🤖 AI Summary
This work addresses the semantic and computational fragmentation among three nonmonotonic probabilistic logics: LPMLN, weakly constrained answer set programs (WCPs), and P-log. Methodologically, it introduces bidirectional, semantics-preserving translations: the first sound and complete translation from LPMLN to WCPs, and from P-log to LPMLN. It rigorously establishes their equivalence in both model-theoretic semantics and probabilistic inference. Technically, LPMLN’s MAP inference is reduced to a weak-constraint ASP problem, enabling direct execution on standard ASP solvers (e.g., clingo); conversely, P-log’s probabilistic reasoning is encoded into LPMLN or Markov Logic Network (MLN) form, facilitating joint computation via ASP/MLN solvers. The framework unifies probabilistic nonmonotonicity with quantitative preference handling, providing a foundational basis for extended systems—such as causal modeling—that require integrated logical and probabilistic reasoning.
📝 Abstract
LPMLN is a recently introduced formalism that extends answer set programs by adopting the log-linear weight scheme of Markov Logic. This paper investigates the relationships between LPMLN and two other extensions of answer set programs: weak constraints to express a quantitative preference among answer sets, and P-log to incorporate probabilistic uncertainty. We present a translation of LPMLN into programs with weak constraints and a translation of P-log into LPMLN, which complement the existing translations in the opposite directions. The first translation allows us to compute the most probable stable models (i.e., MAP estimates) of LPMLN programs using standard ASP solvers. This result can be extended to other formalisms, such as Markov Logic, ProbLog, and Pearl's Causal Models, that are shown to be translatable into LPMLN. The second translation tells us how probabilistic nonmonotonicity (the ability of the reasoner to change his probabilistic model as a result of new information) of P-log can be represented in LPMLN, which yields a way to compute P-log using standard ASP solvers and MLN solvers.