Thomas Gruber & , Yumi Iwasaki 0 , Benjamin Kuipers

This document describes a compositional modeling language, CML, which is a general declarative modeling language for logically specifying the symbolic and mathematical properties of the structure and behavior of physical systems . CML is intended to facilitate model sharing between research groups, many of which have long been using similar languages . These languages are based primarily on the language originally defined by Qualitative Process theory [Forbus 1984] and include the languages used for the Qualitative Physics Compiler (QPC) [Crawford 1990 ; Farquhar 1993 ; Farquhar 1994], compositional model formulation [Falkenhainer 1991 ], and the Device Modeling Environment (DME) [Low and Iwasaki 1993] . CML is an attempt to synthesize and provide a clean redesign of these languages . 12 QR-96 1 . Introduction Compositional modeling is an effective paradigm for formulating a behavior model of physical system by composing descriptions of symbolic and mathematical properties of individual system components . This paper describes Compositional Modeling Language (CML), which is a general declarative modeling language for representing physical knowledge required for compositional modeling . CML is intended to facilitate model sharing between research groups, many of which has long been using A Compositional Modeling Language **Xerox Wilson Center 800 Philips Rd., M/S 128-51E Webster, NY 14580 falken@ wrc.xerox.com $Qualitative Reasoning Group The Institute for the Learning Sciences Northwestern University 1890 Maple Avenue Evanston, IL 60201 forbus@ ils.nwu.edu %University of Texas at Austin Department of Computer Science Austin, TX 78712 kuipers@ cs.utexas.edu similar languages . These languages are based primarily on the language originally defined by Qualitative Process Theory [Forbus 1984] and include the languages used for the Qualitative Physics Compiler [Farquhar 1994], compositional model formulation [Falkenhainer 1991], and the Device Modeling Environment [Low and Iwasaki 1993] . CML is an attempt to synthesize and provide a clean redesign of these languages . The specification of CML has been formulated by researchers involved in those projects . CML was designed with efficiency, expressiveness and ease of use in mind . The language is restricted enough to allow efficient implementation of procedures to predict behavior. The syntax is simple and readable so that a person familiar with the domain will be able to read and easily understand an expression of knowledge of the domain in the language . The language supports lumped parameter ordinary differential equations that are common in engineering modeling. Finally, the language supports a variety of different approaches to representing physical phenomena ; it allows the definition and use of domain theories that use components, process, bond graphs, kinematic pairs, etc ., and also supports both relational and object-oriented specification styles . CML specifies a set of top-level forms for defining models and an ontology of primitive functions, relations, and constants . CML is intended to be an open, evolving language, of which this document describes the base language . Various extensions will undoubtedly be defined as they naturally arise in the course of its use by different people . An important goal in designing the base language is to support as much sharing as is reasonably possible . Also, to facilitate sharing the content of CML knowledge bases, CML is filly translatable to the knowledge interchange format (KIF)[Genesereth and Fikes 1992], and we have adopted conventions established by KIF wherever possible. 1 .1 . Patterns of Use A typical implementation supporting CML might be used as follows : To predict the behavior of a physical system in some domain, knowledge about the physics of the domain is captured in a general purpose domain theory that describes classes of relevant objects, phenomena and systems . The domain theory of chemical processing plants, for example, might include physical phenomena such as mass and heat flows, boiling, evaporation, and condensation ; it would also include chemical reactions, the effects of catalysts, and models of components such as reaction vessels, pumps, controllers, and filters . A domain theory in CML consists of a set of quantified definitions, called model fragments, each of which describes some partial piece of the domain's physics, such as processes (e.g ., liquid flows), devices (e.g ., transistors), and objects (e .g ., containers) . Each definition applies whenever there exists a set of participants for whom the stated conditions are satisfied . A specific system or situation being modeled is called a scenario . A model of the scenario consists of fragments that logically follow from the domain theory and the scenario definition . For example, consider the situation depicted in Figure 1 . A scenario representing this situation would state that there is a can containing some water placed over a gas heater . In addition, the scenario may also state whether or not the gas heater is initially on, the initial temperature and volume of the water and so on . In order to reason about this situation, the domain theory must contain the definitions of a can, contained water, a gas heater, as well as the definitions of relevant physical processes such as heat flow and evaporation . The definitions of these objects and processes must specify their numeric and non-numeric attributes, such as water-level and fame-lit-p . The types of values such attributes take, for example "a numeric, timedependent quantity whose dimension is length" must also be specified in the domain theory . Once the domain theory has been constructed, it can be used to model many different physical devices under a variety of different conditions . The user specifies a scenario that defines an initial configuration of the device, the initial values of some of the parameters that are relevant to modeling it, and perhaps conditions that further 1 KIF provides a standard encoding and semantics for a first order logic with set theory and some minor extensions such as a restricted quote and the ability to refer to relations directly . characterize the system . The CML implementation would automatically identify model fragments that are applicable in the scenario . These model fragments would be composed into a single model that comprises both a symbolic description as well as a set of governing equations . The equations may be solved or simulated to produce a behavioral description . Because the conditions under which the model fragments hold are explicit in the domain theory, the system would be able to construct automatically additional models that describe the device as it moves into new operating regions . Figure 1 : An example situation with a can of water and a heater 1.2 . Notation and Syntax The CML syntax is based on the Common Lisp standard [Steele 1990] ; a sequence of characters is a legal CML expression only if it is acceptable to the Common Lisp reader with standard settings . In this document, we will adopt the following notational conventions : Variables are marked with a ? prefix, to distinguish them from object and relation constants . Where the syntax allows for a finite series of items indexed from 1 to n, the first item of the sequence is given with the subscript 1 and the remaining n1 items are abbreviated by " . . . n " . For example, ( ( participant L :type t 1) . . . n)