The `paper`

is available locally. The
concurrent paper referenced is Set-at-a-Time Solving in Weighted Logic Programs (2017).

Rejected from ICLP’17, but this was a precursor to chapter 3 of my thesis.

Abstract:

Our concurrent paper has considered the semantics of an arithmetic circuit solver extended to work on potentially infinite circuits that are described by weighted logic programs. That paper assumed a sound, decidable theory of sets of terms. Unfortunately, the required operationsset subtraction, intersection, union, projection, subset testing, and cardinality counting are not all expressible or decidable in classes of tree automata sufficiently capable to describe runtime quantities within our weighted logic programs. The present work investigates the possibilityeliminating the need for set difference by representing a (piecewise-constant) function on trees as a finite collection of constant functions on varying domains. Functions on narrower domains override the “default” values given for wider domains. The last vestige of set subtractionencapsulated within a cardinality counting operation (where the difference itself need not be expressed as an automaton).

BibTeX:

```
@TechReport{filardo:towardsdefault,
author = {Filardo, Nathaniel Wesley and Eisner, Jason},
title = {Towards Weighted Default Reasoning},
year = {2017},
month = {6}
}
```