Spatio-Temporal Reasoning About Agent Behavior

There are many applications where we wish to reason about spatio-temporal aspects of an agent's behavior. This dissertation examines several facets of this type of reasoning. First, given a model of past agent behavior, we wish to reason about the probability that an agent takes a given action at a certain time. Previous work combining temporal and probabilistic reasoning has made either independence or Markov assumptions. This work introduces Annotated Probabilistic Temporal (APT) logic which makes neither assumption. Statements in APT logic consist of rules of the form "Formula G becomes true with a probability [L,U] within T time units after formula F becomes true'' and can be written by experts or extracted automatically. We explore the problem of entailment - finding the probability that an agent performs a given action at a certain time based on such a model. We study this problem's complexity and develop a sound, but incomplete fixpoint operator as a heuristic - implementing it and testing it on automatically generated models from several datasets. Second, agent behavior often results in "observations'' at geospatial locations that imply the existence of other, unobserved, locations we wish to find ("partners"). In this dissertation, we formalize this notion with "geospatial abduction problems" (GAPs). GAPs try to infer a set of partner locations for a set of observations and a model representing the relationship between observations and partners for a given agent. This dissertation presents exact and approximate algorithms for solving GAPs as well as an implemented software package for addressing these problems called SCARE (the Spatio-Cultural Abductive Reasoning Engine). We tested SCARE on counter-insurgency data from Iraq and obtained good results. We then provide an adversarial extension to GAPs as follows: given a fixed set of observations, if an adversary has probabilistic knowledge of how an agent were to find a corresponding set of partners, he would place the partners in locations that minimize the expected number of partners found by the agent. We examine this problem, along with its complement by studying their computational complexity, developing algorithms, and implementing approximation schemes. We also introduce a class of problems called geospatial optimization problems (GOPs). Here the agent has a set of actions that modify attributes of a geospatial region and he wishes to select a limited number of such actions (with respect to some budget and other constraints) in a manner that maximizes a benefit function. We study the complexity of this problem and develop exact methods. We then develop an approximation algorithm with a guarantee. For some real-world applications, such as epidemiology, there is an underlying diffusion process that also affects geospatial proprieties. We address this with social network optimization problems (SNOPs) where given a weighted, labeled, directed graph we seek to find a set of vertices, that if given some initial property, optimize an aggregate study with respect to such diffusion. We develop and implement a heuristic that obtains a guarantee for a large class of such problems

Evolutionary approach to bilingualism

The ability to learn multiple languages simultaneously is a fundamental human linguistic capacity. Yet there has been little attempt to explain this in evolutionary terms. Perhaps one reason for this lack of attention is the idea that monolingualism is the default, most basic state and so needs to be explained before considering bilingualism. When thinking about bilingualism in this light, a paradox appears: Intuitively, learning two languages is harder than learning one, yet bilingualism is prevalent in the world. Previous explanations for linguistic diversity involve appeals to adaptation for group resistance to freeriders. However, the first statement of the paradox is a property of individuals, while the second part is a property of populations. This thesis shows that the properties of cultural transmission mean that the link between individual learning and population-level phenomena can be complex. A simple Bayesian model shows that just because learning one language is easier than two, it doesn't mean that monolingualism will be the most prevalent property of populations. Although this appears to resolve the paradox, by building models of bilingual language evolution the complexity of the problem is revealed. A bilingual is typically defined as an individual with "native-like control of two languages" (Bloomfield, 1933, p. 56), but how do we define a native speaker? How do we measure proficiency? How do we define a language? How can we draw boundaries between languages that are changing over large timescales and spoken by populations with dynamic structures? This thesis argues that there is no psychological reality to the concept of discrete, monolithic, static `languages' - they are epiphenomena that emerge from the way individuals use low-level linguistic features. Furthermore, dynamic social structures are what drives levels of bilingualism. This leads to a concrete definition of bilingualism: The amount of linguistic optionality that is conditioned on social variables. However, integrating continuous variation and dynamic social structures into existing top-down models is difficult because many make monolingual assumptions. Subsequently, introducing bilingualism into these models makes them qualitatively more complicated. The assumptions that are valid for studying the general processes of cultural transmission may not be suitable for asking questions about bilingualism. I present a bottom-up model that is specifically designed to address the bilingual paradox. In this model, individuals have a general learning mechanism that conditions linguistic variation on semantic variables and social variables such as the identity of the speaker. If speaker identity is an important conditioning factor, then `bilingualism' emerges. The mechanism required to learn one language in this model can also learn multiple languages. This suggests that the bilingual paradox derives from focussing on the wrong kind of question. Rather than having to explain the ability to learn multiple languages simultaneously as an adaptation, we should be asking how and why humans developed a flexible language learning mechanism. This argument coincides with a move in the field of bilingualism away from asking `how are monolinguals and bilinguals different?' to `how does the distribution of variation affect the way children learn?'. In this case, while studies of language evolution look at how learning biases affect linguistic variation, studies of bilingualism look at how linguistic variation affects learning biases. I suggest that the two fields have a lot to offer each other