|Abstract||Online trading invariably involves dealings between strangers, so it is important for one party to be able to judge objectively the trustworthiness of the other. In such a setting, the decision to trust a user may sensibly be based on that user’s past behaviour. We introduce a speciﬁcation language based on linear temporal logic for expressing a policy for categorising the behaviour patterns of a user depending on its transaction history. We also present an algorithm for checking whether the transaction history obeys the stated policy. To be useful in a real setting, such a language should allow one to express realistic policies which may involve parameter quantiﬁcation and quantitative or statistical patterns. We introduce several extensions of linear temporal logic to cater for such needs: a restricted form of universal and existential quantiﬁcation; arbitrary computable functions and relations in the term language; and a “counting” quantiﬁer for counting how many times a formula holds in the past. We then show that model checking a transaction history against a policy, which we call the history-based transaction monitoring problem, is PSPACE-complete in the size of the policy formula and the length of the history, assuming that the underlying interpreted functions and relations are polynomially computable. The problem becomes decidable in polynomial time when the policies are ﬁxed. We also consider the problem of transaction monitoring in the case where not all the parameters of actions are observable. We formulate two such “partial observability” monitoring problems, and show their decidability under certain restrictions.|
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