Online research in philosophy

In this paper we present the syntax and semantics of a temporal action language named Alan, which was designed to model interactive multimedia presentations where the Markov property does not always hold. In general, Alan allows the specification of systems where the future state of the world depends not only on the current state, but also on the past states of the world. To the best of our knowledge, Alan is the first action language which incorporates causality with temporal formulas. (...) In the process of defining the effect of actions we define the closure with respect to a path rather than to a state, and show that the non-Markovian model is an extension of the traditional Markovian model. Finally, we establish relationship between theories of Alan and logic programs. (shrink)

One of the cardinal assumptions about the nature of grammar is that it is a formal system, meaning that the operations and symbols in the grammar should have a precise meaning, so that one can tell precisely how it functions, and whether a given structure is in fact created by the grammar. The issue of how much information is available to the grammar, viewed as a computational device that computes structures, is called the issue of computational complexity. The computational powers (...) of various grammars, and the capacity of recognition devices to characterize as licit or not the structures that they generate, has been the province of mathematical linguistics, but has also occasionally been felt to have implications for empirical syntactic theory. One central question that has raised its head over the years is the question of whether or not grammar ( which is now referred to as CHL, for Computation of Human Language (Chomsky (1995)) is Markovian, an issue first raised in Chomsky (1957). For a computational device to be Markovian, it can only make reference to the current state that the device is in, when deciding what the next state of the device can be; it cannot, for example, make reference to alternative states, earlier states, future states, or , as a consequence of its being a formal system, factors outside of the computational device. (shrink)

Reinforcement schemes are a class of non-Markovian stochastic processes. Their non-Markovian nature allows them to model some kind of memory of the past. One subclass of such models are those in which the past is exponentially discounted or forgotten. Often, models in this subclass have the property of becoming trapped with probability 1 in some degenerate state. While previous work has concentrated on such limit results, we concentrate here on a contrary effect, namely that the time to become trapped may (...) increase exponentially in 1/x as the discount rate, 1− x, approaches 1. As a result, the time to become trapped may easily exceed the lifetime of the simulation or of the physical data being modeled. In such a case, the quasi-stationary behavior is more germane. We apply our results to a model of social network formation based on ternary (three-person) interactions with uniform positive reinforcement. (shrink)