[Paper Review] Constraint Monotonicity, Epistemic Splitting and Foundedness Are Too Strong in Answer Set Programming.

Yi-Dong Shen, Thomas Eiter|arXiv (Cornell University)|Oct 1, 2020

Logic, Reasoning, and Knowledge4 citations

TL;DR

This paper challenges the use of constraint monotonicity, epistemic splitting, and foundedness as essential criteria for evaluating answer set semantics in epistemic logic programs. It demonstrates that these properties are overly restrictive and may exclude valid answer sets, arguing they should not be required as necessary conditions for any semantics.

ABSTRACT

Recently, some researchers in the community of answer set programming introduced the notions of subjective constraint monotonicity, epistemic splitting, and foundedness for epistemic logic programs, aiming to use them as main criteria/intuitions to compare different answer set semantics proposed in the literature on how they comply with these intuitions. In this note we demonstrate that these three properties are too strong and may exclude some desired answer sets/world views. Therefore, such properties should not be used as necessary conditions for answer set semantics.

Motivation & Objective

• To evaluate the role of constraint monotonicity, epistemic splitting, and foundedness as criteria for assessing answer set semantics in epistemic logic programs.
• To identify whether these properties are overly restrictive and may exclude legitimate answer sets or world views.
• To argue that these three properties should not be treated as necessary conditions for a sound and complete answer set semantics.

Proposed method

• The paper analyzes existing answer set semantics for epistemic logic programs through the lens of three proposed intuitions: constraint monotonicity, epistemic splitting, and foundedness.
• It constructs counterexamples to show that semantics satisfying these properties may still exclude valid world views.
• It formally demonstrates that the enforcement of these properties imposes unwarranted restrictions on the set of acceptable answer sets.
• It uses logical reasoning and model-theoretic analysis to show that the exclusion of certain world views under these constraints undermines the expressiveness of epistemic logic programming.

Experimental results

Research questions

• RQ1 Is constraint monotonicity a necessary property for a well-founded answer set semantics in epistemic logic programs?
• RQ2 Can epistemic splitting be required without excluding valid world views in epistemic answer set semantics?
• RQ3 Does the principle of foundedness exclude desirable answer sets in epistemic logic programs?
• RQ4 Are these three intuitions—monotonicity, splitting, and foundedness—too strong to serve as mandatory criteria for semantics evaluation?

Key findings

• Constraint monotonicity may exclude valid answer sets, making it too strong a requirement for epistemic answer set semantics.
• Epistemic splitting, while intuitive, can lead to the exclusion of legitimate world views under certain semantics.
• Foundedness, as a criterion, may also rule out acceptable answer sets, thus limiting the expressiveness of epistemic logic programs.
• The three properties—monotonicity, epistemic splitting, and foundedness—should not be used as necessary conditions for evaluating answer set semantics.