This dissertation centers on the application of the mental space theory to expand our understanding of the role lexical discourse markers (LDMs) play in discourse. LDMs have been recognized by many researchers for their discourse connective function(s) (Levinson, 1983; Schiffrin, 1987; Blakemore, 1989, 2000, 2001, 2002; Fraser, 1996, 1999, 2006). As lexical expressions play various roles in mental space, LDMs are lexical expressions and, thus, they play some type of role in mental space. The goal of this study is to illuminate the mental space role of LDMs. Three lectures given using American Sign Language (ASL) are examined. Using these lectures, lexical discourse markers are identified using the following criteria: LDMs are lexical expressions, signify a relationship between previous and upcoming discourse, and encode functional meaning. After their identification, the mental space role of one ASL LDM that occurs most frequently in all of the ASL lectures data is examined through mental space theory. In this study, BUT is identified as the most frequently occurring ASL LDM in all three ASL lectures data; thus, it is this ASL LDM that is examined in detail in this study. The examination includes the investigation of their linguistic characteristics that led to their identification as ASL LDM and the subsequent analysis of their mental space role. The analysis of the mental space role of BUT reveals that its function is to stop the Presupposition Float from propagating further into future spaces in order to allow for understanding of the subsequent introduction of deviating information. This study illustrates how the use of mental space theory to analyze LDMs contributes to furthering our understanding of human languages. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]