# Qualitative Process Theory

Every domain theory requires an organizing principle--some ontological commitment which provides structure and coherence. QP theory organizes domain theories around the notion of physical processes. Every change in the physical system is directly or indirectly caused by processes. Processes affect objects by causing quantities associated with them to change, and communicate with each other through shared parameters.

QP theory introduced the quantity space representation of numerical values in terms of ordinal relationships, and qualitative proportionalities, the use of monotonic functional dependencies to form a language for qualitative differential equations. Both techniques have been widely adopted and are now considered standard in qualitative physics.

 ```(defProcess (heat-flow ?src ?dst ?path) ;; The physical process being defined Individuals ((?src :conditions (Quantity (heat ?src))) ;; Kinds of entities (?dst :conditions (Quantity (heat ?dst))) ;; it occurs among (?path :type Heat-Path :conditions (Heat-Connection ?path ?src ?dst))) Preconditions ((Heat-Aligned ?path)) ;; Non-dynamical antecedents QuanityConditions ((greater-than (A (temperature ?src)) ;; Dynamical (A (temperature ?dst)))) ;; antecedents Relations ((Quantity flow-rate) ;; Consequences (Q= flow-rate (- (temperature ?src) (temperature ?dst)))) Influences ((I+ (heat ?dst) (A flow-rate)) ;; Direct causal effects (I- (heat ?src) (A flow-rate)))) ``` A physical process definition

Time-varying relationships, including different states of objects or modes of interaction, are represented by individual views. Views allow QP models to describe significant changes in model structure, such as phase changes in fluids or certain changes in contact relationships. Physical processes are explicitly defined in terms of the individuals that give rise to them, the conditions under which they are true, and their direct consequences (Figure 1). QP theory provides explicit interfaces for communication with other kinds of representations, both in the form of preconditions, which help determine when a process or view is active, and by allowing arbitrary statements in the relations field, which describe what is true when a process or view is active. We believe this ability to gracefully extend QP models will prove essential in constructing realistic domain models that capture a wide range of physical phenomena.

QP theory has been used to create domain theories, ranging from simple models of fluids, motion, and materials, to professional knowledge of chemical engineering. It has been used in programs for making predictions, interpreting measurements, constructing plans, diagnosis, design and learning.

## Selected Relevant Papers

Forbus, K. (1984). Qualitative Process Theory. Artificial Intelligence, 24, 85-168.

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