A simplex language has one set of signals and one set of messages. Some signals may be ambiguous and have more than one meaning. There may also be some meanings that correlate with more than one signal.
A multiplex language has one set of signals and two or more message sets.
A communication system, like a human language, contains one set of signals - the objects at the phonetic level, or sentences written at the orthographic level for most computational linguists. But the adult communication system has two entirely different message systems. One message system, call it the 'Vanity Message System,' is what most linguists study as 'semantics,' 'logical form,' or 'meaning.' The second message set, call it the 'Test Pattern System,' is what some linguists, notably Zellig Harris, called the paraphrase and cooccurrence - or transformational system. The Vanity system can analyze sentences one at a time and ask such questions as: What does this sentence, Sx, mean? What is the logical form of Sx? The Test Pattern System cannot ask any questions about individual sentences, but must phrase all questions in terms of two or more sentences. In the Test Pattern System, one asks questions like: Are Sx and Sy synonymous? If Sx is true, must Sy be true also?
A child learns a language by being exposed to the adult signal system, that is, it hears the sounds made by adults. The child participates in discussing the vanities of the world with the adults by assigning meaning to individual sentences. But the child learns, or rather aligns its universal grammar, with the I- language of the adult community by matching up the Test Patterns in its burgeoning I-language with the Test Patterns in the sentence community it inhabits.
When the child has an I-language that defines the same patterns of synonymy and implication as the adult, independently of what any sentences may or may not mean, then the child has aligned its I-language with that of the speech community.
This assumes that adult speakers may disagree in any number of ways about which sentences are well-formed or ill-formed, and what any given sentence means, but a speech community is defined by examining which sentences adults think are synonymous, have implicational relations, and so on.
Under these assumptions, a child could learn an I-language from someone who only told lies, someone who had a totally wrong view of things in the world, and so on. The meaning or semantic value of any sentence plays no role in the child's recognition that it has learned a language (or set a parameter). The data that sets parameters, and decides that a language has been learned, is the type of data called by Harris paraphrase and cooccurrence, and by others repair sentences.
In short, a language is a code. An adult speaking, encodes the meaning into the sounds. An adult listening decodes the sounds back into their meaning. A child, at the vanity level, is decoding as best it can. But at the test pattern level, the child is cracking the code used by the two adults.
An adult has its linguistic capacities optimized to communicate at the vanity level, but there is a residual redundancy reducing the channel capacity to communicate the test patterns. An adult is optimized as a decoder/encoder and has a multiplex grammar. A child is optimized as a code cracker, that is, a demultiplexer, but it also can encode and decode.