This paper examines how logical structures represent sharp and unsharp propositions in classical and quantum systems. Classical sharp logic is modeled by Boolean algebras, where propositions have bivalent truth values, complements are globally defined, and distributivity holds. Quantum sharp logic is modeled by orthomodular lattices of closed Hilbert-space subspaces or projection operators; it retains definite yes–no outcomes for ideal measurements but rejects the Boolean assumptions of global truth valuation and distributivity. Classical unsharp logic uses fuzzy membership or probabilistic truth values to describe vagueness and incomplete information, whereas quantum unsharp logic is expressed through effects and effect algebras, which capture noisy, inefficient, and generalized measurements. The paper’s central question is which algebraic structure is appropriate for each combination of classical or quantum behavior and sharp or unsharp measurement. The analysis shows that the four cases form a coherent hierarchy: Boolean algebras describe deterministic classical events, orthomodular lattices describe ideal quantum propositions, fuzzy or probabilistic models describe classical partial truth, and effect algebras describe realistic quantum effects. This classification clarifies the mathematical and physical role of unsharpness and explains why effect algebras are needed beyond projection-based quantum logic.
Reliable rainfall–runoff estimation is essential for the hydraulic design and planning of canal systems, particularly in ungauged catchments where streamflow records are unavailable. This study aimed to generate design-storm hydrographs and estimate peak runoff for the Narai Canal catchment in Peshawar, Khyber Pakhtunkhwa, Pakistan, using the Log-Pearson Type III (LP-III) distribution and the WinTR-20 model under ungauged-basin conditions. Rainfall frequency analysis was performed using the LP-III distribution to estimate design rainfall for selected return periods. The Soil Conservation Service (SCS) curve number method implemented in WinTR-20 was then used to simulate runoff hydrographs and peak discharges based on watershed characteristics, including land use, curve number, and time of concentration. The analysis produced design-storm hydrographs and corresponding peak discharge estimates that increased with rainfall intensity and return period. The LP-III distribution adequately characterized design rainfall, while the WinTR-20 model provided physically consistent runoff estimates for evaluating watershed response under different design scenarios. The results demonstrate the influence of watershed characteristics on runoff generation and provide preliminary hydrological estimates for the study area, representing a design-scenario analysis for an ungauged basin rather than a validated rainfall–runoff forecasting model. The generated design hydrographs and peak discharge estimates provide useful information for preliminary canal hydraulic design, drainage planning, and flood-risk assessment. Future studies should incorporate observed streamflow data to calibrate and validate the model before it is applied for operational flood forecasting.
