Probabilities on Sentences in an Expressive Logic

Automated reasoning about uncertain knowledge has many applications. One difficulty when developing such systems is the lack of a completely satisfactory integration of logic and probability. We address this problem directly. Expressive languages like higher-order logic are ideally suited for representing and reasoning about structured knowledge. Uncertain knowledge can be modeled by using graded probabilities rather than binary truth-values. The main technical problem studied in this paper is the following: Given a set of sentences, each having some probability of being true, what probability should be ascribed to other (query) sentences? A natural wish-list, among others, is that the probability distribution (i) is consistent with the knowledge base, (ii) allows for a consistent inference procedure and in particular (iii) reduces to deductive logic in the limit of probabilities being 0 and 1, (iv) allows (Bayesian) inductive reasoning and (v) learning in the limit and in particular (vi) allows confirmation of universally quantified hypotheses/sentences. We translate this wish-list into technical requirements for a prior probability and show that probabilities satisfying all our criteria exist. We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter) examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed theory might be used and approximated in autonomous reasoning agents. Our theory is a step towards a globally consistent and empirically satisfactory unification of probability and logic.Comment: 52 LaTeX pages, 64 definiton/theorems/etc, presented at conference Progic 2011 in New Yor

Two- and three-dimensional viscous computations of a hypersonic inlet flow

The three-dimensional parabolized Navier-Stokes code has been used to investigate the flow through a Mach 7.4 inlet. A two-dimensional parametric study of grid resolution, turbulence modeling and effect of gamma has been done and compared with experimental results. The results show that mesh resolution of the shock waves, real gas effects and turbulence length scaling are very important to get accurate results for hypersonic inlet flows. In addition a three-dimensional calculation of the Mach 7.4 inlet has been done on a straight sideplate configuration. The results show that the glancing shock/boundary layer interaction phenomena causes significant three-dimensional flow in the inlet

The Empowering Leadership of Jesus. Useful Wisdom for HRD Professionals and Practitioners.

Many organizations yearn for an empowering leadership capable of transforming organizations to high performance, quality and productivity, but few achieve this goal. This review investigated Jesus\u27 empowering leadership and what made it so transformative that, even after some 2000 years, his organization is more or less the longest and best-run especially in comparison with many other famous organizations that have come and gone. This study will show that personal example, empowerment, servant leadership, and compassion are the main ingredients in an effective and transforming leadership strategy for organizations. This review will shed some light on what inhibits or enables empowerment m organizations and what leaders need to shake off\u27 in order for them to become truly empowering leaders. Some light has also been shed on the role of HRD Professionals and Practitioners in an attempt to attain empowering leadership in organizations

Best Practices in Managing Social Media for Business

The mixed results of social media impacting on businesses have motivated this research to understand the best practices affecting the brand equity of a company utilizing the social media in business. Literature review of relevant theories is conducted. The industry publications of companies doing well in social media are analyzed to distill the best practices implemented in their social media strategies. Multiple case studies are proposed to determine how these best practices explain the desired business outcome in brand equity. The social media strategy concepts, media richness theory and Hagel III and Armstrong’s framework of virtual member development are suggested in guiding our data collection, analysis and interpretation. This research in progress is expected to contribute to the existing knowledge by providing a prescriptive framework of best practices in utilizing Facebook social network, and integrating and extending existing theories to explain the use of social media for developing brand equity