplied to a formal reasoning or verification system: reusability, automatic evaluation of examples, and verification of consistency and correctness. However, accessibility has not been a priority in the design of formal verification tools that can provide these benefits. In earlier work [Lap09a], we attempt to address this broad problem by proposing several specific design criteria organized around the notion of a natural context: the sphere of awareness a working human user maintains of the relevant constructs, arguments, experiences, and background materials necessary to accomplish the task at hand. This work expands one aspect of the earlier work by considering more extensively an essential capability for any formal reasoning system whose design is oriented around simulating the natural context: native support for a collection of mathematical relations that deal with common constructs in arithmetic and set theory. We provide a formal definition for a context of relations that can be used to both validate and assist formal reasoning activities. We provide a proof that any algorithm that implements this formal structure faithfully will necessary converge. Finally, we consider the efficiency of an implementation of this formal structure that leverages modular implementations of well-known data structures: balanced search trees and transitive closures of hypergraphs.