RELATIONSHIPS BETWEEN SPECIFIED AND UNDERSPECIFIED QUANTIFICATION BY THE THEORY OF ACYCLIC RECURSION

RELATIONSHIPS BETWEEN SPECIFIED AND UNDERSPECIFIED QUANTIFICATION BY THE THEORY OF ACYCLIC RECURSION

Authors:
Roussanka LOUKANOVA

DOI:
10.14201/ADCAIJ2016541942

Volume:
Regular Issue 5 (4), 2016

Keywords: 
recursion; type-theory; semantics; algorithms; denotation; reduction; quantifiers; underspecification

The paper introduces a technique for representing quantifier relations that can have different scope order depending on context. The technique is demonstrated by classes of terms denoting relations, where each of the arguments of a relation term is bound by a different quantifier. We represent a formalization of linking quantifiers with the corresponding argument slots that they bind, across lambda-abstractions and reduction steps. The purpose of the technique is to represent underspecified order of quantification, in the absence of a context and corresponding information about the order. Furthermore, it is used to represent subclasses of larger classes of relations depending on order of quantification or specific relations.

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