A Modal Logic for Subject-Oriented Spatial Reasoning

We present a modal logic for representing and reasoning about space seen from the subject\u27s perspective. The language of our logic comprises modal operators for the relations "in front", "behind", "to the left", and "to the right" of the subject, which introduce the intrinsic frame of reference; and operators for "behind an object", "between the subject and an object", "to the left of an object", and "to the right of an object", employing the relative frame of reference. The language allows us to express nominals, hybrid operators, and a restricted form of distance operators which, as we demonstrate by example, makes the logic interesting for potential applications. We prove that the satisfiability problem in the logic is decidable and in particular PSpace-complete

Computational Complexity of a Core Fragment of Halpern-Shoham Logic

Halpern-Shoham logic (HS) is a highly expressive interval temporal logic but the satisfiability problem of its formulas is undecidable. The main goal in the research area is to introduce fragments of the logic which are of low computational complexity and of expressive power high enough for practical applications. Recently introduced syntactical restrictions imposed on formulas and semantical constraints put on models gave rise to tractable HS fragments for which prototypical real-world applications have already been proposed. One of such fragments is obtained by forbidding diamond modal operators and limiting formulas to the core form, i.e., the Horn form with at most one literal in the antecedent. The fragment was known to be NL-hard and in P but no tight results were known. In the paper we prove its P-completeness in the case where punctual intervals are allowed and the timeline is dense. Importantly, the fragment is not referential, i.e., it does not allow us to express nominals (which label intervals) and satisfaction operators (which enables us to refer to intervals by their labels). We show that by adding nominals and satisfaction operators to the fragment we reach NP-completeness whenever the timeline is dense or the interpretation of modal operators is weakened (excluding the case when punctual intervals are disallowed and the timeline is discrete). Moreover, we prove that in the case of language containing nominals but not satisfaction operators, the fragment is still NP-complete over dense timelines

On Expressiveness of Halpern-Shoham Logic and its Horn Fragments

Abstract: Halpern and Shoham\u27s modal logic of time intervals (HS in short) is an elegant and highly influential propositional interval-based logic. Its Horn fragments and their hybrid extensions have been recently intensively studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. We (1) show what time structures are definable in the language of HS, and (2) determine which HS fragments are capable of expressing: hybrid machinery, i.e., nominals and satisfaction operators, and somewhere, difference, and everywhere modal operators. These results enable us to classify HS Horn fragments according to their expressive power and to gain insight in the interplay between their decidability/computational complexity and expressiveness

Analysis of the Course and Frequency of High Water Stages in Selected Catchments of the Upper Vistula Basin in the South of Poland

The paper presents an analysis of the course and frequency of high water stages in selected catchments of the upper Vistula basin in the south of Poland. The following rivers were investigated: the Dunajec–Nowy Targ-Kowaniec cross-section, the Rudawa–Balice cross-section, the Kamienica–Nowy Sącz cross-section, the Wisłok–Tryńcza cross-section and the San–Przemyśl cross-section. Daily flows from the years 1983–2014 were used to determine maximum annual flows and maximum flows per summer and winter half-year. Selected floods were analyzed with reference to the following metrics: POTX (mean size of the flow determined based on high water stages exceeding the assumed threshold value), POT3F (number of high water stages exceeding the threshold value for each hydrological year), WPOT3F (number of high water stages exceeding the threshold value for the winter half-year and), LOPT3F (number of high water stages exceeding the threshold value for the summer half-year). The determined metrics were analyzed for trend (Mann-Kendall test), homogeneity (Kruskal-Wallis test), and heteroscedasticity (Levene test). Additionally, periodograms were used to determine periodicity of time series for maximum annual flows. The resulting computations indicated upward trends in the analyzed flood metrics but they were not significant in any case. Therefore, in the years 1983–2014 no factors were observed that would significantly affect the size and frequency of high water runoff from the investigated catchments

Estimation of CN Parameter for Small Agricultural Watersheds Using Asymptotic Functions

This paper investigates a possibility of using asymptotic functions to determine the value of curve number (CN) parameter as a function of rainfall in small agricultural watersheds. It also compares the actually calculated CN with its values provided in the Soil Conservation Service (SCS) National Engineering Handbook Section 4: Hydrology (NEH-4) and Technical Release 20 (TR-20). The analysis showed that empirical CN values presented in the National Engineering Handbook tables differed from the actually observed values. Calculations revealed a strong correlation between the observed CN and precipitation (P). In three of the analyzed watersheds, a typical pattern of the observed CN stabilization during abundant precipitation was perceived. It was found that Model 2, based on a kinetics equation, most effectively described the P-CN relationship. In most cases, the observed CN in the investigated watersheds was similar to the empirical CN, corresponding to average moisture conditions set out by NEH-4. Model 2 also provided the greatest stability of CN at 90% sampled event rainfall

Analysis of the Course and Frequency of High Water Stages in Selected Catchments of the Upper Vistula Basin in the South of Poland

The paper presents an analysis of the course and frequency of high water stages in selected catchments of the upper Vistula basin in the south of Poland. The following rivers were investigated: the Dunajec–Nowy Targ-Kowaniec cross-section, the Rudawa–Balice cross-section, the Kamienica–Nowy Sącz cross-section, the Wisłok–Tryńcza cross-section and the San–Przemyśl cross-section. Daily flows from the years 1983–2014 were used to determine maximum annual flows and maximum flows per summer and winter half-year. Selected floods were analyzed with reference to the following metrics: POTX (mean size of the flow determined based on high water stages exceeding the assumed threshold value), POT3F (number of high water stages exceeding the threshold value for each hydrological year), WPOT3F (number of high water stages exceeding the threshold value for the winter half-year and), LOPT3F (number of high water stages exceeding the threshold value for the summer half-year). The determined metrics were analyzed for trend (Mann-Kendall test), homogeneity (Kruskal-Wallis test), and heteroscedasticity (Levene test). Additionally, periodograms were used to determine periodicity of time series for maximum annual flows. The resulting computations indicated upward trends in the analyzed flood metrics but they were not significant in any case. Therefore, in the years 1983–2014 no factors were observed that would significantly affect the size and frequency of high water runoff from the investigated catchments

Influence of Rainfall Events and Surface Inclination on Overland and Subsurface Runoff Formation on Low-Permeable Soil

This paper presents the results of laboratory tests that allowed us to determine the effect of the soil surface inclination and its initial moisture content on the formation of overland and subsurface runoff. The experiments were carried out for the soil that is commonly present in the southern part of Poland, including the Outer Carpathians. The results of these measurements served as a reference for overland runoff calculations using the Richards model, simplified Green–Ampt model, and the empirical model (MSME). The results of the measurements showed that, for low-permeable soil, overland runoff is the dominant form. It was shown that a slope in the range of 2.5–5.0% does not have a significant effect on the amount of overland runoff, but affects its dynamics. The measurements also showed that the starting time and amount of overland runoff are strictly associated with the initial soil moisture content. High soil moisture content in the period preceding the onset of rainfall causes faster generation and an increase in overland runoff, which is caused by the saturation of the surface layer of the soil. This mechanism was confirmed by the results of calculations using the Richards model and measurements of the electrical resistance of the soil. Theoretical calculations showed that the results of the runoff calculations using the Richards and Green–Ampt models are strongly dependent on the hydraulic properties of the soil adopted for the analysis. It was also demonstrated that the modified MSME model satisfactorily estimates the amount of overland and subsurface runoff, but requires parameter calibration based on existing hydrological data