reasoning experiment, from which one can infer the strategy that the reasoner was
following. At the third level are the tactics from which a strategy is composed,
such as drawing a diagram of a premise, or adding information from a premise to
an existing model. At the fourth, and lowest level, are the processes that underlie
the tactics, that is, the largely unconscious processes that support, say, making an
immediate inference, or using the meaning of a premise to control a drawing.
These unconscious processes are perhaps comparable to the "instruction set" of a
computer chip. Is all thinking analyzable in these terms? We conjecture that goal-
driven thinking is open to metacognitive insights, governed by a strategy, and
depends on tactics, which in tum rely on unconscious processes.

The strategies and tactics of reasoning call for a nondeterministic theory,
which, as we have illustrated, can take the form of a grammar that is used to parse
reasoners' protocols. The strategies and tactics that we have observed both in
sentential and quantified reasoning are not easily reconciled with formal rules of
inference, but they do seem to be compatible with the unconscious processes that
construct and manipulate mental models. The study of strategies in reasoning,
unlike strategies in other domains (e.g., Lemaire & Siegler, 1995), has barely
begun. There are three pressing goals. Future studies should delineate the "space"
of possible strategies, and their effectiveness and efficiency. They should account
for the sequences of strategies that reasoners pass through as they gain experience
and expertise. Logic, one could say, is the ultimate strategy that some highly gifted
individuals attain. But the "Holy Grail" for future research is the discovery of how
logically-untrained individuals discover new strategies of reasoning.

We thank our colleague Walter Schaeken for organizing the workshop at which this chapter
was presented and for his advice over the years. We are also grateful for the help of many
colleagues, including Bruno Bara, Ruth Byrne, Vittorio Girotto, Paolo Legrenzi, and
Yingrui Yang. The research was supported in part by ARPA (CAETI) contracts N66001-
94-C-6045 and N66001-95-C-8605.

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