Strict General Setting for Building Decision Procedures into Theorem Provers

The efficient and flexible incorporating of decision procedures into theorem provers is very important for their successful use. There are several approaches for combining and augmenting of decision procedures; some of them support handling uninterpreted functions, congruence closure, lemma invoking etc. In this paper we present a variant of one general setting for building decision procedures into theorem provers (gs framework [18]). That setting is based on macro inference rules motivated by techniques used in different approaches. The general setting enables a simple describing of different combination/augmentation schemes. In this paper, we further develop and extend this setting by an imposed ordering on the macro inference rules. That ordering leads to a ”strict setting”. It makes implementing and using variants of well-known or new schemes within this framework a very easy task even for a non-expert user. Also, this setting enables easy comparison of different combination/augmentation schemes and combination of their ideas

Men Will Be Boys: Regressive Nostalgia in The Virgin Suicides

The Virgin Suicides by Jeffrey Eugenides is widely considered a cult-classic novel. However, the text reveals much deeper concepts that at first may miss the eye. The first-person plural narration of the male narrators unveils a regressive nostalgia where they cannot move on from the suicides of the Lisbon sisters, which occurred in the 1970s, twenty years prior. This paper describes the gendered relationship between the present day of the novel, the 1990s, as a male possessiveness over the 1970s as a female past

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

The Evolution of Endurance Running and the Tyranny of Ethnography: A Reply to Pickering and Bunn (2007)

Endurance running (ER) poses a conundrum for paleoanthropologists. As summarized in Bramble and Lieberman (2004), human ER capabilities, which are unique among primates, either match or exceed those of mammals adapted for running (cursors), including dogs and equids. Because many of the biomechanical and physiological challenges of human ER are so different from those of walking, we can conclude that human ER capabilities did not arise merely as a by-product of selection for walking. Instead, the available evidence suggests that an array of features that improve ER performance were selected in the genus Homo, and they were probably present to some extent by the appearance of Homo erectus at approximately 1.9 Ma. Yet, ER is no longer necessary for human survival, even among extant foragers such as the Hadza or the Bushmen. Thus, a puzzle that paleoanthropologists must solve is identifying what past behaviors - behaviors no longer common among living foragers - favored the evolution of ER. Pickering and Bunn’s (2007) criticisms of the ER hypothesis center on two issues: first, that early Homo lacked the tracking abilities necessary for successful pursuit hunts, and second, that recent ethnographic evidence suggests that modern hunter-gatherers rarely use ER to either hunt or scavenge. These arguments are based on a presumptive link between modern human- like cognition and tracking abilities, as well as the notion that the modern ethnographic record provides an adequate reflection of past behaviors. Both of these assumptions are flawed. Although tracking is complex, there is little evidence to suggest that early hominids lacked the tracking abilities of much less encephalized carnivores. Additionally, as noted by Marlowe (2005), comparatively recent inventions, such as the bow and arrow, the spear thrower, nets, and even the spear point, fundamentally altered how humans hunt and scavenge. A strict reliance on the recent ethnographic record, what Wobst (1978) termed the ‘‘tyranny of ethnography,’’ is a fundamentally problematic way of testing hypotheses of past hunting behavior. Even so, a review of the ethnographic evidence reveals errors in Pickering and Bunn’s contentions.Anthropolog

Facilitating the Decentralised Exchange of Cryptocurrencies in an Order-Driven Market

This article discusses a protocol to facilitate decentralised exchanges on an order-driven market through a consortium of market services operators. We discuss whether this hybrid protocol combining a centralised initiation phase with a decentralised execution phase outperforms fully centralised exchanges with regards to efficiency and security. Here, a fully efficient and fully secure protocol is defined as one where traders incur no trading costs or opportunity costs and counterparty risk is absent. We devise a protocol addressing the main downsides in the decentralised exchange process that uses a facilitating distributed ledger, maintains an order book and monitors the order status in real-time to provide accurate exchange rate information and performance scoring of participants. We show how performance ratings can lower opportunity costs and how a rolling benchmark rate of verifiable trades can be used to establish a trustworthy exchange rate between cryptocurrencies. The formal validation of the proposed technical mechanisms is the subject of future work

Combination of convex theories: Modularity, deduction completeness, and explanation

AbstractDecision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple “sat/unsat” answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson–Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories