Studying Algebraic Structures Using Prover9 and Mace4

In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We will see that these tools, when combined with human insight and traditional algebraic methods, help us to explore the problem space quickly and effectively. The counter-example generator rapidly rules out many false conjectures, while the theorem prover is often much more efficient than a human being at verifying algebraic identities. The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops. We will see how this approach helped us to discover new theorems and to find new or improved proofs of known results. We also make some suggestions for how one might deploy these tools to supplement a more conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics Research and Teaching", Mathematics Education in the Digital Era 14, edited by G. Hanna et al. (eds.), published by Springe

Logics for Petri nets with propagating failures

Petri nets play a central role in the formal modelling of a wide range of complex systems and scenarios. Their ability to handle with both concurrency and resource awareness justifies their spread in the current formal development practices. On the logic side, Dynamic Logics are widely accepted as the de facto formalisms to reason about computational systems. However, as usual, the application to new situations raises new challenges and issues. The ubiquity of failures in the execution of current systems, interpreted in these models as triggered events that are not followed by the corresponding transition, entails not only the adjustment of these structures to deal with this reality, but also the introduction of new logics adequate to this emerging phenomenon. This paper contributes to this challenge by exploring a combination of two previous works of the authors, namely the Propositional Dynamic Logic for Petri Nets [1] and a parametric construction of multi-valued dynamic logics presented in [13]. This exercise results in a new family of Dynamic Logics for Petri Nets suitable to deal with firing failures.publishe

Verification for Everyone? An Overview of Dynamic Logic

This note, reporting the homonym keynote presented in the International Symposium on Molecular Logic and Computational Synthetic Biology 2018, traces an informal roadmap on Dynamic Logic (DL) field, focusing on its versatility and resilience to be adjusted and adopted in a wide class of application domains and computational paradigms. The exposition argues the room for developments on tagging DL to the analysis of synthetic biologic domain.publishe

Sexuality and Body Image After Uterine Artery Embolization and Hysterectomy in the Treatment of Uterine Fibroids: A Randomized Comparison

In this paper the effect of uterine artery embolization (UAE) on sexual functioning and body image is investigated in a randomized comparison to hysterectomy for symptomatic uterine fibroids. The EMbolization versus hysterectoMY (EMMY) trial is a randomized controlled study, conducted at 28 Dutch hospitals. Patients were allocated hysterectomy (n = 89) or UAE (n = 88). Two validated questionnaires (the Sexual Activity Questionnaire [SAQ] and the Body Image Scale [BIS]) were completed by all patients at baseline, 6 weeks, and 6, 12, 18, and 24 months after treatment. Repeated measurements on SAQ scores revealed no differences between the groups. There was a trend toward improved sexual function in both groups at 2 years, although this failed to reach statistical significance except for the dimensions discomfort and habit in the UAE arm. Overall quality of sexual life deteriorated in a minority of cases at all time points, with no significant differences between the groups (at 24 months: UAE, 29.3%, versus hysterectomy, 23.5%; p = 0.32). At 24 months the BIS score had improved in both groups compared to baseline, but the change was only significant in the UAE group (p = 0.009). In conclusion, at 24 months no differences in sexuality and body image were observed between the UAE and the hysterectomy group. On average, both after UAE and hysterectomy sexual functioning and body image scores improved, but significantly so only after UAE

Complexity of equational theory of relational algebras with standard projection elements

The class $\mathsf{TPA}$ of t rue p airing a lgebras is defined to be the class of relation algebras expanded with concrete set theoretical projection functions. The main results of the present paper is that neither the equational theory of $\mathsf{TPA}$ nor the first order theory of $\mathsf{TPA}$ are decidable. Moreover, we show that the set of all equations valid in $\mathsf{TPA}$ is exactly on the $\Pi ^1_1$ level. We consider the class $\mathsf{TPA}^-$ of the relation algebra reducts of $\mathsf{TPA}$’s, as well. We prove that the equational theory of $\mathsf{TPA}^-$ is much simpler, namely, it is recursively enumerable. We also give motivation for our results and some connections to related work

Service Interaction Flow Analysis Technique for Service Personalization

Abstract Service interaction flows are difficult to capture, analyze, outline, and represent for research and design purposes. We examine how variation of personalized service flows in technology-mediated service interaction can be modeled and analyzed to provide information on how service personalization could support interaction. We have analyzed service interaction cases in a context of technology-mediated car rental service. With the analysis technique we propose, inspired by Interaction Analysis method, we were able to capture and model the situational service interaction. Our contribution regarding technology-mediated service interaction design is twofold: First, with the increased understanding on the role of personalization in managing variation in technology-mediated service interaction, our study contributes to designing service management information systems and human-computer interfaces that support personalized service interaction flows. Second, we provide a new analysis technique for situated interaction analysis, particularly when the aim is to understand personalization in service interaction flows

Daily intake of antioxidants in relation to survival among adult patients diagnosed with malignant glioma

<p>Abstract</p> <p>Background</p> <p>Malignant glioma is a rare cancer with poor survival. The influence of diet and antioxidant intake on glioma survival is not well understood. The current study examines the association between antioxidant intake and survival after glioma diagnosis.</p> <p>Methods</p> <p>Adult patients diagnosed with malignant glioma during 1991-1994 and 1997-2001 were enrolled in a population-based study. Diagnosis was confirmed by review of pathology specimens. A modified food-frequency questionnaire interview was completed by each glioma patient or a designated proxy. Intake of each food item was converted to grams consumed/day. From this nutrient database, 16 antioxidants, calcium, a total antioxidant index and 3 macronutrients were available for survival analysis. Cox regression estimated mortality hazard ratios associated with each nutrient and the antioxidant index adjusting for potential confounders. Nutrient values were categorized into tertiles. Models were stratified by histology (Grades II, III, and IV) and conducted for all (including proxy) subjects and for a subset of self-reported subjects.</p> <p>Results</p> <p>Geometric mean values for 11 fat-soluble and 6 water-soluble individual antioxidants, antioxidant index and 3 macronutrients were virtually the same when comparing all cases (n = 748) to self-reported cases only (n = 450). For patients diagnosed with Grade II and Grade III histology, moderate (915.8-2118.3 mcg) intake of fat-soluble lycopene was associated with poorer survival when compared to low intake (0.0-914.8 mcg), for self-reported cases only. High intake of vitamin E and moderate/high intake of secoisolariciresinol among Grade III patients indicated greater survival for all cases. In Grade IV patients, moderate/high intake of cryptoxanthin and high intake of secoisolariciresinol were associated with poorer survival among all cases. Among Grade II patients, moderate intake of water-soluble folate was associated with greater survival for all cases; high intake of vitamin C and genistein and the highest level of the antioxidant index were associated with poorer survival for all cases.</p> <p>Conclusions</p> <p>The associations observed in our study suggest that the influence of some antioxidants on survival following a diagnosis of malignant glioma are inconsistent and vary by histology group. Further research in a large sample of glioma patients is needed to confirm/refute our results.</p

Gender differences in the use of cardiovascular interventions in HIV-positive persons; the D:A:D Study

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