A Complete Cyclic Proof System for Inductive Entailments in First Order Logic

International audienceIn this paper we develop a cyclic proof system for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions are quantifier-free formulae of first order logic. The proof system consists of a small set of inference rules, inspired by a top-down language inclusion algorithm for tree automata [9]. We show the proof system to be sound, in general, and complete, under certain semantic restrictions involving the set of constraints in the inductive system. Moreover, we investigate the computational complexity of checking these restrictions, when the function symbols in the logic are given the canonical Herbrand interpretation

An Entailment Checker for Separation Logic with Inductive Definitions

In this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formulae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

An Entailment Checker for Separation Logic with Inductive Definitions An Entailment Checker for Separation Logic with Inductive Definitions

International audienceIn this paper, we present Inductor, a checker for entailments between mutually recursive predicates, whose inductive definitions contain ground constraints belonging to the quantifier-free fragment of Separation Logic. Our tool implements a proof-search method for a cyclic proof system that we have shown to be sound and complete, under certain semantic restrictions involving the set of constraints in a given inductive system. Dedicated decision procedures from the DPLL(T)-based SMT solver CVC4 are used to establish the satisfiability of Separation Logic formu-lae. Given inductive predicate definitions, an entailment query, and a proof-search strategy, Inductor uses a compact tree structure to explore all derivations enabled by the strategy. A successful result is accompanied by a proof, while an unsuccessful one is supported by a counterexample

Reasoning in the Bernays-Schönfinkel-Ramsey Fragment of Separation Logic

International audienceSeparation Logic (SL) is a well-known assertion language used in Hoare-style modular proof systems for programs with dynamically allocated data structures. In this paper we investigate the fragment of first-order SL restricted to the Bernays-Schönfinkel-Ramsey quantifier prefix ∃ * ∀ * , where the quantified variables range over the set of memory locations. When this set is uninterpreted (has no associated theory) the fragment is PSPACE-complete, which matches the complexity of the quantifier-free fragment [7]. However, SL becomes undecid-able when the quantifier prefix belongs to ∃ * ∀ * ∃ * instead, or when the memory locations are interpreted as integers with linear arithmetic constraints, thus setting a sharp boundary for decidability within SL. We have implemented a decision procedure for the decidable fragment of ∃ * ∀ * SL as a specialized solver inside a DPLL(T) architecture, within the CVC4 SMT solver. The evaluation of our implementation was carried out using two sets of verification conditions, produced by (i) unfolding inductive predicates, and (ii) a weakest precondition-based verification condition generator. Experimental data shows that automated quantifier instantiation has little overhead, compared to manual model-based instantiation

Assessment of pollutant transport and river water quality using mathematical models

This paper presents (1) general considerations related to the development of two mathematical models for non-conservative transport of nitrate and ammonium under unsteady water flow conditions; (2) their application to predict the transport of pollutant in both customary and accidental pollutant release circumstances; and (2) a discussion related to models use in water quality management. The studied river stretch is part of the River Swale in England, where pollutants are discharged by multiple point sources and also by tributaries. Experimental data was used for model development and verification. The models are useful to (i) assess the downstream river distance affected by pollutant release; (ii) estimate environmental damage; (iii) support decisions on where and how to counteract pollutant discharge; and (iv) also to support the further development of more refined water quality simulation tool

How opportune is multigene testing in metastatic colorectal cancer? A review

Personalized treatment in oncology is the most innovative method of care. The best method to establish personalized treatment is by genetic characterization of the malignant cell. Theoretically, the more detailed the characterization, the more effective the choice of treatment becomes. Currently, there are fast and relatively low-cost options that allow such genetic characterization. However, test results sometimes do not detect targetable alterations and, even if they do detect, the use of the treatment-alteration combination does not always generate a satisfactory oncological response. The present paper aims to answer two questions. First, how targetable can the most common gene alterations in colorectal cancer be. Second, whether it makes sense to use broad molecular testing as a standard in all metastatic patients

Digital divide, skills and perceptions on digitalisation in the European Union - Towards a smart labour market

The new technologies, the digitalisation of processes and automation of work will change the manner of doing business, working and living. The effects of digitalisation on the economy, society and quality of life imply significant challenges of the labour market. All the participants will be concerned: authorities, companies and ordinary people. The objective of this research is to analyse the perceptions of the EU citizens about digitalisation and to highlight the differences among specific socio-demographic groups. The analysis is grounded on a composite methodology, comprising several statistical and econometric methods that provide scientific support to achieved conclusions: statistical analysis (with the primary goal to shed light on the EU citizens' perceptions about their digital technology skills), TwoStep Cluster Analysis (TSCA) (with the purpose to identify the ‘digital vulnerable groups’ and then the ‘digital vulnerable countries’ in terms of the exposure to digital divide) and logistic regression (with the main aim to quantify the impact of the relevant factors on citizens’ perceptions about digitalisation). We identified a group of respondents evaluating themselves as having meagre digital skills, very afraid that robots could steal their jobs and with low usage of the internet. They are elderly, with a low level of education, manual workers or not working, with a relatively low level of income and little Internet use. The originality of our approach is given by the fact that we focused on investigating if digital divide leads to the creation of vulnerable groups (citizens and/or countries) and if there are specific patterns in terms of the perception on being skilled in the use of digital technologies in daily life or at work and of the understanding that robots replace human on the labour market. We aim to find relevant factors for the labour market to assume targeted measures that should be taken for a better match of supply and demand on the labour market and for creating a smart labour market. It is highly needed to increase the people's confidence in their skills level and to make the most of digitalisation of the societies. The results show consistent patterns in term of socio-demographic characteristics and perception towards digitalisation. The latter will have a meaningful impact on the economy and the society in the European Union in the next period. That is why a positive attitude towards digitalisation is essential for transforming this relatively new challenge into an excellent opportunity for the future