Massimo Fabris

Norms on terms and their use in proving universal termination of a logic program

Abstract In this paper semi-linear norms , a class of functions to weight the terms occurring in a program, are defined and studied. All the functions in this class have the nice property of allowing a syntactical characterization of rigid terms , i.e. terms whose weight does not change under substitution. Based on these norms, a general proof method for universal termination of pure Prolog programs can be adapted to deal with a large class of programs in a simple way. The proof method requires pre/post specifications well-behaved with respect to substitutions to be associated with each predicate symbol in the program, and ordering functions not increasing with respect to substitutions to be associated with cycles in the program. The specification collects information on term properties which are useful to prove that the ordering functions actually decrease at each traversal of each cycle. Some examples of termination proof are also given.

Proving Termination of Logic Programs by Exploiting Term Properties

In this paper semi-linear norms, a class of functions to weight the terms occurring in a program, are defined and studied. All the functions in this class have the nice property of allowing a syntactical characterization of rigid terms, that is terms whose weight does not change under substitution. Based on these norms, a general proof method for termination of pure Prolog programs can be adapted to deal with a large class of programs in a simple way. The simplified method requires pre/post specifications well-behaved with respect to substitutions, quite a general case in practice, and ordering functions not increasing with respect to substitutions, which can be based on semi-linear norms, to be associated to program predicates. A few examples of this simplified proof method are given.

The morphological evolution of the Sciara del Fuoco since 1868: reconstructing the effusive activity at Stromboli volcano

The morphological evolution of the Sciara del Fuoco, Stromboli, is described from a time series dataset formed by Digital Elevation Models and orthophotos derived by digitising historical contour maps compiled in 1868 and 1937 and by processing data from aerial surveys carried out between 1954 and 2009. All maps were co-registered in the same reference system and used to build a quantitative reconstruction of the morphological changes of the Sciara del Fuoco slope. The changes mainly relate to the emplacement of many lava flows and their successive erosion. A comparative quantitative analysis yields estimates of areas and volumes of the lava fields formed on the sub-aerial part of the Sciara del Fuoco during a number of effusive events between 1937 and 2001, some of them never assessed before. The results of the analysis constrain the interpretation of the evolution and the magnitude of the recent effusive activity at the Stromboli volcano. Despite some uncertainties due to widely spaced observation periods, the results integrate all available topographic knowledge and contribute to an understanding of the main characteristics of the recent effusive eruptive styles at Stromboli volcano.

Subsidence above depleted gas fields

Purpose – The purpose of this paper is to give an explanation of the new data available about surface subsidence above the depleted gas reservoir Ravenna Terra. These data confirm the existence after end of exploitation of a reversed subsidence bowl with minimum subsidence above the reservoir, as opposed to conventional subsidence bowls during exploitation which show maximum subsidence in the same location. Design/methodology/approach – The paper analyses these new data about the existence after end of exploitation of a reversed subsidence bowl. The observed behaviour is reproduced successfully with a fully coupled two phase flow code in deforming reservoir rocks which incorporates a constitutive model for partially saturated porous media. Findings – The paper provides successful simulations. These allow affirming with confidence that the explanation for the peculiar behaviour is reservoir flooding and partially saturated rock behaviour. Research limitations/implications – Further research: other case stu...

Testing Sentinel-1A Data in Landslide Monitoring: A Case Study from North-Eastern Italian Pre-Alps

Open image in new window The main aim of this study is to test the effectiveness of Sentinel-1A Synthetic Aperture Radar (SAR) data in monitoring scarcely urbanized slopes affected by slow-moving instabilities. To this end, geological and geomorphological surveys were carried out, satellite SAR data were processed and a GPS network system was installed. The study area, named Rovegliana, is located in the North-Eastern sector of the Italian pre-Alps. Rovegliana slopes are covered by eluvial, colluvial and landslide debris deposits which are mainly affected by superficial phenomena such as creep and soil slips. In situ surveys and Advanced Differential SAR Interferometry (A-DInSAR) processing of ERS, ENVISAT and COSMO Sky-MED SAR data pointed out that the instabilities are active with constant velocities up to 10 mm/year. Only the central and eastern sectors of the area were subjected to an acceleration after an exceptional rainfall event occurred in November 2010. GPS monitoring started in October 2015 and has been implemented through four campaigns made up of high precision geodetic measures of possible soil deformations of 22 vertices of a Global Navigation Satellite System (GNSS) static network. These vertices have been connected by a network to obtain a robust system. Comparing results from historical interferometric data, GPS measurements and interferometry processing of Sentinel SAR data acquired in the period 2015–2016, make it possible to verify if Sentinel data, characterized by short revisiting time, can be used as useful tool to define the spatio-temporal evolution of the recorded instabilities, overcoming the limits of applying interferometric techniques caused by temporal decorrelation due to the presence of vegetation cover, increasing the possibility to obtain significant information about landslide dynamics from SAR data. Moreover, we expect that the high number of planned acquisitions will improve the accuracy of deformation measurements.

Estimation of land subsidence in deltaic areas through differential SAR interferometry: the Po River Delta case study (Northeast Italy)

ABSTRACT River deltas are very complex environments vulnerable to flooding. Most of the world’s deltas are facing the immediate threat of land subsidence that jeopardizes the safety of millions of people worldwide. In Italy, the Po River Delta (PRD) (Northeast Italy) is an area historically affected by high rate of subsidence due to natural and anthropic factors. Even if the subsidence rates remarkably reduced during the last three decades, this process continues to be alarming in particular in low-lying sectors and along the coastline, where the loss of elevation, combined with the sea-level rise, increases the risk related to flooding. In this study, we monitored the subsidence affecting the entire PRD area with advanced differential interferometric synthetic aperture radar (A-DInSAR) techniques applied to three C-band SAR data sets acquired by the European Remote Sensing satellites, Environmental Satellite, and Sentinel-1A satellite in the last 25 years (from 1992 to 2017). The results of the interferometric processing, consisting of both mean velocity and displacement time series along the satellite line of sight, validated by comparison with levelling and global positioning system measurements, show increasing subsidence moving from the inland to the coastline, with maximum deformation velocities, for the most recent data, in the order of −30 mm year−1. In particular, many embankments near the coastal area are affected by high values of subsidence, which increase the flooding hazard of the entire deltaic territory. This work shows the importance of adopting A-DInSAR techniques to update the knowledge of the extent and rates of deformation of subsiding areas in low-lying territories such as river deltas. The outputs of such monitoring can be of primary importance for the future protection of the territory and the flooding risk mitigation.