Declarative knowledge in ACT-R is represented in terms of chunks (Miller, 1956; Servan-Schreiber, 1991) which are configurations of elements that encode various things that we know. Figure 1.1 is a graphical display of a chunk encoding the addition fact that 3+4=7. This chunk can also be represented textually:
Fact3+4 isa ADDITION-FACT addend1 Three addend2 Four sum Seven
In the above text, Fact3+4 is just an arbitrary name given to the chunk. It is followed by a series of slots and associated values. The first slot, isa, is special and gives the type of the chunk. The remaining slots (addend1, addend2, and sum) are associated with this addition-fact type and their values define the 3+4=7 fact. It serves essentially to interassociate the slot values of the chunk. The Sji's in Figure 1.1 refer to associative strengths between slot values and chunks and the Bi refers to the base-level activation of the chunk. These quantities are relevant to calculating the activation levels of such chunks. These activation processes determine the availability of the knowledge as Chapter 3 will develop.
Production rules specify how to retrieve and use such declarative knowledge to solve problems. As an example of procedural knowledge the model below gives a production set for solving multicolumn addition problems. This production set consists of a set of productions where each production is a condition-action pair. The condition specifies what must be true for the production rule to apply and the action specifies a set of things to do if the production applies. The conditions test for the state of the current goal and chunks in declarative memory while the actions can change the goal state.