This paper presents a novel modeling approach for neural systems with point-process inputs and outputs (binary time-series of 0's and 1's) that utilizes Boolean operators of modulo-2 multiplication and addition, corresponding to the logical AND and OR operations respectively. The form of the employed mathematical model is akin to a "Boolean-Volterra" model that contains the product terms of all relevant input lags in a hierarchical order, where terms of order higher than first represent nonlinear interactions among the various lagged values of each input point-process or among lagged values of various inputs (if multiple inputs exist) as they reflect on the output. The coefficients of this Boolean model are also binary variables that indicate the presence or absence of the respective term in each specific model/system. Simulations are used to explore the properties of such models and the feasibility of accurate estimation of such models from short data-records in the presence of noise (i.e. spurious spikes). The results demonstrate the feasibility of obtaining reliable estimates of such models, even in the presence of considerable noise in the input and/or output, thus making the proposed approach an attractive candidate for modeling neural systems in a practical context.