MOLOG: A system that extends PROLOG with modal logic
New Generation Computing
Modal and temporal logic programming
Temporal logics and their applications
A logical analysis of modules in logic programming
Journal of Logic Programming
Automated deduction in nonclassical logics
Automated deduction in nonclassical logics
Journal of Automated Reasoning
Foundations of disjunctive logic programming
Foundations of disjunctive logic programming
Multimodal logic programming using equational and order-sorted logic
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
Towards a unified theory of intensional logic programming
Journal of Logic Programming
Handbook of logic in computer science (vol. 2)
Logic programming in a fragment of intuitionistic linear logic
Papers presented at the IEEE symposium on Logic in computer science
A multimodal logic to define modules in logic programming
ILPS '93 Proceedings of the 1993 international symposium on Logic programming
Forum: a multiple-conclusion specification logic
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Abductive planning with sensing
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Representing scope in intuitionistic deductions
Theoretical Computer Science
First-order modal logic
Distributed concurrent linear logic programming
Theoretical Computer Science - Special issue on linear logic, 1
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Modality in dialogue: planning, pragmatics and computation
Modality in dialogue: planning, pragmatics and computation
Normal multimodal logics with interaction axioms
Labelled deduction
Labelled Modal Logics: Quantifiers
Journal of Logic, Language and Information
Optimized Translation of Multi Modal Logic into Predicate Logic
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
T-String Unification: Unifying Prefixes in Non-classical Proof Methods
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Proof-Search in Intuitionistic Logic Based on Constraint Satisfaction
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Free Variable Tableaux for Propositional Modal Logics
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
E-Unification for Subsystems of S4
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
Programming in Modal Logic: An Extension of PROLOG based on Modal Logic
Proceedings of the 5th Conference on Logic Programming '86
Uniform proofs and disjunctive logic programming
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Formalizing Context (Expanded Notes)
Formalizing Context (Expanded Notes)
On goal-directed provability in classical logic
Computer Languages
Proceedings of the tenth ACM SIGPLAN international conference on Functional programming
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This article explores goal-directed proof search in first-order multimodal logic. I focus on a family of modal logics which offer the expressive power to specify modular goals and local assumptions. A modular goal must be proved from designated assumptions; conversely, a local assumption can only be used to prove a designated goal. Indefinite modal specifications can avoid combinatorial interactions among independent ambiguities by making separate goals modular and corresponding disjunctive alternatives local. Such specifications can effectively guarantee that provable goals have short proofs. The key result of this article is to establish a sound and complete goal-directed proof system that actively uses the modularity and locality of modal logic to constrain proof search. In particular, logically independent, local ambiguities will not interact in proof search. The challenge is that, in goal-directed proof, a modal prover cannot simply reason locally, in a module, because modularity is a property of formulas rather than proof problems. The result therefore requires prior proof-theoretic justifications of logic programming to be extended, strengthened, and combined with new proof-theoretic analyses of modal deduction.