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The paper deals with the fundamental rule of extensional logics, namely the rule of Existential Generalization. This rule can be applied in the situation when a function f is applied on its argument a to obtain the value of f at a. If the application does not fail, i.e., if the function f is defined at a, then we can existentially quantify, and derive that there is the value f(a). Our system is based on Transparent Intensional Logic (TIL). Since TIL is a hyperintensional, partial, typed lambda calculus, we examine...

P systems are powerful computational devices, whose structure and functionality are inspired by living cells and organisms. P colonies are one of the types of P systems working with objects. They are formed from one-membrane agents placed in the shared environment and they use very simple rules. It was proved that P colonies are computationally complete devices. In the paper, we investigate the application of P colonies to simulate logical operators. It is obtained in a constructive way. In the first steps we show...