Deductive synthesis of recursive plans in linear logic

Linear logic has previously been shown to be suitable for describing and deductively solving planning problems involving conjunction and disjunction. We introduce a recursively defined datatype and a corresponding induction rule, thereby allowing recursive plans to be synthesised. In order to make explicit the relationship between proofs and plans, we enhance the linear logic deduction rules to handle plans as a form of proof term

Deductive synthesis of recursive plans in linear logic

Centre for Intelligent Systems and their ApplicationsConventionally, the problem of plan formation in Artificial Intelligence deals with the generation of plans in the form of a sequence of actions. This thesis describes an approach to extending the expressiveness of plans to include conditional branches and recursion. This allows problems to be solved at a higher level, such that a single plan in such a language is capable of solving a class of problems rather than a single problem instance. A plan of fixed size may solve arbitrarily large problem instances. To form such plans, we take a deductive planning approach, in which the formation of the plan goes hand-in-hand with the construction of the proof that the plan specification is realisable. The formalism used here for specifying and reasoning with planning problems is Girard's Institutionistic Linear Logic (ILL), which is attractive for planning problems because state change can be expressed directly as linear implication, with no need for frame axioms. We extract plans by means of the relationship between proofs in ILL and programs in the style of Abramsky. We extend the ILL proof rules to account for induction over inductively defined types, thereby allowing recursive plans to be synthesised. We also adapt Abramsky's framework to partially evaluate and execute the plans in the extended language. We give a proof search algorithm tailored towards the fragment of the ILL employed (excluding induction rule selection). A system implementation, Lino, comprises modules for proof checking, automated proof search, plan extraction and partial evaluation of plans. We demonstrate the encodings and solutions in our framework of various planning domains involving recursion. We compare the capabilities of our approach with the previous approaches of Manna and Waldinger, Ghassem-Sani and Steel, and Stephen and Biundo. We claim that our approach gives a good balance between coverage of problems that can be described and the tractability of proof search

Plan generation using a method of deductive program synthesis

In this paper we introduce a planning approach based on a method of deductive program synthesis. The program synthesis system we rely upon takes first-order specifications and from these derives recursive programs automatically. It uses a set of transformation rules whose applications are guided by an overall strategy. Additionally several heuristics are involved which considerably reduce the search space. We show by means of an example taken from the blocks world how even recursive plans can be obtained with this method. Some modifications of the synthesis strategy and heuristics are discussed, which are necessary to obtain a powerful and automatic planning system. Finally it is shown how subplans can be introduced and generated separately

A new logical framework for deductive planning

In this paper we present a logical framework for defining consistent axiomatizations of planning domains. A language to define basic actions and structured plans is embedded in a logic. This allows general properties of a whole planning scenario to be proved as well as plans to be formed deductively. In particular, frame assertions and domain constraints as invariants of the basic actions can be formulated and proved. Even for complex plans most frame assertions are obtained by purely syntactic analysis. In such cases the formal proof can be generated in a uniform way. The formalism we introduce is especially useful when treating recursive plans. A tactical theorem prover, the Karlsruhe Interactive Verifier KIV is used to implement this logical framework

Recursive Program Optimization Through Inductive Synthesis Proof Transformation

The research described in this paper involved developing transformation techniques which increase the efficiency of the noriginal program, the source, by transforming its synthesis proof into one, the target, which yields a computationally more efficient algorithm. We describe a working proof transformation system which, by exploiting the duality between mathematical induction and recursion, employs the novel strategy of optimizing recursive programs by transforming inductive proofs. We compare and contrast this approach with the more traditional approaches to program transformation, and highlight the benefits of proof transformation with regards to search, correctness, automatability and generality

09501 Abstracts Collection -- Software Synthesis

From 06.12.09 to 11.12.09, the Dagstuhl Seminar 09501 ``Software Synthesis \u27\u27 in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Application of shape grammar theory to underground rail station design and passenger evacuation

This paper outlines the development of a computer design environment that generates station ‘reference’ plans for analysis by designers at the project feasibility stage. The developed program uses the theoretical concept of shape grammar, based upon principles of recognition and replacement of a particular shape to enable the generation of station layouts. The developed novel shape grammar rules produce multiple plans of accurately sized infrastructure faster than by traditional means. A finite set of station infrastructure elements and a finite set of connection possibilities for them, directed by regulations and the logical processes of station usage, allows for increasingly complex composite shapes to be automatically produced, some of which are credible station layouts at ‘reference’ block plan level. The proposed method of generating shape grammar plans is aligned to London Underground standards, in particular to the Station Planning Standards and Guidelines 5th edition (SPSG5 2007) and the BS-7974 fire safety engineering process. Quantitative testing is via existing evacuation modelling software. The prototype system, named SGEvac, has both the scope and potential for redevelopment to any other country’s design legislation