Location of Repository

Verified Planning by Deductive Synthesis in Intuitionistic Linear Logic

By L. Dixon, Alan Bundy and A. Smaill


We describe a new formalisation in Isabelle/HOL of Intuitionistic Linear Logic and consider the support this provides\ud for constructing plans by proving the achievability of given\ud planning goals. The plans so found are provably correct, by\ud construction. This representation of plans in linear logic provides a concise account of planning with sensing actions, allows the creation and deletion of objects, and solves the frame\ud problem in an elegant way. Within this setting, we show\ud how planning algorithms are implemented as search strategies within a theorem proving system. This allows us to provide a flexible methodology for developing search strategies\ud that is independent of soundness issues. This feature is illustrated in two ways. Firstly, following ideas from logic programming, we show how a significant symmetry in search,\ud caused by context splitting, can be pruned by using a derived\ud inference rule. Secondly, we show how domain specific constraints on synthesis are supported and how they can be used\ud to find contingent or conformant plans. We illustrate the approach with example planning scenarios

Year: 2009
OAI identifier: oai:www.era.lib.ed.ac.uk:1842/4773

Suggested articles



  1. (2002). A linear logical framework. doi
  2. (1998). A relevant analysis of natural deduction. doi
  3. (1998). A skeptic’s approach to combining HOL and Maple.
  4. (2004). Artificial intelligence and grids: Workflow planning and beyond. doi
  5. (1993). Classical AI planning as theorem proving: The case of a fragment of linear logic.
  6. (1993). Computational interpretations of linear logic. doi
  7. (2005). Constraints and ai planning. doi
  8. (1992). Decision problems for propositional linear logic. doi
  9. (2001). Deductive Synthesis of Recursive Plans in Linear Logic. doi
  10. (1979). Edinburgh LCF - A mechanised logic of computation, doi
  11. (2000). Efficient resource management for linear logic proof search. doi
  12. (2003). Formalising the grid - the 1st step to automate grid application assembly using deductive synthesis.
  13. (1998). Foundations for a calculus of situations.
  14. (1993). Generating plans in linear logic II: A geometry of conjunctive actions. doi
  15. (2004). Implementing efficient resource management for linear logic programming. doi
  16. (2004). Integrated proof transformation services.
  17. (2005). Interactive and hierarchical tracing of techniques
  18. (1994). Isabelle: A Generic Theorem Prover. doi
  19. (1996). Issues in the development of human-computer mixed-initiative planning systems. Cognitive Technology: In Search of a Human Interface 20. doi
  20. (1996). Linear deductive planning.
  21. (1995). Linear logic with Isabelle: pruning the proof search tree. doi
  22. (1987). Linear logic. doi
  23. (1997). Linear Type Theories, Semantics and Action Calculi.
  24. (1994). Logic programming in a fragment of intuitionistic linear logic. doi
  25. (1992). Logic programming with focusing proofs in linear logic. doi
  26. (1995). Mechanizing linear logic in Isabelle.
  27. (2005). Nominal techniques in Isabelle/HOL. doi
  28. (1992). Planning as satisfiability. doi
  29. (2009). Plans, actions and dialogue using linear logic. doi
  30. (2009). Plans, actionsand dialogue using linear logic.
  31. (2002). Plans, affordances, and combinatory grammar.
  32. (2000). Proof terms for simply typed higher order logic. doi
  33. (2002). Resource-conscious AI planning with conjunctions and disjunctions.
  34. (2002). Resource-conscious AI planning with conjunctionsanddisjunctions.
  35. (2003). Resource-distribution via boolean constraints. doi
  36. (1972). Some new directions in robot problem solving.
  37. (2001). The classical AI planning problems in the mirror of horn linear logic: semantics, expressibility, complexity. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.