Background and Notation Sample Clauses
The 'Background and notation' clause serves to provide essential context and define the key terms, symbols, or references used throughout the agreement. It typically outlines the relevant background information necessary for understanding the contract and establishes a consistent set of notations or definitions that will be used in subsequent clauses. By doing so, this clause ensures that all parties have a shared understanding of the terminology and context, reducing the risk of ambiguity or misinterpretation later in the document.
Background and Notation. Contracts regulate the behaviour of agents or par- ties that are acting concurrently. In this Section, we present notation used to describe these agents and their behaviour in order to be able to formalize con- tracts in the following sections. Structurally, the underlying system consists of several indexed agents running in parallel, using ▇▇▇▇- ▇▇▇▇▇ A, A1 to represent the individual agents. The sys- tem as a whole will consist of the parallel composition of all agents indexed by a finite set I i.e. the system i P1 I, where A = A1 ¨ ¨ ¨ Al ¨ ¨ ¨ An, and A1 = will be of the form i I Ai. We will use variables A, A1 to denote the state of the system as a whole. A1 ¨ ¨ ¨ A1l ¨ ¨ ¨ A1n. We will also write A a,S agents will be assumed to consist of actions over Act, and the agents’ behaviour will be assumed to con- can perform action a involving the agents in set S: A ,S df 1 a,S 1 sist of (i) a relation indicating how their state changes whenever such action occurs; and (ii) a relation indi- cating how they change over time. Time will be taken to range over the non-negative reals: T = R+. Agents semantics are thus represented as timed labelled ▇▇▇▇- sition systems: −Ñ = DA ¨ A −Ña A . The lack of such a transi- tion is written as: ▇ . In order to formalize violation of contracts, we will use predicates over agent behaviour. • A −aÑ A1, for a P Act, indicates that agent A changes to A1 upon performing action a. As it is usual in process algebrae [▇▇, 1991], the execu- tion of actions does not consume time. The ▇▇▇▇- sition A −aÛ indicates that agent A cannot perform P ::= tt | ff | xa, ky | xa, ky | P v Q | P ^ Q P P P In the grammar above, k I ranges over agent indices, a Act over actions, and P, Q P over pred- icates. =
a: A −aÛ df ¬DA1 ¨ A −aÑ A1. ą A1, for d 0 P T, indicates that agent A Predicates tt and ff denote true and false respec- tively. Predicate xa, ky means that agent k may per- evolves to A after d time units pass. form action a. However, since some actions may re- Assumptions: We will assume that agents are non- blocking: for any agent A, there is an agent state A1 such that either (i) A −aÑ A1 (for some a P Act); or (ii) quire involvement by several agents, we use the pred- icate a, k to indicate that agent k wants to perform action a, but this action is not offered by any other x y A1 (for some d ą 0 P T). We also assume the agent for synchronisation. For instance, an agent c x y may want to purchase a ticket (action: ticket) to go following...
Background and Notation. Contracts regulate the behaviour of agents or par- ties that are acting concurrently. In this Section, we present notation used to describe these agents and their behaviour in order to be able to formalize con- tracts in the following sections. Structurally, the underlying system consists of several indexed agents running in parallel, using ▇▇▇▇- ▇▇▇▇▇ A, A1 to represent the individual agents. The sys- tem as a whole will consist of the parallel composition of all agents indexed by a finite set I i.e. the system will be of the form i I Ai. We will use variables A, A1 to denote the state of the system as a whole.
Background and Notation