A general first-order solution to the ramification problem with cycles

We provide a solution to the ramification problem that integrates findings of different axiomatic approaches to ramification from the last ten to fifteen years. For the first time, we present a solution that: (1) is independent of a particular time structure, (2) is formulated in classical first-order logic, (3) treats cycles – a notoriously difficult aspect – properly, and (4) is assessed against a state-transition semantics via a formal correctness proof.This is achieved as follows: We introduce indirect effect laws that enable us to specify ramifications that are triggered by activation of a formula rather than just an atomic effect. We characterise the intended models of these indirect effect laws by a state-transition semantics. Afterwards, we show how to compile a class of indirect effect laws into first-order effect axioms that then solve the ramification and frame problems. We finally prove the resulting effect axioms sound and complete with respect to the semantics defined earlier.     

The Concurrent,Continuous Fluent Calculus

The Fluent Calculus belongs to the established predicate calculus formalisms for reasoning about actions. Its underlying concept of state update axioms provides a solution to the basic representational and inferential Frame Problems in pure first-order logic. Extending a recent research result, we present a Fluent Calculus to reason about domains involving continuous change and where actions occur concurrently.