Game logic and its applications I

This paper provides a logic framework for investigations of game theoretical problems. We adopt an infinitary extension of classical predicate logic as the base logic of the framework. The reason for an infinitary extension is to express the common knowledge concept explicitly. Depending upon the choice of axioms on the knowledge operators, there is a hierarchy of logics. The limit case is an infinitary predicate extension of modal propositional logic KD4, and is of special interest in applications. In Part I, we develop the basic framework, and show some applications: an epistemic axiomatization of Nash equilibrium and formal undecidability on the playability of a game. To show the formal undecidability, we use a term existence theorem, which will be proved in Part II.The authors thank Hiroakira Ono for helpful discussions and encouragements from the early stage of this research project, and Philippe Mongin, Mitio Takano and a referee of this journal for comments on earlier versions of this paper. The first and second authors are partially supported, respectively, by Tokyo Center of Economic Research and Grant-in-Aids for Scientific Research 04640215, Ministry of Education, Science and Culture.Presented by H. Ono     

Game Logic and its Applications II

This paper provides a Genzten style formulation of the game logic framework GLm (0 m ), and proves the cut-elimination theorem for GLm. As its application, we prove the term existence theorem for GL used in Part I.     

Localization of electrocutaneous stimuli on the fingers and forearm: Effects of electrode configuration and body axis

Four experiments were done on the effects of electrode configuration (concentric vs. unifocal) and body axis (longitudinal vs. transverse) on localization of electrocutaneous pulse stimuli at the fingers and forearm. Subjects pointed to the apparent location of current pulses. For the transverse placement of electrodes, pulses were localized correctly, whatever the configuration and the body site might be. In addition, intrasubject variability at the forearm was smaller for the transverse axis than for the longitudinal axis. For the longitudinal placement of electrodes, pulses were localized as a function of configuration and body site. At the fingers, concentric electrodes provided precise localization but unifocal electrodes provided a great mislocalization; and intrasubject variability of localization was larger for the unifocal electrodes than for the concentric electrodes. At the forearm, whatever the configuration might be, the pulses were localized more proximally than the stimulus site; and intrasubject variability of localization did not differ between the configurations. These results are related to Boring’s anchor theory, apparent distance between two points, and the localization of other somatosensory stimuli.     

Offender and crime characteristics of female serial arsonists in Japan

This study of Japanese female serial arsonists examined their crimes and background characteristics. The data were a sample from the national police register containing arson cases resulting in charges in Japan between 1982 and 2005. Serial arsonists were 6% of the arson offenders and 12% of these were female, resulting in 83 female serial arsonist data sets. The mean age was 37.6 years and 43% were unemployed. Nearly half were married. Only 28% had a documented history of mental problems and 22% had a prior arrest, usually for theft (19%). Female serial arsonists are characterised by going to a place near their home with a lighter and setting fire directly to combustible materials. Non‐metric multidimensional scaling was used to analyse 33 variables related to the offences. The arsons could be differentiated in terms of either expressive or instrumental sources of action. Expressive arsons were opportunistic and impulsive acts, motivated by emotional distress. The fires were mostly set close to home. Expressive arsons were characteristic of 66% of the females. Instrumental arsons were often motivated by revenge and involved planned and goal‐directed behaviours. They were committed by 13% of the females. Instrumental arsonists tended to travel further from home. Copyright © 2007 John Wiley & Sons, Ltd.     

Nanomachining of nanocrystalline nickel by focused ion beam

Nanocrystalline and sub-microcrystalline samples of nickel have been machined by a focused Ga⁺ ion beam (30?keV and 187?pA) at doses of 8.92?×?10¹⁶?–?2.68?×?10¹⁸ ions/cm² and their surface topography was investigated by atomic force microscopy (AFM). Values of the root-mean-square (RMS) roughness increase with increasing ion dose. The surfaces of the nanocrystalline Ni were smoother than those of the sub-microcrystalline Ni, indicating that smoothing due to diffusion for the former works more effectively than that for the latter.     

PACAP centrally mediates emotional stress-induced corticosterone responses in mice

Pituitary adenylate cyclase-activating polypeptide (PACAP) is a pleiotropic neuropeptide widely distributed in the nervous system. Recently, PACAP was shown to be involved in restraint stress-induced corticosterone release and concomitant expression of the genes involved in hypothalamic-pituitary-adrenal (HPA) axis activation. Therefore, in this study, we have addressed the types of stressors and the levels of the HPA axis in which PACAP signaling is involved using mice lacking PACAP (PACAP?/?). Among four different types of stressors, open-field exposure, cold exposure, ether inhalation, and restraint, the corticosterone response to open-field exposure and restraint, which are categorized as emotional stressors, but not the other two, was markedly attenuated in PACAP?/? mice. Peripheral administration of corticotropin releasing factor (CRF) or adrenocorticotropic hormone induced corticosterone increase similarly in PACAP?/? and wild-type mice. In addition, the restraint stress-induced c-Fos expression was significantly decreased in the paraventricular nucleus (PVN) and medial amygdala (MeA), but not the medial prefrontal cortex, in PACAP?/? mice. In the PVN of PACAP?/? mice, the stress-induced c-Fos expression was blunted in the CRF neurons. These results suggest that PACAP is critically involved in activation of the MeA and PVN CRF neurons to centrally regulate the HPA axis response to emotional stressors.     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

Microstructural characterization and high-temperature strength of hot-pressed silicon nitride ceramics with Lu2O3 additives

The microstructures of two hot-pressed Si₃N₄ ceramics, with 3.33 and 12.51 wt% Lu₂O₃ additive, have been characterized using transmission electron microscopy. The microstructures of both samples consisted of elongated β-Si₃N₄ grains and a secondary phase, contained in pockets surrounded by the grains, with a crystalline or amorphous form. In the 3.33 wt% Lu₂O₃-containing Si₃N₄ ceramic, all the multiple-grain junctions were completely crystalline while, in the 12.51 wt% Lu₂O₃-containing Si₃N₄ ceramic, approximately half the junctions were devitrified. A thin intergranular amorphous film present between the two-grain boundary was common; however, a film-free grain boundary was observed in the 12.51 wt% Lu₂O₃ sample. The film-free grain boundary was determined to be approximately 35%. Both ceramics fractured in four-point flexure between 1200 and 1600°C. Their high-temperature strength is closely associated with the nature of the grain-boundary phase formed during the sintering process.