This paper concerns model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter systems are undecidable, but we have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL* can be simulated by quantification over tuples of natural numbers, eventually allowing translation of (...) the whole Presburger-CTL* into Presburger arithmetic, thereby enabling effective model checking. We provide evidence that our results are close to optimal with respect to the class of counter systems described above. (shrink)

Abstract: The standard picture of rationality requires that the agent acts so as to realize her most preferred alternative in the light of her own desires and beliefs. However, there are circumstances where such an agent can predict that she will act against her preferences. The story of Ulysses and the Sirens is the paradigmatic example of such cases. In those circumstances the orthodoxy requires the agent to be ‘sophisticated’. That is to say, she should take into account her expected (...) future choices and prevent her future self to act in certain ways. She should ‘bind’ herself to a certain course of action. This is a form of causal commitment. It is generally recognized that this form of self-commitment is the only one that is available to a rational agent. Rational commitment, where the agent gives herself a reason to act in a certain way rather than making herself act in that way, is considered not feasible. In this paper, I question this verdict. I sketch the broad outlines of a model of rational commitment, which takes as its starting point Michael Bratman’s ‘planning theory’ of intention. There are two important objections against this theory (one by John Broome and one by the Dutch philosopher Govert den Hartogh.) Both criticisms claim that such a theory is a form of ‘bootstrapping’ reasons for action into existence. In the remainder of the paper, I will defend the theory against these objections. This way, I hope to establish that defending the feasibility of rational commitment is not an obvious mistake. (shrink)