Combining explicit negation and negation by failure via Belnap's logic

AbstractThis paper deals with logic programs containing two kinds of negation: negation as failure and explicit negation. This allows two different forms of reasoning in the presence of incomplete information. Such programs have been introduced by Gelfond and Lifschitz and called extended programs. We provide them with a logical semantics in the style of Kunen, based on Belnap's four-valued logic, and an answer sets' semantics that is shown to be equivalent to that of Gelfond and Lifschitz.The proofs rely on a translation into normal programs, and on a variant of Fitting's extension of logic programming to bilattices

Observation of a kilogram-scale oscillator near its quantum ground state

We introduce a novel cooling technique capable of approaching the quantum ground state of a kilogram-scale system—an interferometric gravitational wave detector. The detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) operate within a factor of 10 of the standard quantum limit (SQL), providing a displacement sensitivity of 10[superscript −18] m in a 100 Hz band centered on 150 Hz. With a new feedback strategy, we dynamically shift the resonant frequency of a 2.7 kg pendulum mode to lie within this optimal band, where its effective temperature falls as low as 1.4 μK, and its occupation number reaches about 200 quanta. This work shows how the exquisite sensitivity necessary to detect gravitational waves can be made available to probe the validity of quantum mechanics on an enormous mass scale.Alfred P. Sloan FoundationUnited States. National Aeronautics and Space AdministrationDavid & Lucile Packard FoundationResearch CorporationNational Science Foundation (U.S.

Searching for a Stochastic Background of Gravitational Waves with LIGO

The Laser Interferometer Gravitational-wave Observatory (LIGO) has performed the fourth science run, S4, with significantly improved interferometer sensitivities with respect to previous runs. Using data acquired during this science run, we place a limit on the amplitude of a stochastic background of gravitational waves. For a frequency independent spectrum, the new limit is $\Omega_{\rm GW} < 6.5 \times 10^{-5}$. This is currently the most sensitive result in the frequency range 51-150 Hz, with a factor of 13 improvement over the previous LIGO result. We discuss complementarity of the new result with other constraints on a stochastic background of gravitational waves, and we investigate implications of the new result for different models of this background.Comment: 37 pages, 16 figure

Complete Sets of Connectives and Complete Sequent Calculus for Belnap&apos;s Logic

This paper presents a sequent calculus for Belnap&apos;s four-valued logic, and proves its soundness and completeness with respect to model theory. The proofs are adaptations of Gallier&apos;s proofs for classical logic. It is also shown that the extensions of the classical connectives : and to the fourvalued case do not form a complete set, and a new connective is introduced to obtain the completeness of the connectives. 1 INTRODUCTION The interest of three-valued logic for computer science has been motivated by research on the semantics of negation in logic programming, from the model-theoretical [4, 11, 12] and the proof-theoretical viewpoints [14]. Moving from three-valued to four-valued logic provides a framework for logic programs dealing with missing or conflicting information, e.g information distributed over several sites [6]. It also sheds a new light on the stable model semantics for logic programming (see [3]), allowing to define a new stable model, the largest one in a certain ord..

On differentiation and homeostatic behaviours of Boolean dynamical systems

International audienceWe study rules proposed by the biologist R. Thomas relating the structure of a concurrent system of interacting genes (represented by a signed directed graph called a regulatory graph) with its dynamical properties. We prove that the results in [10] are stable under projection, and this enables us to relax the assumptions under which they are valid. More precisely, we relate here the presence of a positive (resp. negative) circuit in a regulatory graph to a more general form of biological differentiation (resp. of homeostasis)

Concurrent Constraint Programming and Non-Commutative Logic

. This paper presents a connection between the intuitionistic fragment of a non-commutative version of linear logic introduced by the first author (NLI) and concurrent constraint programming (CC). We refine existing logical characterizations of operational aspects of CC, by providing a logical interpretation of finer observable properties of CC programs, namely stores, successes and suspensions. 1 Introduction The class CC(X ) of Concurrent Constraint programming languages introduced by Saraswat [29] in 1987 arises as a natural combination of constraint logic programming [11] and concurrent logic programming, with a synchronization mechanism based on constraint entailment [16]. CC programming is a model of concurrent computation, where agents communicate through a shared store, represented by a constraint, which expresses some partial information on the values of the variables involved in the computation. An agent may add information c to the store (agent tell(c)), or ask the store t..