Constraint Monotonicity, Epistemic Splitting and Foundedness Could in General Be Too Strong in Answer Set Programming

TL;DR

This paper critically examines the notions of constraint monotonicity, epistemic splitting, and foundedness in epistemic logic programs, arguing they may be overly restrictive and should not be mandatory for answer set semantics.

Contribution

The paper challenges the assumption that these three properties are essential, showing they can exclude valid answer sets and suggesting they should not be universally enforced.

Findings

These properties can be too strong and exclude desired answer sets.

Examples demonstrate the limitations of these notions in practice.

They should not be regarded as mandatory properties for answer set semantics.

Abstract

Recently, the notions of subjective constraint monotonicity, epistemic splitting, and foundedness have been introduced for epistemic logic programs, with the aim to use them as main criteria respectively intuitions to compare different answer set semantics proposed in the literature on how they comply with these intuitions. In this note, we consider these three notions and demonstrate on some examples that they may be too strong in general and may exclude some desired answer sets respectively world views. In conclusion, these properties should not be regarded as mandatory properties that every answer set semantics must satisfy in general.