Inductive inference from theory laden data (Q1206808)

The main result of this paper is a demonstration of necessary and sufficient conditions for the existence of a method that can detect the semantic status of a given string over a given relativistic system (defined in the paper). This theorem may be thought of as a generalization of \textit{D. Angluin's} necessary and sufficient conditions for language acquisition from positive data [Inf. Control 45, 117-135 (1980; Zbl 0459.68051)]. The positive side of the proof, together with establishing completeness of our technique for proving relativistic problems unsolvable, involves the construction of a relativistic inductive method. The negative side of the proof may be viewed as a completeness theorem for this method, in the following sense: given a specification of how truth, syntax, and observability can possibly depend upon conceptual scheme (i.e. given a relativistic system) and given a string in \(\Sigma^*\), the method will detect the semantic status of the string if and only if it is possible to do so. Similar results are given for truth-stable and scheme-stable truth detection.