Our work aims at assisting people in the collaborative building of a theory, in such a way that each individual is allowed to formulate and empirically test his own partial understanding, and can without extra effort contribute to a testable theory shared by the whole group. A multi-disciplinary survey touching on the underlying biological mechanisms supporting cognition, linguistic communication as a means for sharing and formalizing, and the theory building process, leads to a series of requirements for an 'abstract machine' able to compose partial theories within a conversation. The 'Austin' abstract machine, based on three speech acts: 'assertives', 'directives' and 'commissives', is then fully specified, where 'conversational patterns' concurrently achieve the processing of information. Good properties are demonstrated: end in finite time, confluence (the result is not affected by the concurrency), reasonable complexity, natural composition of programs recognized by the abstract machine, graphical analysis facilities. A generative grammar based on conceptual graphs is proposed for the sentences embedded in the speech acts. 'Collaboratively solving a Sudoku' illustrates this grammar, then is implemented on a Java prototype of the abstract machine. By comparison to 'concurrent logic programming', and then to 'blackboard architecture', 'Austin' appears as a trade-off between the controllability of the declarative paradigm and the expressivity of the imperative techniques.