Point and Interval Strategies

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This monograph develops a general theory of goal representation that challenges the dominant assumption that goals are best modeled as precise scalar targets. Across decision theory, psychology, economics and artificial intelligence goals are typically formalized as points in outcome space. This work demonstrates that such a representation is structurally restrictive and dynamically fragile. The central thesis is that a goal should not be understood as a value, but as a structure of admissible states. This leads to a fundamental distinction between point strategies, defined by zero-measure sets, and interval strategies, defined by positive-measure regions. The transition from point to interval is shown to induce a shift from binary to continuous evaluation, from singular to extended attractors, and from fragile to stable behavioral dynamics.

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