Intuitionistic implication makes model checking hard

We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov's logic KC. We show that the model checking problem is P-complete for the implicational fragments of all these intuitionistic logics. For BPL and FPL we reach P-hardness even on the implicational fragment with only one variable. The same hardness results are obtained for the strictly implicational fragments of their modal companions. Moreover, we investigate whether formulas with less variables and additional connectives make model checking easier. Whereas for variable free formulas outside of the implicational fragment, FPL model checking is shown to be in LOGCFL, the problem remains P-complete for BPL.Comment: 29 pages, 10 figure

External forcing of earthquake swarms at Alpine regions: example from a seismic meteorological network at Mt. Hochstaufen SE-Bavaria

In the last few years, it has been shown that above-average rainfall and the following diffusion of excess water into subsurface structures is able to trigger earthquake swarms in the uppermost brittle portion of the Earth's crust. However, there is still an ongoing debate on whether the crust already needs to be in a critical-to-failure state or whether it is sufficient that water is transported rapidly within channels and veins of karst or similar geological formations to the underlying, earthquake-generating layers. Also unknown is the role of other forcing mechanisms, possible co-variables and probably necessary tectonic loading in the triggering process of earthquakes. Because of these problems, we do not use an explicit physical model but instead analyze the meteorological and geophysical data via sophisticated statistical models. ewline We are interested in the influence of a more complete set of possible forcing parameters, including the influence of synthetic earth tides, on the occurrence of earthquake swarms. In this context, regression models are the adequate tool, since the calculation of simple correlations can be confounded by the other variables. Since our outcome variable (the number of quakes) is a count, we use Poisson regression models that include the plausible assumption of a Poisson distribution for the counts. For this study, we use nearly continuous recordings of a seismic and meteorological network in the years 2002–2008 at Mt. Hochstaufen in SE-Bavaria. Our non-linear regression model reveals correlations between external forces and the triggering of earthquakes. In addition to the still dominant influence of rainfall, theoretical estimated tidal tilt show some weak influence on the swarm generation. However, the influence of the modeled trend functions shows that rain is by far not the most important forcing mechanism present in the data

On Interpretability between some weak essential undecidable theories.

We introduce two essentially undecidable first-order theories WT and T. The intended model for the theories is a term model. We prove that WT is mutually interpretable with Robinson’s R. Moreover, we prove that Robinson’s Q is interpretable in T