🤖 AI Summary
This study addresses the limitation of existing multimodal logic programming systems restricted to Horn clauses by proposing MMLP, a system supporting arbitrary formulas as both programs and queries. Grounded in nested proof calculus and a permission set unification algorithm, the approach integrates finite syntactic certificates with focused search strategies to achieve cut-free completeness and termination under Hilbert semantics. Experimental results demonstrate that MMLP produces correct answers with complete solution coverage. While equivalent to KDI4s5-MPROLOG on common fragments, MMLP significantly overcomes prior syntactic constraints, offering enhanced expressiveness and theoretical completeness for multimodal logic programming.
📝 Abstract
This paper presents a first-order multimodal logic programming system called MMLP. The system accepts arbitrary formulas as both programs and queries, without restricting either side to Horn clauses or a separate goal grammar. Its declarative semantics is given independently by a Hilbert system for selected D, T, I, B, 4, and 5 modal principles. Execution uses a nested proof calculus with finite grammar certificates for modal propagation. Certificate reachability is equivalent to the associated Horn closure, certificate existence is decidable, and the calculus is cut-free complete. For quantified answer computation, we give a unification algorithm based on permission sets that controls eigenparameter scope. The algorithm always terminates and fails exactly when no admissible solution exists. A successful run returns a unifier that is itself admissible and through which all admissible solutions factor. Computed answers are declaratively correct, and each declaratively correct answer is an ordinary output instance of a computed answer. In proof search, MMLP admits syntactic focalization and a fair and complete enumeration of focused answers. It represents exactly the same answer substitutions as Nguyen's pure logical KDI4s5-MPROLOG on their common fragment, while admitting a strictly larger program and query language.