Identification through Inductive Verification. Application to Monotone Quantifiers
Nina Gierasimczuk

Abstract:
Identification through Inductive Verification.
Application to Monotone Quantifiers
Nina Gierasimczuk

Abstract:
In this paper we are concerned with some general properties of
scientific hypotheses. We investigate the relationship between the
situation when the task is to verify a given hypothesis, and when a
scientist has to pick a correct hypothesis from an arbitrary class of
alternatives. Both these procedures are based on induction. We
understand hypotheses as generalized quantifiers of types <1> or
<1,1>. Some of their formal features, like monotonicity, appear to be
of great relevance. We first focus on monotonicity, extendability and
persistence of quantifiers. They are investigated in context of
epistemological verifiability of scientific hypotheses. In the second
part we show that some of these properties imply learnability. As a
result two strong paradigms are joined: the paradigm of computational
epistemology, which goes back to the notion of identification in the
limit as formulated by E.M. Gold in 1967, and the paradigm of
investigating natural language determiners in terms of generalized
quantifiers in finite models.