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A production system consists of a collection of if–then rules that together form an information-processing model of some cognitive task, or range of tasks. Production systems have some special properties that make them highly suited to modeling cognition. From their origins as models of problem solving, production systems have grown to become a major formalism for modeling cognitive skill and aspects of learning. Since the 1990s, they have become increasingly identiﬁed with the topic of integrated cognitive architectures.
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1. What Is A Production System?
A production system is a model of cognitive processing, consisting of a collection of rules (called production rules, or just productions). Each rule has two parts: a condition part and an action part. The meaning of the rule is that when the condition holds true, then the action is taken. The basic idea is best illustrated with a nonpsychological example. Consider the following simple production system, with just two rules, describing the behavior of a thermostat in controlling a heating system:
Rule 1: if temperature < 20ºC → turn on heating. Rule 2: if temperature > 20ºC → turn oﬀ heating. When the room temperature is below 20ºC, the condition part of Rule 1 is true, so the thermostat takes the action speciﬁed by the rule and turns on the heating. (The rule is said to ﬁre.) When the temperature is above 20ºC, Rule 2 similarly ﬁres and turns oﬀ the heating. Taken together, the two rules specify a process which describes the behavior of the thermostat.
A production system serving as a cognitive model usually has many more than two rules, perhaps as many as thousands. The production system operates in a cyclic fashion. First, a rule whose conditions are satisﬁed is identiﬁed. Then, that rule is ﬁred, i.e., its action or actions are carried out. Usually, the actions will change the current situation in some way, so that now a diﬀerent rule has its conditions satisﬁed, and the cycle repeats. This process is referred to as the recognize–act cycle, because the condition parts of the rules can be regarded as forming an active network which monitors the current situation and recognizes when each individual rule is applicable, triggering the act of ﬁring the rule.
1.1 Production System Architecture
A particular production system operates within a deﬁnite structure of memories and processes known as its architecture. (For clariﬁcation of the term ‘architecture’ used in that sense). The architecture of a production system includes at least two memories: the production memory, and the data memory.
The production memory holds the rules. It is taken to be a long-term memory, in that its contents persist over time. Indeed, usually it is assumed that a production rule, once acquired, is never lost from memory.
The data memory holds the dynamic information about the task being worked on. (In the research literature, this memory is often described as the ‘working memory,’ but that terminology is avoided here because of the possible confusion with the psychological notion of working memory, with which it has a close but not straightforward relationship, see Working Memory, Psychology of.) The data memory is taken to be a short-term memory whose contents disappear with time, indeed possibly during the processing of a task. It holds the information which is tested by the condition part of production rules. In other words, the conditions of production rules consist of tests or patterns which are matched against the contents of the data memory.
1.2 Conﬂict Resolution
In a production system with more than a small number of rules, it is almost inevitable that sometimes more than one production rule has its conditions satisﬁed. Such an occurrence is known as conﬂict. Some production system architectures simply ﬁre, in parallel, all the rules whose conditions are satisﬁed. Most architectures, however, insist that a single rule be chosen to ﬁre.
The procedure for selecting a single rule to ﬁre from those that have their conditions satisﬁed, is known as conﬂict resolution. Diﬀerent production system architectures use diﬀerent principles for conﬂict resolution, which take account of factors such as the recency of the data being matched against, the activation levels of the data, the complexity of the rule conditions, the order in which rules were acquired, and so on.
2. Origins In Problem Solving
Production systems were introduced into psychology by Newell and Simon (1972) in their study of human problem solving. There is a natural connection between production systems and the way that Newell and Simon analyse their data.
Newell and Simon (1972) recorded participants thinking aloud as they solved puzzles in logic, chess, or cryptarithmetic (where digits have to be substituted systematically for letters to make a correct arithmetic problem). Such recordings are known as verbal protocols. Newell and Simon use the protocols to reconstruct the problem-solving steps taken by the participant. They then look for regularities in the participant’s behavior. If, for example, whenever the participant assigns a digit to a letter, he or she then scans for another place where the letter is used, it is natural to express that regularity in the form of a production-like rule: ‘if digit newly assigned to letter, then scan for occurrence of letter.’ With some further attention to detail, a collection of such rules can be treated as a production system, and it then becomes an empirical question as to how well the production system models the participant’s problem solving.
3. Properties Of Production Systems
A production system speciﬁes a computational process, and is therefore a kind of programming language. However, production systems diﬀer from ordinary computer programming languages in a number of ways.
(a) Parallel and serial processing. Production systems exhibit aspects of both parallel and serial processing, corresponding to the two phases of the recognize–act cycle. The recognize phase, i.e., the testing of conditions, occurs in parallel, across possibly hundreds of thousands of rules. In the act phase, a single rule is chosen for ﬁring, so the actions are carried out one at a time.
(b) Independence of the rules. Each rule in a production system is potentially independent of all the other rules. Each rule can be written to be self- contained, expressing an item of knowledge which the problem solver is postulated to know.
(c) Interruptible and ﬂexible control. A production system is not forced to follow a ﬁxed control structure, such as a rigid hierarchy of routines and subroutines. Because the processing at each step is determined by what the rule conditions ‘recognize’ in the data memory, the control can be very ﬂexible. For the same reason, it is interruptible. If relevant information appears in the data memory, the production system can abandon its current line of processing and follow a new one.
These and other properties make production systems well suited to the modeling of cognitive performance and cognitive skill.
4. Models Of Cognitive Skill
Production systems have been written to model many diﬀerent cognitive skills. Although only a few researchers have actually written production system models, their inﬂuence, as with other forms of computer modeling, has been far beyond their number. Production systems have now become a medium of choice for theorizing about cognitive skill, especially for skills requiring a large body of knowledge. This section summarizes just a small sample of the published work.
4.1 Written Subtraction
A model of errors in children’s written, multicolumn subtraction illustrates how some of the properties of production systems support their application as cognitive models. Young and O’Shea (1981) present a simple production system, of around a dozen rules, for performing subtraction correctly. They proceed to show how small perturbations of the model reproduce many of the errors commonly found in 10 to 12-year-old children’s performance.
Several of the most common errors arise by simply omitting one or more rules from the production system. For example, if the rule is omitted that initiates borrowing when the lower digit is larger than the upper, then the model never borrows but instead just subtracts the smaller from the larger digit in each column—a mistake common among children. The implication is that some children have failed to acquire the appropriate rule. Other errors arise by adding erroneous rules, or erroneous versions of rules, to the production system. For example, children who usually subtract correctly but simply copy the lower digit when subtracting from zero can be modeled by adding the corresponding zero-pattern rule to the production system. Although inappropriate for subtraction, that rule is appropriate for addition, suggesting that some children have not acquired suﬃciently distinctive conditions for the rule.
The ability to add and remove rules in this fashion and still leave a model which runs and faithfully reﬂects children’s behavior, depends critically upon several of the properties of production systems mentioned above. Young and O’Shea (1981) discuss the crucial role of the independence of the rules, of the ﬂexible control structure, and of the particular conﬂict-resolution principles used in the model.
Reading is another practically important cognitive skill which has been modeled with production systems. Just and Carpenter (1987) present an ambitious model of the reading and comprehension of single sentences and connected text. Their production system provides an integrated model of the cognitive processes involved in reading, from word encoding and lexical access, through syntax and semantics, to textual understanding. Many aspects of the model are based upon data from participants’ eye movements.
4.3 Knowledge-Intensive Cognitive Skill
Production systems are well suited to building models that encode and deploy large amounts of knowledge. For this reason, they are frequently used in the construction of expert systems, a branch of applied artiﬁcial intelligence that developed in the 1970s at around the same time as production systems were making their appearance in psychology. On the same grounds, production systems are much used in psychological models of expert skill, such as medical diagnosis, chess playing, and many other domains of knowledge.
5. Learning And Development
The ability to add rules to a production system, mentioned in Sect. 4.1 in the context of subtraction, raises the possibility of modeling certain aspects of learning and cognitive development by ‘growing’ a production system, one rule at a time, to correspond to the gradual acquisition of a cognitive skill. Some of the earliest applications of production systems were in the ﬁeld of learning and development (see Klahr et al. 1987). It continues to be an active area of research. Simon and Halford (1995), for example, report on several computational models of the mechanisms of developmental transition, among which production systems ﬁgure prominently.
6. The Emergence Of Cognitive Architectures
Since the 1990s, production systems have become increasingly identiﬁed with the newly emerging topic of integrated cognitive architectures, of which the main exemplars are SOAR (Newell 1990) and ACT (Anderson and Lebiere 1998)Cognitive Theory: SOAR; Cognitive Theory: ACT ).
The primary advantage of locating a production system within a broader, more encompassing theory is that the architectural details of the production system are determined in a principled way, and ﬁxed. In consequence, the architecture of the production system becomes theory-laden, no longer serving just as a convenient and expressive notation but also carrying part of the burden of explanation. This removes extraneous degrees of freedom from the modeler, thereby leading to stronger explanations and theories.
- Anderson J R, Lebiere C 1998 The Atomic Components of Thought. Erlbaum, Mahwah, NJ
- Just M A, Carpenter P A 1987 The Psychology of Reading and Language Comprehension. Allyn and Bacon, Boston
- Klahr D, Langley P, Neches R (eds.) 1987 Production System Models of Learning and Development. MIT Press, Cambridge, MA
- Newell A 1990 Uniﬁed Theories of Cognition. Harvard University Press, Cambridge, MA
- Newell A, Simon H A 1972 Human Problem Solving. PrenticeHall, Englewood Cliﬀs, NJ
- Simon T J, Halford G S (eds.) 1995 Developing Cognitive Competence: New Approaches to Process Modeling. Erlbaum, Hillsdale NJ
- Young R M, O’Shea T 1981 Errors in children’s subtraction. Cognitive Science 5: 153–177