[Paper Review] A New Approach for Revising Logic Programs

Zhiqiang Zhuang, James P. Delgrande+2 more|arXiv (Cornell University)|Mar 31, 2016

Logic, Reasoning, and Knowledge13 references3 citations

TL;DR

This paper proposes a novel belief revision framework for non-monotonic logic programs under answer set semantics, introducing the slp-revision function that resolves inconsistencies by combining minimal removal and strategic addition of rules. The key contribution is a representation theorem proving that the proposed revision function satisfies a set of rational postulates and is uniquely characterized by syntactic minimality and consistency constraints.

ABSTRACT

Belief revision has been studied mainly with respect to background logics that are monotonic in character. In this paper we study belief revision when the underlying logic is non-monotonic instead--an inherently interesting problem that is under explored. In particular, we will focus on the revision of a body of beliefs that is represented as a logic program under the answer set semantics, while the new information is also similarly represented as a logic program. Our approach is driven by the observation that unlike in a monotonic setting where, when necessary, consistency in a revised body of beliefs is maintained by jettisoning some old beliefs, in a non-monotonic setting consistency can be restored by adding new beliefs as well. We will define a syntactic revision function and subsequently provide representation theorem for characterising it.

Motivation & Objective

• To address the gap in belief revision for non-monotonic reasoning, particularly in logic programs under answer set semantics.
• To develop a revision mechanism that allows both removal and addition of rules to restore consistency, unlike monotonic belief revision.
• To formalize a syntactic revision function that preserves minimal change and ensures consistency with new information.
• To provide a representation theorem that characterizes the revision function using a set of rational postulates.
• To demonstrate that inconsistency in logic programs can be resolved not only by removing old beliefs but also by adding new ones, reflecting real-world reasoning dynamics.

Proposed method

• Define a syntactic revision function called slp-revision that revises a logic program $P$ by another $Q$ by first selecting a consistent program $R$ that minimally differs from $P$ and is consistent with $Q$.
• Construct the revised program as $P*Q = R \cup Q$, where $R$ is selected from the set of all programs $X$ such that $X \cup Q$ is consistent and $X$ minimally differs from $P$.
• Introduce a selection function $\gamma(P\updownarrow Q)$ defined as $((P*Q)\cap P) \cup ((P*Q)\setminus Q)$, which captures the minimal change component from $P$.
• Formalize a set of rational postulates: (s * s), (s * c), (s * f), (s * rr), (s * er), (s * mr), and (s * u), modeling consistency, minimality, and rationality.
• Prove a representation theorem showing that any revision function satisfying the postulates must be equivalent to the slp-revision function.
• Use set-theoretic reasoning and consistency constraints to show that the function is well-defined and uniquely determined by the postulates.

Experimental results

Research questions

• RQ1 How can belief revision be meaningfully extended to non-monotonic logic programs under answer set semantics?
• RQ2 What are the rational postulates that a revision function for logic programs should satisfy?
• RQ3 Can inconsistency in a logic program be resolved not only by removing old beliefs but also by adding new ones?
• RQ4 How can minimal change be formally captured in a syntactic revision function for logic programs?
• RQ5 Is there a representation theorem that uniquely characterizes a revision function based on its postulates?

Key findings

• The slp-revision function successfully resolves inconsistencies in logic programs by allowing both removal and addition of rules, reflecting non-monotonic reasoning dynamics.
• The revision function is uniquely characterized by a set of rational postulates, proving that any function satisfying these postulates must be equivalent to slp-revision.
• The representation theorem establishes that the selection function $\gamma(P\updownarrow Q)$ is well-defined and yields a consistent, minimal revision of $P$ by $Q$.
• The function satisfies (s * u), ensuring that when $P$ and $Q$ are inconsistent, the revision preserves $P$ if $Q$ is inconsistent, maintaining rationality.
• The proof shows that any alternative revision function satisfying the postulates must yield the same result, confirming the uniqueness and rationality of the construction.
• The framework demonstrates that in non-monotonic settings, consistency can be restored by adding new information—such as $Admin(John)$—rather than only removing existing rules.