A constraint describes a relationship that should be maintained, for example that the equality A + B = C holds between three variables, that a set of displayed objects are aligned, or that the elements in a data structure are consistent with a graphic display of this structure. Constraint solvers have been successfully applied to problems in computer graphics including geometric design and user interface construction. This paper presents the SkyBlue constraint solver, an efficient incremental algorithm that uses local propagation to maintain sets of required and preferential constraints. SkyBlue is a successor to the DeltaBlue algorithm, which was used as the constraint solver in the ThingLab II user interface development environment. DeltaBlue has two limitations: cycles of constraints are prohibited, and the procedures used to satisfy a constraint can only have a single output. SkyBlue relaxes these restrictions, allowing cycles of constraints to be constructed (although SkyBlue may...

Adequate problem representations require the identification of abstractions and approximations that are well suited to the task at hand. In this paper we introduce a new class of approximations, called causal approximations, that are commonly found in modeling the physical world. Causal approximations support the efficient generation of parsimonious causal explanations, which play an important role in reasoning about engineered devices. The central problem to be solved in generating parsimonious causal explanations is the identification of a simplest model that explains the phenomenon of interest. We formalize this problem and show that it is, in general, intractable. In this formalization, simplicity of models is based on the intuition that using more approximate models of fewer phenomena leads to simpler models. We then show that when all the approximations are causal approximations, the above problem can be solved in polynomial time.

This paper summarizes basic concepts and principles that I have found to be useful in dealing with causal reasoning. The paper is written as a companion to a lecture under the same title, to be presented at IJCAI-99, and is intended to supplement the lecture with technical details and pointers to more elaborate discussions in the literature. The ruling conception will be to treat causation as a computational schema devised to identify the invariant relationships in the environment, so as to facilitate reliable prediction of the effect of actions. This conception, as well as several of its satellite principles and tools, has been guiding paradigm for several research communities in AI, most notably those connected with causal discovery, troubleshooting, planning under uncertainty and modeling the behavior of physical systems. My hopes are to encourage a broader and more effective usage of causal modeling by explicating these common principles in simple and familiar mathematical form. Af...

We show that the usual notion of constraint propagation is but one of a number of similar inferences useful in quantitative reasoning about physical objects. These inferences are expressed formally as rules for the propagation of "labeled intervals " through equations. We prove the rules ' correctness and illustrate their utility for reasoning about objects (such as motors or transmissions) which assume a continuum of different states. The inferences are the basis of a "mechanical design compiler", which has correctly produced detailed designs from "high level " descriptions for a variety of power transmission and temperature sensing systems. 1

We describe a program called SketchIT capable of producing multiple families of designs from asinglesketch. The program is given a rough sketch (drawn using line segments for part faces and icons for springs and kinematic joints) and a description of the desired behavior. The sketch is “rough” in the sense that taken literally, it may not work. From this single, perhaps flawed sketch and the behavior description, the program produces an entire family of working designs. The program also produces design variants, each of which is itself a family of designs. SketchIT represents each family of designs with a “behavior ensuring parametric model ” (BEP-Model), a parametric model augmented with a set of constraints that ensure the geometry provides the desired behavior. The construction of the BEP-Model from the sketch and behavior description is the primary task and source of difficulty in this undertaking. SketchIT begins by abstracting the sketch to produce a qualitative configuration space (qcspace) which it then uses as its primary representation of behavior. SketchIT modifies this initial

We present Pika, an implemented self-explanatory simulator that is more than 5000 times faster than SimGen Mk2 [ Forbus and Falkenhainer, 1992 ] , the previous state of the art. Like SimGen, Pika automatically prepares and runs a numeric simulation of a physical device specified as a particular instantiation of a general domain theory, and it is capable of explaining its reasoning and the simulated behavior. Unlike SimGen, Pika's modeling language allows arbitrary algebraic and differential equations with no prespecified causal direction; Pika infers the appropriate causality and solves the equations as necessary to prepare for numeric integration. Introduction Science and engineering have used numeric simulation productively for years. Simulation programs, however, have been laboriously hand-crafted, intricate, and difficult to understand and change. There has been much recent work on automating their construction (e.g. [ Yang, 1992, Rosenberg and Karnopp, 1983, Abelson...

In practice, constraint satisfaction problems are often structured. By exploiting this structure, solving algorithms can make important gains in performance. In this paper, we focus on structured continuous CSPs defined by systems of equations. We use graph decomposition techniques to decompose the constraint graph into a directed acyclic graph of small blocks. We present new algorithms to solve decomposed problems which solve the blocks in partial order and perform intelligent backtracking when a block has no solution. For under-constrained problems, the solution space can be explored by choosing some variables as input parameters. However, in this case, the decomposition is no longer unique and some choices lead to decompositions with smaller blocks than others. We present an algorithm for selecting the input parameters that lead to good decompositions. First experimental results indicate that, even on small problems, significant speedups can be obtained using these algorithms.

Effective problem solving requires building adequate models that embody the simplifications, abstractions, and approximations that parsimoniously describe the relevant system phenomena for the task at hand. Compositional modeling is a framework for constructing adequate device models by composing model fragments selected from a model fragment library. While model selection using compositional modeling has been shown to be intractable, it is tractable when all model fragment approximations are causal approximations . This paper addresses the reasoning and knowledge representation issues that arise in building practical systems for constructing adequate device models that provide parsimonious causal explanations of how a device functions. We make four important contributions. First, we present a representation of class level descriptions of model fragments and their relationships. The representation yields a practical model fragment library organization that facilitates knowledge base co...

or hydraulic power transmission system, plus specifications and a utility function, and returns catalog numbers from predefined catalogs for the optimal selection of components implementing the design. Unlike programs for designing single components or systems, this program provides the designer with a high level "language" in which to compose new designs. It then performs some of the detailed design process for him. The process of "compilation", or transformation from a high to a low level description, is based on a formalization of quantitative inferences about hierarchically organized sets of artifacts and operating conditions. This allows design compilation without the exhaustive enumeration of alternatives. The paper introduces the formalism, illustrating its use with examples. It then outlines some differences from previous work, and summarizes early tests and conclusions.

Engineering conceptual design can be de ned as that phase of the product development process during which the designer takes a speci cation for a product to be designed and generates many broad solutions to it. This paper presents an constraint-based approach to supporting interactive conceptual design. The approach is based upon an expressive and general technique for modeling: the design knowledge which a designer can exploit during a design project; the life-cycle environment which the nal product faces; the design speci cation which de nes the set of requirements that the product must satisfy; and the structure of the various schemes that are developed by the designer.