A Dual Aspect Theory of Shared Intention

In this article I propose an original view of the nature of shared intention. In contrast to psychological views (Bratman, Searle, Tuomela) and normative views (Gilbert), I argue that both functional roles played by attitudes of individual participants and interpersonal obligations are factors of central and independent significance for explaining what shared intention is. It is widely agreed that shared intention (I) normally motivates participants to act, and (II) normally creates obligations between them. I argue that the view I propose can explain why it is not a mere accident that both (I) and (II) are true of shared intention, while psychological and normative views cannot. The basic idea is that shared intention involves a structure of attitudes of individuals –including, most importantly, attitudes of reliance – which normally plays the relevant motivating roles and creates the relevant obligations

Propagation of L1L^{1} and L∞L^{\infty} Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann Equation

We consider the $n$-dimensional space homogeneous Boltzmann equation for elastic collisions for variable hard potentials with Grad (angular) cutoff. We prove sharp moment inequalities, the propagation of $L^1$-Maxwellian weighted estimates, and consequently, the propagation $L^\infty$-Maxwellian weighted estimates to all derivatives of the initial value problem associated to the afore mentioned problem. More specifically, we extend to all derivatives of the initial value problem associated to this class of Boltzmann equations corresponding sharp moment (Povzner) inequalities and time propagation of $L^1$-Maxwellian weighted estimates as originally developed A.V. Bobylev in the case of hard spheres in 3 dimensions; an improved sharp moments inequalities to a larger class of angular cross sections and $L^1$-exponential bounds in the case of stationary states to Boltzmann equations for inelastic interaction problems with `heating' sources, by A.V. Bobylev, I.M. Gamba and V.Panferov, where high energy tail decay rates depend on the inelasticity coefficient and the the type of `heating' source; and more recently, extended to variable hard potentials with angular cutoff by I.M. Gamba, V. Panferov and C. Villani in the elastic case collision case and so $L^1$-Maxwellian weighted estimated were shown to propagate if initial states have such property. In addition, we also extend to all derivatives the propagation of $L^\infty$-Maxwellian weighted estimates to solutions of the initial value problem to the Boltzmann equations for elastic collisions for variable hard potentials with Grad (angular) cutoff.Comment: 24 page