Defeasible Conditionals using Answer Set Programming
Racquel Dennison, Jesse Heyninck, Thomas Meyer
TL;DR
This work addresses computing defeasible entailment under Rational Closure within the KLM framework by proposing a declarative Answer Set Programming (ASP) encoding. It provides explicit BaseRank and RC encodings, accompanied by formal proofs of soundness and completeness that align with natural deduction and RC semantics. Empirical evaluation against the InfOCF solver shows substantial runtime improvements and better scalability, highlighting ASP's practical benefits for defeasible reasoning. The results suggest a robust, readable, and extensible approach, with future directions including Lexicographic Closure and broader defeasible formalisms within the KLM framework.
Abstract
Defeasible entailment is concerned with drawing plausible conclusions from incomplete information. A foundational framework for modelling defeasible entailment is the KLM framework. Introduced by Kraus, Lehmann, and Magidor, the KLM framework outlines several key properties for defeasible entailment. One of the most prominent algorithms within this framework is Rational Closure (RC). This paper presents a declarative definition for computing RC using Answer Set Programming (ASP). Our approach enables the automatic construction of the minimal ranked model from a given knowledge base and supports entailment checking for specified queries. We formally prove the correctness of our ASP encoding and conduct empirical evaluations to compare the performance of our implementation with that of existing imperative implementations, specifically the InfOCF solver. The results demonstrate that our ASP-based approach adheres to RC's theoretical foundations and offers improved computational efficiency.