Can we simplify complex logic programs without affecting their meaning? This paper delves into the concept of strong equivalence in logic programming, exploring conditions under which a program's parts can be simplified without altering its overall behavior. The central question revolves around identifying when two logic programs, when combined with any other program, yield the same answer sets. The study introduces monotonic logic as the logic of here-and-there, which is intermediate between classical logic and intuitionistic logic. The main theorem demonstrates that strong equivalence verification can be achieved by checking the equivalence of formulas in a monotonic logic, positioned between classical and intuitionistic logic. The logic of here-and-there provides a framework for ensuring that simplifications preserve the original program's semantics. We learn from it how one can simplify a part of a logic program without looking at the rest of it. This research is valuable for its contributions to logic programming theory, offering insights into program simplification and optimization. The theorem helps to verify the strong equivalence, and this theorem has significant implications for understanding the structure and semantics of logic programs.
Published in ACM Transactions on Computational Logic, this paper is highly relevant to the journal's focus on theoretical aspects of computer science and logic. The study of strong equivalence and its connection to monotonic logic aligns with the journal's emphasis on foundational research in computational logic. Citations of the paper likely appear in works concerning logic programming and knowledge representation.