Extending partial orders to dense linear orders

Extending Partial Orders to Dense Linear Orders

Extending Partial Orders for Sort Reasoning

Although mathematically elegant, partial orders limit the representation of taxonomic knowledge to subsort-supersort (or isa) relationships. We cannot, for example, directly state that two sorts are incompatible or deene one sort as the intersection of a set of other sorts. This poses problems for specifying more complete taxonomic relationships as well as for denotational semantics in sorted l...

Extending Utility Representations of Partial Orders

The problem is considered as to whether a monotone function defined on a subset P of Euclidean space IR can be strictly monotonically extended to IR. It is proved that this is the case if and only if the function is separably increasing. Explicit formulas are given for a class of extensions which involves an arbitrary function. Similar results are obtained for utility functions that represent s...

Reflecting Linear Arithmetic: From Dense Linear Orders to Presburger Arithmetic

This talk presents reflected quantifier elimination procedures for both integer and real linear arithmetic. Reflection means that the algorithms are expressed as recursive functions on recursive data types inside some logic (in our case HOL), are verified in that logic, and can then be applied to the logic itself. After a brief overview of reflection we will discuss a number of quantifier elimi...

Extending Partial Orders on O-minimal Structures to Deenable Total Orders