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Chronolog(MC) is an extension of logic programming based on a linear-time temporal logic with multiple granularity of time called TLC . A Chronolog(MC) program consists of a clock definition, a clock assignment and a program body. Each predicate symbol appearing in the program body is associated with a local clock through the clock definition and assignment. This paper investigates the logical basis of the language, presents a clocked temporal resolution where time-matching is essential, and in particular proposes three algorithms for time-matching. The paper also discusses the declarative semantics of Chronolog(MC) programs in terms of clocked temporal Herbrand models. It is shown that Chronolog(MC) programs also satisfy the minimum model semantics. The language can be used to model a wide range of simulation systems and other relevant tasks where the notion of dynamic change is central.

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Abstract. To develop theories to specify and reason about various aspects of multi-agent systems, many researchers have proposed the use of modal logics such as belief logics, logics of knowledge, and logics of norms. As multi-agent systems operate in dynamic environments, there is also a need to model the evolution of multi-agent systems through time. In order to introduce a temporal dimension to a belief logic, we combine it with a linear-time temporal logic using a powerful technique called fibring for combining logics. We describe a labelled modal tableaux system for the resulting fibred belief logic (FL) which can be used to automatically verify correctness of inter-agent stream authentication protocols. With the resulting fibred belief logic and its associated modal tableaux, one is able to build theories of trust for the description of, and reasoning about, multi-agent systems operating in dynamic environments.

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