The full text of this article:

A formal semantics for Gaia liveness rules and expressions
by Tim Miller, Peter McBurney
International Journal of Agent-Oriented Software Engineering (IJAOSE), Vol. 1, No. 3/4, 2007
Abstract: The Gaia methodology is a development methodology for multi-agent systems that uses the concept of roles to define behaviour. Gaia uses liveness expressions, which are expressions written in a formal syntax that are used to define the ongoing behaviour of a role; and liveness rules, which are expressions specifying the behaviour of roles relative to each other in a system. However, while the syntax is formal, a formal semantics has not been defined, and there is no theory for how to reason about and manipulate these expressions. In this paper, we present a formal semantics for liveness rules and expressions, and discuss our work in developing axioms about them. We also discuss the introduction of a new operator for defining the complement of expressions; that is, the behaviour that falls outside of the liveness expression. This provides more flexibility when reasoning about and manipulating these expressions.

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