Amalia -- A Unified Platform for Parsing and Generation

Contemporary linguistic theories (in particular, HPSG) are declarative in nature: they specify constraints on permissible structures, not how such structures are to be computed. Grammars designed under such theories are, therefore, suitable for both parsing and generation. However, practical implementations of such theories don't usually support bidirectional processing of grammars. We present a grammar development system that includes a compiler of grammars (for parsing and generation) to abstract machine instructions, and an interpreter for the abstract machine language. The generation compiler inverts input grammars (designed for parsing) to a form more suitable for generation. The compiled grammars are then executed by the interpreter using one control strategy, regardless of whether the grammar is the original or the inverted version. We thus obtain a unified, efficient platform for developing reversible grammars.Comment: 8 pages postscrip

A Poly-Connexive Logic

The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory

Does the Implication Elimination Rule Need a Minor Premise?

The paper introduces NJ g , a variant of Gentzen’s NJ natural deduction system, in which the implication elimination rule has no minor premise. The NJ g -systems extends traditional ND-system with a new kind of action in derivations, assumption incorporation, a kind of dual to the assumption discharge action. As a result, the implication (I/E)-rules are invertible and, almost by definition, harmonious and stable, a major condition imposed by proof-theoretic semantics on ND-systems to qualify as meaning-conferring. There is also a proof-term assignment to NJ g -derivations, materialising the Curry-Howard correspondence for this system

Relevant Connexive Logic

In this paper, a connexive extension of the Relevance logic R→ was presented. It is defined by means of a natural deduction system, and a deductively equivalent axiomatic system is presented too. The goal of such an extension is to produce a logic with stronger connection between the antecedent and the consequent of an implication

Can Nondeterminism Help Complementation?

Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA), complementation and determinization have the same state complexity, namely Theta(2^n) where n is the state size. The same similarity between determinization and complementation was found for Buchi automata, where both operations were shown to have 2^\Theta(n lg n) state complexity. An intriguing question is whether there exists a type of omega-automata whose determinization is considerably harder than its complementation. In this paper, we show that for all common types of omega-automata, the determinization problem has the same state complexity as the corresponding complementation problem at the granularity of 2^\Theta(.).Comment: In Proceedings GandALF 2012, arXiv:1210.202