# On Signings and the Well-Founded Semantics

arXiv: https://arxiv.org/abs/2102.06495 · HTML: https://mlsanity.com/paper/2102.06495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2021.

## Built on by (most cited first, 1 of 1)

- [Defeasible Reasoning via Datalog^neg](https://mlsanity.com/paper/2106.10946/) (2021)

## Abstract (arXiv)

In this note, we use Kunen's notion of a signing to establish two theorems about the well-founded semantics of logic programs, in the case where we are interested in only (say) the positive literals of a predicate p that are consequences of the program. The first theorem identifies a class of programs for which the well-founded and Fitting semantics coincide for the positive part of p. The second theorem shows that if a program has a signing then computing the positive part of p under the well-founded semantics requires the computation of only one part of each predicate. This theorem suggests an analysis for query-answering under the well-founded semantics. In the process of proving these results, we use an alternative formulation of the well-founded semantics of logic programs, which might be of independent interest. Under consideration in Theory and Practice of Logic Programming (TPLP)