Textual process descriptions are widely used in organizations since they can be created and understood by virtually everyone. Because of their widespread use, they also provide a valuable source for process analysis, such as compliance checking. However, the inherent ambiguity of natural language impedes the automated analysis of textual process descriptions. While human readers can use their context knowledge to correctly understand statements with multiple possible interpretations, automated tools currently have to make assumptions about their correct meaning. As a result, compliance-checking techniques are prone to draw incorrect conclusions about the proper execution of a process. To provide a comprehensive solution to these reasoning problems, we use this paper to introduce the concept of a behavioral space as a means to deal with behavioral ambiguity in textual process descriptions. A behavioral space captures all possible interpretations of a textual process description in a systematic manner. Thus, it avoids the problem of focusing on a single, possibly incorrect interpretation. We use a quantitative evaluation with a set of 47 textual process descriptions to demonstrate the usefulness of a behavioral space for compliance checking in the context of ambiguous texts.