Interpretability logics and generalized Veltman semantics in Agda

Treballs Finals del Màster de Lògica Pura i Aplicada, Facultat de Filosofia, Universitat de Barcelona, Curs: 2020-2021, Tutor: Joost J. Joosten, Luka Mikec[eng] Sufficiently strong arithmetical theories such as PA can formalize their interpretability predicate. This predicate expresses the concept of relativized interpretability between finite extensions of the theory. Interpretability logics study the provable structural behaviour of the interpretability predicate. Interpretability logics extend the provability logic GL. As such, interpretability logics inherit a number of similarities from GL. For instance, the possibility to give relational semantics. In this thesis we focus on the study of two variations of relational semantics à la Kripke known as ordinary Veltman semantics and generalized Veltman semantics. In the literature we find various definitions of generalized Veltman semantics. In particular, there are several conditions of quasi-transitivity, a property that generalized frames must satisfy. We study the interrelations between all of these conditions and discuss their adequacy. In this thesis we compare the expressiveness of ordinary and generalized Veltman semantics. Furthermore, we give procedures that under some assumptions transform, while preserving modal theoremhood, ordinary models to generalized models and vice versa. We study the frame conditions of various relevant interpretability principles present in the literature. Moreover, we provide novel frame conditions for the the principle R1 and the Rn series of principles from [16] with respect to generalized Veltman semantics. We have formalized our findings in Agda, which is a state-of-the-art proof assistant based on an intuitionistic theory which features dependent types. Apart from giving a solid base to our claims, we hope that our Agda library will provide a rallying point for researchers willing to formalize theorems in the field of interpretability logics, or at least, to encourage more research in that direction. Our work is, to our knowledge, the first attempt at formalizing interpretability logics in any proof assistant.[cat] Teories aritmètiques suficientment fortes tals com PA poden formalitzar el seu predicat d’interpretabilitat. Aquest predicat expressa el concepte d’interpretabilitat relativitzada entre extensions finites de la teoria. Les lògiques d’interpretabilitat estudien el comportament estructural demostrable del predicat d’interpretabilitat. Les lògiques d’interpretabilitat estenen la lògica de demostrabilitat GL. Com a tals, hereten algunes semblances de GL. Per exemple, la possibilitat de definir una semàntica relacional. En aquesta tesi ens centrem en l’estudi de dues variacions de semàntiques relacionals a l’estil Kripke que es coneixen com semàntica ordinària Veltman i semàntica generalitzada Veltman. En la literatura trobem vàries definicions de semàntica generalitzada Veltman. En particular, hi ha diverses condicions de quasi-transitivitat, una propietat que els marcs generalitzats de Veltman han de satisfer. Estudiem les interrelacions entre aquestes condicions i comentem la seva pertinència. En aquesta tesi comparem l’expressivitat de les semàntiques Veltman ordinàries i generalitzades. A més, descrivim procediments que sota certes hipòtesis transformen, preservant els teoremes modals, models ordinaris Veltman a models generalitzats Veltman i viceversa. Estudiem les condicions de marc per diversos principis d’interpretabilitat que es troben a la literatura. A més, donem noves condicions de marc pel principi R1 i la sèrie de principis Rn presentats en [16] respecte semàntica generalitzada Veltman. Hem formalitzat les nostres aportacions en Agda, que és un assistent de demostració modern basat en una lògica intuïcionista amb tipus dependents. A banda de donar solidesa als nostres avenços, esperem que la nostra llibreria d’Agda pugui ser un punt de trobada pels investigadors que desitgin formalitzar teoremes en el camp de les lògiques d’interpretabilitat, o si més no, que encoratgi més investigació en aquesta direcció. La nostra llibreria és, que sapiguem, el primer intent de formalitzar lògiques d’interpretabilitat en algun assistent de la demostració

Anàlisi automàtica de programes Haskell

Expliquem els detalls d'un analitzador automàtic de programes Haskell. L'analitzador és capaç de detectar recursivitat en les definicions d'un programa, transformar definicions per tal de millorar-ne l'eficiència mentre se'n manté la semàntica i verificar la terminació en alguns casos.We present an automatic analyser for Haskell programs. Our analyser is able to spot recursivity within the definitions of a program, transform those definitions in order to enhance the overall efficiency while maintaining semantics and check termination under certain conditions

Anàlisi automàtica de programes Haskell

Expliquem els detalls d'un analitzador automàtic de programes Haskell. L'analitzador és capaç de detectar recursivitat en les definicions d'un programa, transformar definicions per tal de millorar-ne l'eficiència mentre se'n manté la semàntica i verificar la terminació en alguns casos.We present an automatic analyser for Haskell programs. Our analyser is able to spot recursivity within the definitions of a program, transform those definitions in order to enhance the overall efficiency while maintaining semantics and check termination under certain conditions

Jutge.org: characteristics and experiences

Jutge.org is an open educational online programming judge designed for students and instructors, featuring a repository of problems that is well organized by courses, topics and difficulty. Internally, Jutge.org uses a secure and efficient architecture and integrates modern verification techniques, formal methods, static code analysis and data mining. Jutge.org has exhaustively been used during the last decade at the Universitat Politecnica de Catalunya to strengthen the learn-by-doing approach in several courses. This paper presents the main characteristics of Jutge.org and shows its use and impact in a wide range of courses covering basic programming, data structures, algorithms, artificial intelligence, functional programming and circuit design.Peer ReviewedPostprint (author's final draft

Automatic inductive equational reasoning

We present Phileas, an automatic theorem prover focused on structural induction. Phileas is capable of automatically proving properties about inductively defined data types in Haskell anb reporting a proof in a human readable format

Anàlisi automàtica de programes Haskell

Expliquem els detalls d'un analitzador automàtic de programes Haskell. L'analitzador és capaç de detectar recursivitat en les definicions d'un programa, transformar definicions per tal de millorar-ne l'eficiència mentre se'n manté la semàntica i verificar la terminació en alguns casos.We present an automatic analyser for Haskell programs. Our analyser is able to spot recursivity within the definitions of a program, transform those definitions in order to enhance the overall efficiency while maintaining semantics and check termination under certain conditions

Electrochemically driven host–guest interactions on patterned donor/acceptor self-assembled monolayers

Here, on ITO//Au patterned substrates SAMs of ferrocene (Fc) on the Au regions and of anthraquinone (AQ) on the ITO areas are prepared, exhibiting three stable redox states. Furthermore, by selectively oxidizing or reducing the Fc or AQ units, respectively, the surface properties are locally modified. As a proof-of-concept, such a confinement of the properties is exploited to locally form host–guest complexes with b-cyclodextrin on specific surface regions depending on the applied voltage.This work was funded by ERC StG 2012-306826 e-GAMES, ITN iSwitch 642196, Networking Research Center on Bioengineering, Biomaterials, and Nanomedicine (CIBER-BBN), the Generalitat de Catalunya (2017-SGR-918) and the Spanish Ministry of Economy and Competitiveness, through the FANCY CTQ2016-80030-R project and the ‘‘Severo Ochoa’’ Programme for Centers of Excellence in R&D (SEV-2015-0496). M. S. M. is enrolled in the Materials Science PhD Program of UAB. E. C. F. and B. J. R. are grateful for support by the Deutsche Forschungsgemeinschaft (SFB 858).Peer reviewe

Healthy life-year costs of treatment speed from arrival to endovascular thrombectomy in patients with ischemic stroke

Importance The benefits of endovascular thrombectomy (EVT) are time dependent. Prior studies may have underestimated the time-benefit association because time of onset is imprecisely known. Objective To assess the lifetime outcomes associated with speed of endovascular thrombectomy in patients with acute ischemic stroke due to large-vessel occlusion (LVO). Data Sources PubMed was searched for randomized clinical trials of stent retriever thrombectomy devices vs medical therapy in patients with anterior circulation LVO within 12 hours of last known well time, and for which a peer-reviewed, complete primary results article was published by August 1, 2020. Study Selection All randomized clinical trials of stent retriever thrombectomy devices vs medical therapy in patients with anterior circulation LVO within 12 hours of last known well time were included. Data Extraction/Synthesis Patient-level data regarding presenting clinical and imaging features and functional outcomes were pooled from the 7 retrieved randomized clinical trials of stent retriever thrombectomy devices (entirely or predominantly) vs medical therapy. All 7 identified trials published in a peer-reviewed journal (by August 1, 2020) contributed data. Detailed time metrics were collected including last known well–to-door (LKWTD) time; last known well/onset-to-puncture (LKWTP) time; last known well–to-reperfusion (LKWR) time; door-to-puncture (DTP) time; and door-to-reperfusion (DTR) time. Main Outcomes and Measures Change in healthy life-years measured as disability-adjusted life-years (DALYs). DALYs were calculated as the sum of years of life lost (YLL) owing to premature mortality and years of healthy life lost because of disability (YLD). Disability weights were assigned using the utility-weighted modified Rankin Scale. Age-specific life expectancies without stroke were calculated from 2017 US National Vital Statistics. Results Among the 781 EVT-treated patients, 406 (52.0%) were early-treated (LKWTP ≤4 hours) and 375 (48.0%) were late-treated (LKWTP >4-12 hours). In early-treated patients, LKWTD was 188 minutes (interquartile range, 151.3-214.8 minutes) and DTP 105 minutes (interquartile range, 76-135 minutes). Among the 298 of 380 (78.4%) patients with substantial reperfusion, median DTR time was 145.0 minutes (interquartile range, 111.5-185.5 minutes). Care process delays were associated with worse clinical outcomes in LKW-to-intervention intervals in early-treated patients and in door-to-intervention intervals in early-treated and late-treated patients, and not associated with LKWTD intervals, eg, in early-treated patients, for each 10-minute delay, healthy life-years lost were DTP 1.8 months vs LKWTD 0.0 months; P < .001. Considering granular time increments, the amount of healthy life-time lost associated with each 1 second of delay was DTP 2.2 hours and DTR 2.4 hours. Conclusions and Relevance In this study, care delays were associated with loss of healthy life-years in patients with acute ischemic stroke treated with EVT, particularly in the postarrival time period. The finding that every 1 second of delay was associated with loss of 2.2 hours of healthy life may encourage continuous quality improvement in door-to-treatment times

Effect of general anaesthesia on functional outcome in patients with anterior circulation ischaemic stroke having endovascular thrombectomy versus standard care: a meta-analysis of individual patient data

Background: General anaesthesia (GA) during endovascular thrombectomy has been associated with worse patient outcomes in observational studies compared with patients treated without GA. We assessed functional outcome in ischaemic stroke patients with large vessel anterior circulation occlusion undergoing endovascular thrombectomy under GA, versus thrombectomy not under GA (with or without sedation) versus standard care (ie, no thrombectomy), stratified by the use of GA versus standard care. Methods: For this meta-analysis, patient-level data were pooled from all patients included in randomised trials in PuMed published between Jan 1, 2010, and May 31, 2017, that compared endovascular thrombectomy predominantly done with stent retrievers with standard care in anterior circulation ischaemic stroke patients (HERMES Collaboration). The primary outcome was functional outcome assessed by ordinal analysis of the modified Rankin scale (mRS) at 90 days in the GA and non-GA subgroups of patients treated with endovascular therapy versus those patients treated with standard care, adjusted for baseline prognostic variables. To account for between-trial variance we used mixed-effects modelling with a random effect for trials incorporated in all models. Bias was assessed using the Cochrane method. The meta-analysis was prospectively designed, but not registered. Findings: Seven trials were identified by our search; of 1764 patients included in these trials, 871 were allocated to endovascular thrombectomy and 893 were assigned standard care. After exclusion of 74 patients (72 did not undergo the procedure and two had missing data on anaesthetic strategy), 236 (30%) of 797 patients who had endovascular procedures were treated under GA. At baseline, patients receiving GA were younger and had a shorter delay between stroke onset and randomisation but they had similar pre-treatment clinical severity compared with patients who did not have GA. Endovascular thrombectomy improved functional outcome at 3 months both in patients who had GA (adjusted common odds ratio (cOR) 1·52, 95% CI 1·09–2·11, p=0·014) and in those who did not have GA (adjusted cOR 2·33, 95% CI 1·75–3·10, p<0·0001) versus standard care. However, outcomes were significantly better for patients who did not receive GA versus those who received GA (covariate-adjusted cOR 1·53, 95% CI 1·14–2·04, p=0·0044). The risk of bias and variability between studies was assessed to be low. Interpretation: Worse outcomes after endovascular thrombectomy were associated with GA, after adjustment for baseline prognostic variables. These data support avoidance of GA whenever possible. The procedure did, however, remain effective versus standard care in patients treated under GA, indicating that treatment should not be withheld in those who require anaesthesia for medical reasons