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In this paper, we propose a formulation of the spatial search problem, where a mobile searching agent seeks to locate a stationary target in a given search region or declare that the target is absent. The objective is to minimize the expected time until this search decision of target's presence (and location) or absence is made. Bayesian update expressions for the integration of observations, including false-positive and false-negative detections, are derived to facilitate both theoretical and numerical analyses of various computationally efficient (semi-)adaptive search strategies. Closed-form expressions for the search decision evolution and analytic bounds on the expected time to decision are provided under assumptions on search environment and/or sensor characteristics. Simulation studies validate the probabilistic search formulation and comparatively demonstrate the effectiveness of the proposed search strategies.