Recursive Rules with Aggregation: A Simple Unified Semantics

Many computation problems, including complex reasoning problems in particular, are most clearly and easily specified using logical rules. However, such reasoning problems in practical applications, especially for large applications and when faced with uncertain situations, require the use of recursive rules with aggregation such as counts and sums. Unfortunately, even the meaning of such rules has been challenging and remains a subject with significant complication and disagreement by experts. As a simple example, consider a single rule for Tom to attend the logic seminar: Tom will attend the logic seminar if the number of people who will attend it is at least 20. What does the rule mean?