Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

The sources of moral motivation : studies on empathy, guilt, shame and values

The goals of this study were to analyze the forms of emotional tendencies that are likely to motivate moral behaviors, and to find correlates for these tendencies. In study 1, students narratives of their own guilt or shame experiences were analyzed. The results showed that pure shame was more likely to motivate avoidance than reparation, whereas guilt and combination of guilt and shame were likely to motivate reparation. However, all types of emotion could lead to chronic rumination if the person was not clearly responsible for the situation. In study 2, the relations of empathy with two measures of guilt were examined in a sample of 13- to 16-year-olds (N=113). Empathy was measured using Davis s IRI and guilt by Tangney s TOSCA and Hoffman s semi-projective story completion method that includes two different scenarios, guilt over cheating and guilt over inaction. Empathy correlated more strongly with both measures of guilt than the two measures correlated with each other. Hoffman s guilt over inaction was more strongly associated with empathy measures in girls than in boys, whereas for guilt over cheating the pattern was the opposite. Girls and boys who describe themselves as empathetic may emphasize different aspect of morality and feel guilty in different contexts. In study 3, cultural and gender differences in guilt and shame (TOSCA) and value priorities (the Schwartz Value Survey) were studied in samples of Finnish (N=156) and Peruvian (N=159) adolescents. Gender differences were found to be larger and more stereotypical among the Finns than among the Peruvians. Finnish girls were more prone to guilt and shame than boys were, whereas among the Peruvians there was no gender difference in guilt, and boys were more shame-prone than girls. The results support the view that psychological gender differences are largest individualistic societies. In study 4, the relations of value priorities to guilt, shame and empathy were examined in two samples, one of 15 19-year-old high school students (N = 207), and the other of military conscripts (N = 503). Guilt was, in both samples, positively related to valuing universalism, benevolence, tradition, and conformity, and negatively related to valuing power, hedonism, stimulation, and self-direction. The results for empathy were similar, but the relation to the openness conservation value dimension was weaker. Shame and personal distress were weakly related to values. In sum, shame without guilt and the TOSCA shame scale are tendencies that are unlikely to motivate moral behavior in Finnish cultural context. Guilt is likely to be connected to positive social behaviors, but excessive guilt can cause psychological problems. Moral emotional tendencies are related to culture, cultural conceptions of gender and to individual value priorities.