Identification through Inductive Verification Application to Monotone Quantifiers
نویسنده
چکیده
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 (see e.g. [7, 6]), which goes back to the notion of identification in the limit as formulated in [5], and the paradigm of investigating natural language determiners in terms of generalized quantifiers in finite models (see e.g.[1]).
منابع مشابه
Monotonicity in quantifier verification
Monotonicity is considered to be one of the key properties of languages both in logic and linguistics. In model theory it contributes to definability (see e.g. Väänänen and Westerståhl, 2002), in linguistics it is used, among other applications, to explain the phenomenon of negative polarity items (see e.g. Ladusaw, 1979). There are also strong links between monotonicity and learnability (see e...
متن کاملPragmatic effects in processing superlative and comparative quantifiers
I present and discuss results of the experiment in which I investigate processing of so-called superlative quantifiers, such as at most n and at least n (where n represents a bare numeral), as well as their (presumably) logically equivalent though linguistically different forms, i.e. the disjunctive and the comparative form. Generalized Quantifier Theory (GQT ) defines those superlative quantif...
متن کاملUsing Dynamic Symbolic Execution to Improve Deductive Verification
One of the most challenging problems in deductive program verification is to find inductive program invariants typically expressed using quantifiers. With strong-enough invariants, existing provers can often prove that a program satisfies its specification. However, provers by themselves do not find such invariants. We propose to automatically generate executable test cases from failed proof at...
متن کاملScope Dominance with Upward Monotone Quantifiers
We give a complete characterization of the class of upward monotone generalized quantifiers Q1 and Q2 over countable domains that satisfy the scheme Q1x Q2y ! Q2y Q1x . This generalizes the characterization of such quantifiers over finite domains, according to which the scheme holds iff either Q1 is 9 or Q2 is 8 (excluding trivial cases). Our result shows that in infinite domains, there are mor...
متن کاملOn the Expressive Power of Monotone Natural Language Quantifiers over Finite Models
We study definability in terms of monotone generalized quantifiers satisfying Isomorphism closure, Conservativity and Extension. Among the quantifiers with the latter three properties — here called CE quantifiers — one finds the interpretations of determiner phrases in natural languages. The property of monotonicity is also linguistically ubiquitous, though some determiners like an even number ...
متن کامل