54,854 research outputs found
Proof planning for logic program synthesis
The area of logic program synthesis is attracting increased interest. Most efforts
have concentrated on applying techniques from functional program synthesis to
logic program synthesis. This thesis investigates a new approach: Synthesizing
logic programs automatically via middle-out reasoning in proof planning.[Bundy et al 90a] suggested middle-out reasoning in proof planning. Middleout
reasoning uses variables to represent unknown details of a proof. UnificaÂŹ
tion instantiates the variables in the subsequent planning, while proof planning
provides the necessary search control.Middle-out reasoning is used for synthesis by planning the verification of an
unknown logic program: The program body is represented with a meta-variable.
The planning results both in an instantiation of the program body and a plan for
the verification of that program. If the plan executes successfully, the synthesized
program is partially correct and complete.Middle-out reasoning is also used to select induction schemes. Finding an
appropriate induction scheme in synthesis is difficult, because the recursion in
the program, which is unknown at the outset, determines the induction in the
proof. In middle-out induction, we set up a schematic step case by representing
the constructors applied to the induction variables with meta-variables. Once
the step case is complete, the instantiated variables correspond to an induction
appropriate to the recursion of the program.The results reported in this thesis are encouraging. The approach has been
implemented as an extension to the proof planner CUM [Bundy et al 90c], called
Periwinkle, which has been used to synthesize a variety of programs fully automatically
Logic Program Synthesis via Proof Planning
We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a verification proof. The approach is a two-level one: At the object level, we prove program verification conjectures in a sorted, first-order theory. The conjectures are of the form . At the meta-level, we plan the object-level verification with an unspecified program definition. The definition is represented with a (second-order) meta-level variable, which becomes instantiated in the course of the planning. This technique is an application of the Clam proof planning system. Clam is currently powerful enough to plan verification proofs for given programs. We show that, if Clam's use of middle-out reasoning is extended, it will also be able to synthesize programs
Middle-Out Reasoning for Logic Program Synthesis
We propose a novel approach to automating the synthesis of logic programs: Logic programs are synthesized as a by-product of the planning of a verification proof. The approach is a two-level one: At the object level, we prove program verification conjectures in a sorted, first-order theory. The conjectures are of the form 8args \Gamma\Gamma\Gamma\Gamma! : prog(args \Gamma\Gamma\Gamma\Gamma! ) $ spec(args \Gamma\Gamma\Gamma\Gamma! ). At the meta-level, we plan the object-level verification with an unspecified program definition. The definition is represented with a (second-order) meta-level variable, which becomes instantiated in the course of the planning
From Uncertainty Data to Robust Policies for Temporal Logic Planning
We consider the problem of synthesizing robust disturbance feedback policies
for systems performing complex tasks. We formulate the tasks as linear temporal
logic specifications and encode them into an optimization framework via
mixed-integer constraints. Both the system dynamics and the specifications are
known but affected by uncertainty. The distribution of the uncertainty is
unknown, however realizations can be obtained. We introduce a data-driven
approach where the constraints are fulfilled for a set of realizations and
provide probabilistic generalization guarantees as a function of the number of
considered realizations. We use separate chance constraints for the
satisfaction of the specification and operational constraints. This allows us
to quantify their violation probabilities independently. We compute disturbance
feedback policies as solutions of mixed-integer linear or quadratic
optimization problems. By using feedback we can exploit information of past
realizations and provide feasibility for a wider range of situations compared
to static input sequences. We demonstrate the proposed method on two robust
motion-planning case studies for autonomous driving
Relational Rippling: a General Approach
We propose a new version of rippling, called relational rippling. Rippling is a heuristic for guiding proof search, especially in the step cases of inductive proofs. Relational rippling is designed for representations in which value passing is by shared existential variables, as opposed to function nesting. Thus relational rippling can be used to guide reasoning about logic programs or circuits represented as relations. We give an informal motivation and introduction to relational rippling. More details, including formal definitions and termination proofs can be found in the longer version of this paper, [Bundy and Lombart, 1995]
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