Weighted Automata and Logics for Infinite Nested Words

Nested words introduced by Alur and Madhusudan are used to capture structures with both linear and hierarchical order, e.g. XML documents, without losing valuable closure properties. Furthermore, Alur and Madhusudan introduced automata and equivalent logics for both finite and infinite nested words, thus extending B\"uchi's theorem to nested words. Recently, average and discounted computations of weights in quantitative systems found much interest. Here, we will introduce and investigate weighted automata models and weighted MSO logics for infinite nested words. As weight structures we consider valuation monoids which incorporate average and discounted computations of weights as well as the classical semirings. We show that under suitable assumptions, two resp. three fragments of our weighted logics can be transformed into each other. Moreover, we show that the logic fragments have the same expressive power as weighted nested word automata.Comment: LATA 2014, 12 page

Automatic annotation of the Penn-treebank with LFG f-structure information

Lexical-Functional Grammar f-structures are abstract syntactic representations approximating basic predicate-argument structure. Treebanks annotated with f-structure information are required as training resources for stochastic versions of unification and constraint-based grammars and for the automatic extraction of such resources. In a number of papers (Frank, 2000; Sadler, van Genabith and Way, 2000) have developed methods for automatically annotating treebank resources with f-structure information. However, to date, these methods have only been applied to treebank fragments of the order of a few hundred trees. In the present paper we present a new method that scales and has been applied to a complete treebank, in our case the WSJ section of Penn-II (Marcus et al, 1994), with more than 1,000,000 words in about 50,000 sentences

Logic Meets Algebra: the Case of Regular Languages

The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical formalism required to define them. The algebraic point of view on automata is an essential complement of this classification: by providing alternative, algebraic characterizations for the classes, it often yields the only opportunity for the design of algorithms that decide expressibility in some logical fragment. We survey the existing results relating the expressibility of regular languages in logical fragments of MSO[S] with algebraic properties of their minimal automata. In particular, we show that many of the best known results in this area share the same underlying mechanics and rely on a very strong relation between logical substitutions and block-products of pseudovarieties of monoid. We also explain the impact of these connections on circuit complexity theory.Comment: 37 page

Short answers in Scottish Gaelic and their theoretical implications

This article presents an analysis of a novel short answer strategy in Scottish Gaelic, called the Verb-Answer, which differs from standard fragment answers in allowing us to directly observe some of the clausal structure in which it is embedded. It is shown that the Verb-Answer is identical to the fragment answer in virtually all other respects, demanding a unified analysis, and it is demonstrated that pursuing a unified analysis is problematic for Direct Interpretation approaches to short answers, but straightforward for the Silent Structure approach of Morgan (1973) and Merchant (2004). The extended typology of short answer strategies therefore provides an argument in favour of the latter approach to elliptical phenomena

An Automata Theoretic Approach to the Zero-One Law for Regular Languages: Algorithmic and Logical Aspects

A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeys the zero-one law if and only if its syntactic monoid has a zero element, by means of Eilenberg's variety theoretic approach. Our proof gives an effective automata characterisation of the zero-one law for regular languages, and it leads to a linear time algorithm for testing whether a given regular language is zero-one. In addition, we discuss the logical aspects of the zero-one law for regular languages.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Portable extraction of partially structured facts from the web

A novel fact extraction task is defined to fill a gap between current information retrieval and information extraction technologies. It is shown that it is possible to extract useful partially structured facts about different kinds of entities in a broad domain, i.e. all kinds of places depicted in tourist images. Importantly the approach does not rely on existing linguistic resources (gazetteers, taggers, parsers, etc.) and it ported easily and cheaply between two very different languages (English and Latvian). Previous fact extraction from the web has focused on the extraction of structured data, e.g. (Building-LocatedIn-Town). In contrast we extract richer and more interesting facts, such as a fact explaining why a building was built. Enough structure is maintained to facilitate subsequent processing of the information. For example, this partial structure enables straightforward template-based text generation. We report positive results for the correctness and interest of English and Latvian facts and for the utility of the extracted facts in enhancing image captions

Existentially Closed Models in the Framework of Arithmetic

We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on existentially closed models of fragments of arithmetic.Ministerio de Educación y Ciencia MTM2011–2684

Solving headswitching translation cases in LFG-DOT

It has been shown that LFG-MT (Kaplan et al., 1989) has difficulties with Headswitching data (Sadler et al., 1989, 1990; Sadler & Thompson, 1991). We revisit these arguments in this paper. Despite attempts at solving these problematic constructions using approaches based on linear logic (Van Genabith et al., 1998) and restriction (Kaplan & Wedekind, 1993), we point out further problems which are introduced. We then show how LFG-DOP (Bod & Kaplan, 1998) can be extended to serve as a novel hybrid model for MT, LFG-DOT (Way, 1999, 2001), which promises to improve upon the DOT model of translation (Poutsma 1998, 2000) as well as LFG-MT. LFG-DOT improves the robustness of LFG-MT through the use of the LFG-DOP Discard operator, which produces generalized fragments by discarding certain f-structure features. LFG-DOT can, therefore, deal with ill-formed or previously unseen input where LFG-MT cannot. Finally, we demonstrate that LFG-DOT can cope with such translational phenomena which prove problematic for other LFG-based models of translation