# A framework for Conditional Reasoning in Answer Set Programming

arXiv: https://arxiv.org/abs/2506.03997 · HTML: https://mlsanity.com/paper/2506.03997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 40 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Builds on (most cited first, 8 of 8)

- [An ASP approach for reasoning in a concept-aware multipreferential lightweight DL](https://mlsanity.com/paper/2006.04387/) (2020)
- [On Rational Entailment for Propositional Typicality Logic](https://mlsanity.com/paper/1809.10946/) (2018)
- [A framework for a modular multi-concept lexicographic closure semantics](https://mlsanity.com/paper/2009.00964/) (2020)
- [Reasoning on Multi-Relational Contextual Hierarchies via Answer Set Programming with Algebraic Measures](https://mlsanity.com/paper/2108.03100/) (2021)
- [ASP for Minimal Entailment in a Rational Extension of SROEL](https://mlsanity.com/paper/1608.02450/) (2016)
- [Defeasible Reasoning in SROEL: from Rational Entailment to Rational Closure](https://mlsanity.com/paper/1803.08885/) (2018)
- [Complexity and scalability of defeasible reasoning in many-valued weighted knowledge bases with typicality](https://mlsanity.com/paper/2303.04534/) (2023)
- [A preferential interpretation of MultiLayer Perceptrons in a conditional logic with typicality](https://mlsanity.com/paper/2305.00304/) (2023)

## Abstract (arXiv)

In this paper we introduce a Conditional Answer Set Programming framework (Conditional ASP) for the definition of conditional extensions of Answer Set Programming (ASP). The approach builds on a conditional logic with typicality, and on the combination of a conditional knowledge base with an ASP program, and allows for conditional reasoning over the answer sets of the program. The formalism relies on a multi-preferential semantics, and on the KLM preferential semantics, as a special case. Conditional entailment is encoded in ASP and a complexity upper-bound is provided.