A Generalized Framework for Virtual Substitution

We generalize the framework of virtual substitution for real quantifier elimination to arbitrary but bounded degrees. We make explicit the representation of test points in elimination sets using roots of parametric univariate polynomials described by Thom codes. Our approach follows an early suggestion by Weispfenning, which has never been carried out explicitly. Inspired by virtual substitution for linear formulas, we show how to systematically construct elimination sets containing only test points representing lower bounds

Deciding First-Order Satisfiability when Universal and Existential Variables are Separated

We introduce a new decidable fragment of first-order logic with equality, which strictly generalizes two already well-known ones -- the Bernays-Sch\"onfinkel-Ramsey (BSR) Fragment and the Monadic Fragment. The defining principle is the syntactic separation of universally quantified variables from existentially quantified ones at the level of atoms. Thus, our classification neither rests on restrictions on quantifier prefixes (as in the BSR case) nor on restrictions on the arity of predicate symbols (as in the monadic case). We demonstrate that the new fragment exhibits the finite model property and derive a non-elementary upper bound on the computing time required for deciding satisfiability in the new fragment. For the subfragment of prenex sentences with the quantifier prefix $\exists^* \forall^* \exists^*$ the satisfiability problem is shown to be complete for NEXPTIME. Finally, we discuss how automated reasoning procedures can take advantage of our results.Comment: Extended version of our LICS 2016 conference paper, 23 page

Better Answers to Real Questions

We consider existential problems over the reals. Extended quantifier elimination generalizes the concept of regular quantifier elimination by providing in addition answers, which are descriptions of possible assignments for the quantified variables. Implementations of extended quantifier elimination via virtual substitution have been successfully applied to various problems in science and engineering. So far, the answers produced by these implementations included infinitesimal and infinite numbers, which are hard to interpret in practice. We introduce here a post-processing procedure to convert, for fixed parameters, all answers into standard real numbers. The relevance of our procedure is demonstrated by application of our implementation to various examples from the literature, where it significantly improves the quality of the results

Consciousness regained? Philosophical arguments for and against reductive physicalism

This paper is an overview of recent discussions concerning the mind-body problem, which is being addressed at the interface between philosophy and neuroscience. It focuses on phenomenal features of consciousness or "qualia," which are distinguished from various related issues. Then follows a discussion of various influential skeptical arguments that question the possibility of reductive explanations of qualia in physicalist terms: knowledge arguments, conceivability arguments, the argument of multiple realizability, and the explanatory gap argument. None of the arguments is found to be very convincing. It does not necessarily follow that reductive physicalism is the only option, but it is defensible. However, constant conceptual and methodological reflection is required, alongside ongoing research, to keep such a view free from dogmatism and naivety

Feasibility of UV lasing without inversion in mercury vapor

We investigate the feasibility of UV lasing without inversion at a wavelength of $253.7$ nm utilizing interacting dark resonances in mercury vapor. Our theoretical analysis starts with radiation damped optical Bloch equations for all relevant 13 atomic levels. These master equations are generalized by considering technical phase noise of the driving lasers. From the Doppler broadened complex susceptibility we obtain the stationary output power from semiclassical laser theory. The finite overlap of the driving Gaussian laser beams defines an ellipsoidal inhomogeneous gain distribution. Therefore, we evaluate the intra-cavity field inside a ring laser self-consistently with Fourier optics. This analysis confirms the feasibility of UV lasing and reveals its dependence on experimental parameters.Comment: changes were made according to reviewer comments (accepted for publication in JOSA B

Inequity Aversion and Individual Behavior in Public Good Games: An Experimental Investigation

We present a simple two-steps procedure for a within-subject test of the inequity aversion model of Fehr and Schmidt (1999). In the first step, subjects played modified ultimatum and dictator games and were classified according to their preferences. In the second step, subjects with specific preferences according to the Fehr and Schmidt model were matched into pairs and interacted with each other in a standard public good game and a public good game with punishment possibility. Our results show that the specific composition of groups significantly influences the subjects' performance in the public good games. We identify the aversion against advantageous inequity and the information about the coplayer's type as the main influencing factors for the behavior of subjects. --individual preferences,inequity aversion,experimental economics,public goods

Inequity Aversion and Individual Behavior in Public Good Games: An Experimental Investigation

We present a simple two-steps procedure for a within-subject test of the inequity aversion model of Fehr and Schmidt (1999). In the first step, subjects played modified ultimatum and dictator games and were classified according to their preferences. In the second step, subjects with specific preferences according to the Fehr and Schmidt model were matched into pairs and interacted with each other in a standard public good game and a public good game with punishment possibility. Our results show that the specific composition of groups significantly influences the subjects' performance in the public good games. We identify the aversion against advantageous inequity and the information about the coplayer's type as the main influencing factors for the behavior of subjects. --individual preferences,inequity aversion,experimental economics,public goods

Tools=Theories=Data? On Some Circular Dynamics in Cognitive Science

Algunos instrumentos han jugado un papel tan importante en la investigación psicológica que se han convertido en metáforas para el contenido mismo de la investigación, o han conducido a la generación de nuevos conceptos y teorías en psicología. Este capítulo pro-porciona dos casos prácticos relacionados que apoyan esta afirmación. Desde la llamada ―revolución cognitiva‖ de la década de 1960, la mente humana ha sido descrita teóricamen-te como un ―estadístico intuitivo‖ (una persona que piensa de forma intuitiva en términos estadísticos) o como un programa de ordenador. Estas teorías han sido fuertemente inspira-das por las herramientas introducidas en la investigación psicológica antes de la difusión de tales teorías en la comunidad psicológica: la estadística inferencial y el ordenador digital. Aquí discutimos los pros y los contras de las metáforas. Las metáforas pueden ser ventajo-sas, pues abren nuevas áreas de investigación, llevan a nuevas preguntas y datos; pero las metáforas pueden también incluir pérdidas, ya que siempre recalcan algunos aspectos y de-jan otros fuera. Además, en lugar de teorías que son evaluadas por datos recogidos median-te herramientas de investigación aparentemente neutrales, hay una tendencia hacia teorías que se ajustan al funcionamiento o a los usos de herramientas específicas de investigación. Tal tendencia se ve en ocasiones reforzada por los datos que sólo pueden ser producidos por las nuevas herramientas. Los científicos deberían ser conscientes de esta dinámica para evi-tar circularidades en su teorización.Some instruments have played such a strong role in psychological research that they have become metaphors for the subject matter of such research itself, or that they have lead to the generation of new psychological concepts and theories. This chapter provides two re-lated case studies for this claim. Since the so-called “cognitive revolution” of the 1960s, the human mind has been theoretically described as an “intuitive statistician” or as a com-puter program. Such theories have been strongly inspired by the tools introduced into psychological research somewhat before the spreading of such theories within the psychologi-cal community: inferential statistics and the digital computer. We discuss both the pros and cons of the metaphors. Metaphors can be advantageous, as they can open up new re-search areas, questions, and data; but metaphors can also include losses, because they al-ways emphasize some aspects and leave others out. Moreover, instead of the theories be-ing evaluated by data gathered by means of seemingly neutral research tools, there is a bi-as towards theories which match with the functioning or uses of specific research tools, a bias which is sometimes reinforced by data which can only be produced by the new tools. Scientists should be aware of such a dynamics in order to avoid circularities in their theo-rizing