Using a model based on\textit {probabilistic functions}(\textit {PF}), it's introduced the concept of\textit {perfect zero knowledge}(\textit {PZK})\textit {commitment scheme}(\textit {CS}) allowing\textit {quasigroupic}\textit {homomorphic commitment}(\textit {QHC}). Using\textit {QHC} of (modular sum in ), application is considered in interactive argument systems (\textit {IAS}) for several languages. In four of the examples--generalized nand ($\Lnandalpha $), string equality (), string inequality () and graph three-colourations ()--complexity improvements are obtained, in comparison to other established results. Motivation then arises to define a general framework for\textit {PZK}-\textit {IAS} for membership in language with committed alphabet (\textit {MLCA}), such that the properties of soundness and\textit {PZK} result from high-level parametrizable aspects. A general simulator is constructed for sequential and (most interestingly) for parallel versions of execution. It therefore becomes easier to conceptualize functionalities of this kind of\textit {IAS} without the consideration of low level aspects of cryptographic primitives. The constructed framework is able to embrace\AcroCS\; allowing\textit {QHC} of functions that are not themselves quasigroupic. Several theoretical considerations are made, namely recognizing a necessary requirements to demand on an eventual\AcroCS\; allowing\textit {QHC} of some complete function in a Boolean sense.