Desires, norms and constraints

This paper deals with modeling mental states of a rational agent, in particular states based on agent’s desires. It shows that the world the agent belongs to forces it to restrict its desires. More precisely, desires of a rational agent are restricted by the constraints that exist in the world and which express what is possible or necessary. Furthermore, if the agent is law-abiding, its desires are restricted by the regulations that are defined in the world and which express what is obligatory, permitted or forbidden. This paper characterizes how desires are restricted depending on the fact that the agent is law-abiding or not. This work considers the general case when the agent orders its own desires according to a preference order. The solution is based on modeling desires, regulations and constraints in an unique formal system which is a logic of conditional preferences

Beauville surfaces and finite simple groups

A Beauville surface is a rigid complex surface of the form (C1 x C2)/G, where C1 and C2 are non-singular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates.Comment: 20 page

Beauville surfaces, moduli spaces and finite groups

In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either \PSL(2,p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.Comment: 27 pages. The article arXiv 0910.5402v2 was divided into two parts. This is the second half of the original paper, and it contains the subsections concerning the moduli spac

Commutator maps, measure preservation, and T-systems

Let G be a finite simple group. We show that the commutator map $a : G \times G \to G$ is almost equidistributed as the order of G goes to infinity. This somewhat surprising result has many applications. It shows that for a subset X of G we have $a^{-1}(X)/|G|^2 = |X|/|G| + o(1)$, namely $a$ is almost measure preserving. From this we deduce that almost all elements $g \in G$ can be expressed as commutators $g = [x,y]$ where x,y generate G. This enables us to solve some open problems regarding T-systems and the Product Replacement Algorithm (PRA) graph. We show that the number of T-systems in G with two generators tends to infinity as the order of G goes to infinity. This settles a conjecture of Guralnick and Pak. A similar result follows for the number of connected components of the PRA graph of G with two generators. Some of our results apply for more general finite groups, and more general word maps. Our methods are based on representation theory, combining classical character theory with recent results on character degrees and values in finite simple groups. In particular the so called Witten zeta function plays a key role in the proofs.Comment: 28 pages. This article was submitted to the Transactions of the American Mathematical Society on 21 February 2007 and accepted on 24 June 200

Distribution of goals addressed to a group of agents

The problem investigated in this paper is the distribution of goals addressed to a group of rational agents. Those agents are characterized by their ability (i.e. what they can do), their knowledge about the world and their commitments. The goals of the group are represented by conditional preferences. In order to deduce the actual goals of the group, we determine its ability using each agent’s ability and we suppose that the agents share a common knowledge about the world. The individual goals of an agent are deduced using its ability, the knowledge it has about the world, its own commitments and the commitments of the other agents of the group

Deriving individual obligations from collective obligations

A collective obligation is an obligation directed to a group of agents so that the group, as a whole, is obliged to achieve a given task. The problem investigated here is the impact of collective obligations on individual obligations,i.e. obligations directed to single agents of the group. In this case, we claim that the derivation of individual obligations from collective obligations depends on several parameters among which the ability of the agents (i.e. what they can do) and their own personal commitments (i.e. what they are determined to do). As for checking if these obligations are fulfilled or not, we need to know what are the actual actions performed by the agents

New Beauville surfaces and finite simple groups

In this paper we construct new Beauville surfaces with group either \PSL(2,p^e), or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recent results of Marion.Comment: v4: 18 pages. Final version, to appear in Manuscripta Mat