A framework for Conditional Reasoning in Answer Set Programming
Mario Alviano, Laura Giordano, Daniele Theseider Dupré
TL;DR
The paper tackles conditional reasoning within Answer Set Programming by introducing CondASP, which pairs an ASP program $\Pi$ with a weighted defeasible knowledge base $K$ and employs a multi-preferential, typicality-based semantics to reason over answer sets. It defines per-atom preferences $\leq_{A_i}$ via weights $W_{A_i}(S)$ and constructs a canonical model $\mathcal{M}^{\Pi}_K$ in which entailment $A \rightarrow B$ is captured by $\mathcal{M}^{\Pi}_K \models {\bf T}(A) \rightarrow B$, thereby extending KLM-style conditionals to ASP. The framework preserves several KLM postulates (Reflexivity, Right Weakening, Left Logical Equivalence, And, Or, Cautious Monotonicity) while noting that Rational Monotonicity may fail in general, reflecting typical nonmonotonic behavior. The authors provide ASP-based methods to verify entailment, with a $P^{NP}$ upper bound, and implement online reasoners on the ASP Chef platform, illustrating practical applicability and connections to rational/lexicographic closures and related preference formalisms.
Abstract
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.