Renormalization and forcing of horseshoe orbits

In this paper we deal with the Boyland order of horseshoe orbits. We prove that there exists a set $\mathcal{R}$ of renormalizable horseshoe orbits containing only quasi-one-dimensional ones, that is, for these orbits the Boyland order coincides with the unimodal order

Multiplicative-Additive Focusing for Parsing as Deduction

Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on identifying the essential mathematical structure of derivations. This is trivial in the case of context free grammar, where the parse structures are ordered trees; in the case of categorial grammar, the parse structures are proof nets. However, with respect to multiplicatives intrinsic proof nets have not yet been given for displacement calculus, and proof nets for additives, which have applications to polymorphism, are involved. Here we approach multiplicative-additive spurious ambiguity by means of the proof-theoretic technique of focalisation.Comment: In Proceedings WoF'15, arXiv:1511.0252

Computational coverage of type logical grammar: The Montague test

It is nearly half a century since Montague made his contributions to the field of logical semantics. In this time, computational linguistics has taken an almost entirely statistical turn and mainstream linguistics has adopted an almost entirely non-formal methodology. But in a minority approach reaching back before the linguistic revolution, and to the origins of computing, type logical grammar (TLG) has continued championing the flags of symbolic computation and logical rigor in discrete grammar. In this paper, we aim to concretise a measure of progress for computational grammar in the form of the Montague Test. This is the challenge of providing a computational cover grammar of the Montague fragment. We formulate this Montague Test and show how the challenge is met by the type logical parser/theorem-prover CatLog2.Peer ReviewedPostprint (published version

A Comparison of Nature Inspired Algorithms for Multi-threshold Image Segmentation

In the field of image analysis, segmentation is one of the most important preprocessing steps. One way to achieve segmentation is by mean of threshold selection, where each pixel that belongs to a determined class islabeled according to the selected threshold, giving as a result pixel groups that share visual characteristics in the image. Several methods have been proposed in order to solve threshold selectionproblems; in this work, it is used the method based on the mixture of Gaussian functions to approximate the 1D histogram of a gray level image and whose parameters are calculated using three nature inspired algorithms (Particle Swarm Optimization, Artificial Bee Colony Optimization and Differential Evolution). Each Gaussian function approximates thehistogram, representing a pixel class and therefore a threshold point. Experimental results are shown, comparing in quantitative and qualitative fashion as well as the main advantages and drawbacks of each algorithm, applied to multi-threshold problem.Comment: 16 pages, this is a draft of the final version of the article sent to the Journa

A reply to Kubota and Levine on gapping

In a series of papers Kubota and Levine give an account of gapping and determiner gapping in terms of hybrid type logical grammar, including anomalous scopal interactions with auxiliaries and negative quantifiers. We make three observations: i) under the counterpart assumptions that Kubota and Levine make, the existent displacement type logical grammar account of gapping already accounts for the scopal interactions, ii) Kubota and Levine overgenerate determiner-verb order permutations in determiner gapping conjuncts whereas the immediate adaptation of their proposal to displacement type logical grammar does not do so, and iii) Kubota and Levine do not capture simplex gapping as a special case of complex gapping, but require distinct lexical entries for the two cases; we show how a generalisation of displacement type logical grammar allows both simplex and discontinuous gapping under a single type assignmentPostprint (author's final draft