Alternative Definition of Answer Sets in Answer Set Programming

In this article, we present a new approach to counting models in artificial intelligence, specifically for normal programs. We propose an alternative definition of answer sets that relies on copy variables and operations, which are different from those used in ASProblog. Our algorithm aims to justify only loop atoms, whereas ASProblog considers all founded variables.
Imagine you have a big box of Legos, each one representing a rule in a program. The rules are connected like Lego bricks, forming a bigger structure. We want to count the number of different ways this structure can be built using only certain Lego pieces (loop atoms). Our approach creates fresh Lego pieces (copy variables) that help us find all possible combinations of loop atoms and connect them in different ways.
Our algorithm is like a Lego builder who starts with a small set of loop atoms, adds new ones, and then connects them to form a bigger structure. We use copy variables to keep track of which loop atoms are connected to each other and how they are connected. By counting the number of different ways these connections can be made, we can calculate the number of models for a given program.
One key difference between our approach and ASProblog is that ASProblog considers all founded variables, whereas we focus only on loop atoms. Imagine you have a big box of Legos with many different shapes and colors. ASProblog would count every Lego as a separate model, while our approach looks at the connections between the Lego bricks to find the different ways they can be combined.
Another difference is in how we perform unit propagation. In ASProblog, this process involves only justifying literals from a program and leaving unjustified literals in the residual program. In contrast, our approach adheres to conventional unit propagation techniques and uses copy variables to determine whether all atoms are justified.
In summary, we present a new approach to counting models using connected components, which relies on copy variables and operations different from ASProblog. Our algorithm focuses on loop atoms, whereas ASProblog considers all founded variables. We use copy variables to keep track of connections between loop atoms and perform unit propagation in a way that is similar to conventional techniques.