After arguing about the crucial importance of trust for Agents and MAS, we provide a definition of trust both as a mental state and as a social attitude and relation. We present the mental ingredients of trust: its specific beliefs and goals, with special attention to evaluations and expectations. We show the relation between trust and the mental background of delegation. We explain why trust is a bet, and implies some risks, and analyse the more complex forms of social trust, based on a theory of mind and in particular on morality, reputation and disposition, and authority (three party trust). We explain why promises, contracts, authorities can increase our trust by modifying our mental representations. We present a principled quantification of trust, based on its cognitive ingredients, and use this "degree of trust " as the basis for a rational decision to delegate or not to another agent. We analyze the trust in the information sources and its relation with the general notion of trust. We explain when trust is rational, and why it is not an irrational decision by definition. We also criticise the economic and game-theoretic view of trust for underestimating the importance of cognitive ingredients of trust and for reducing it to subjective probability and risk. The paper is intended to contribute both to the conceptual analysis and to the practical use of trust in social theory and MAS. 1 Premise: the importance of trus
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