Satisfiability Threshold of Random Propositional S5 Theories

Modal logic S5, which isan important knowledge representation and reasoning paradigm, has been successfully applied in various artificial-intelligence-related domains. Similar to the random propositional theories in conjunctive clause form, the phase transition plays an important role in designing efficient algorithms for computing models of propositional S5 theories. In this paper, a new form of S5 formula is proposed, which fixes the number of modal operators and literals in the clauses of the formula. This form consists of reduced 3-3-S5 clauses of the form l1∨l2∨ξ, where ξ takes the form □(l3∨l4∨l5), ◊(l3∧l4∧l5), or a propositional literal, and li(1≤i≤5) is a classical literal. Moreover, it is demonstrated that any S5 formula can be translated into a set of reduced 3-3-S5 clauses while preserving its satisfiability. This work further investigates the probability of a random 3-c-S5 formula with c=1,2,3 being satisfied by random assignment. In particular, we show that the satisfiability threshold of random 3-1-S5 clauses is −ln2(1−Pd−Ps)ln78+Ps·ln34, where Ps and Pd denote the probabilities of different modal operators appearing in a clause. Preliminary experimental results on random 3-1-S5 formulas confirm this theoretical threshold

Computing Sufficient and Necessary Conditions in CTL: A Forgetting Approach

Computation tree logic (CTL) is an essential specification language in the field of formal verification. In systems design and verification, it is often important to update existing knowledge with new attributes and subtract the irrelevant content while preserving the given properties on a known set of atoms. Under the scenario, given a specification, the weakest sufficient condition (WSC) and the strongest necessary condition (SNC) are dual concepts and very informative in formal verification. In this article, we generalize our previous results (i.e., the decomposition, homogeneity properties, and the representation theorem) on forgetting in bounded CTL to the unbounded one. The cost we pay is that, unlike the bounded case, the result of forgetting in CTL may no longer exist. However, SNC and WSC can be obtained by the new forgetting machinery we are presenting. Furthermore, we complement our model-theoretic approach with a resolution-based method to compute forgetting results in CTL. This method is currently the only way to compute forgetting results for CTL and temporal logic. The method always terminates and is sound. That way, we set up the resolution-based approach for computing WSC and SNC in CTL

On Sufficient and Necessary Conditions in Bounded CTL

Computation Tree Logic (CTL) is one of the central formalisms in formal verification. As a specification language, it is used to express a property that the system at hand is expected to satisfy. From both the verification and the system design points of view, some information content of such property might become irrelevant for the system due to various reasons e.g., it might become obsolete by time, or perhaps infeasible due to practical difficulties. Then, the problem arises on how to subtract such piece of information without altering the relevant system behaviour or violating the existing specifications. Moreover, in such a scenario, two crucial notions are informative: the strongest necessary condition (SNC) and the weakest sufficient condition (WSC) of a given property. To address such a scenario in a principled way, we introduce a forgetting-based approach in CTL and show that it can be used to compute SNC and WSC of a property under a given model. We study its theoretical properties and also show that our notion of forgetting satisfies existing essential postulates. Furthermore, we analyse the computational complexity of basic tasks, including various results for the relevant fragment CTLAF

Xueshuantong Injection in Treating Deep Venous Thrombosis: A Systematic Review and Trial Sequential Analysis

Aims. In recent years, the incidence of deep venous thrombosis (DVT) presents an increasing trend year by year. The current evidence regarding the efficacy and safety of Xueshuantong injection for DVT is controversial. This systematic review (SR) aimed to assess the efficacy and safety of Xueshuantong injection in the treatment of DVT systematically and provide an evidence-based reference for clinical treatment. Methods. Nine electronic databases were used to identify the literature consisting of randomized controlled trials (RCTs) with a date of search of 1 November 2020. Clinical effective rate and incidence rate of adverse events were investigated as primary outcomes. Patency rate of femoral vein, patency rate of popliteal vein, patency rate of posterior tibial vein, circumference difference, activated partial thromboplastin time (APTT), and D-dimer (D-D) were investigated as secondary outcomes. Revman 5.4.1 was used to analyze the results. Analysis of the power of evidence was performed with Trial Sequential Analysis (TSA). Results. A total of 12 articles including 1018 patients were included. The results of the meta-analysis showed that the clinical effective rate in the experimental group was higher than that in the control group, the incidence rate of adverse events in the experimental group was higher than that in the control group; after the operation, the patency rate of femoral vein, patency rate of popliteal vein, patency rate of posterior tibial vein, circumference difference, APTT, and D-D in the experimental group were significantly improved compared with those in the control group, and the difference between the groups was statistically significant. TSA suggested that the meta-analysis concerning the clinical effectiveness of Xueshuantong injection in the treatment of DVT was of adequate power to reach firm conclusions. Conclusion. Based on the current analysis, Xueshuantong injection as an add-on treatment provided better treatment effect for DVT with adequate power but this benefit should be considered with caution because of the small number of studies included in the meta-analysis and the high or unclear risk of bias of the included trials, suggesting that further studies are needed

Antibacterial Halloysite‐Modified Chitosan/Polyvinylpyrrolidone Nanofibers for Ultrasensitive Self‐Powered Motion Monitoring

Abstract High flexibility, porosity, and antibacterial activity are extremely desired for wearable health monitoring, which is beneficial to simultaneously promote wearing comfort and safety. In this study, an antibacterial nanofibers‐based triboelectric generator (AN‐TENG) composed of the flexible chitosan/polyvinylpyrrolidone modified with halloysite nanotubes (CTS/PVP/HNTs) nanofibers and cube‐arrays structured Ecoflex film is proposed for simultaneously energy harvesting and self‐powered human motion monitoring. The open‐circuit voltage (280 V), short‐circuit current (3.98 μA), and transferred charge (51 nC) of the CTS/PVP/HNTs nanofibers TENG at the optimal compound concentration are increased by 90.8%, 86.92%, and 96.2%, respectively, compared to the CTS/PVP nanofibers one (size: 3 cm × 3 cm, mechanical force: 10 N @1 Hz), revealing good real‐time monitoring ability for human wrist, elbow, and finger motion. An antibacterial test is carried out to evaluate the antibacterial activity and the antibacterial rate of the nanofibers against Escherichia coli (ATCC 8739) and Staphylococcus aureus (ATCC 6538) based on the current national standard GB/T 31402–2015, indicating good antibacterial properties of the nanofibers. This research offers an ingenious strategy to establish an antibacterial nanofibers‐based TENG for self‐powered motion monitoring and energy harvesting and offers a new insight to improve the practical security of wearable electronic devices