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This paper introduces the concept of Distributed Intelligent integrated Sensing and Communications (DISAC), which expands the capabilities of Integrated Sensing and Communications (ISAC) towards distributed architectures. Additionally, the DISAC framework integrates novel waveform design with new semantic and goal-oriented communication paradigms, enabling ISAC technologies to transition from traditional data fusion to the semantic composition of diverse sensed and shared information. This progress facilitates large-scale, energy-efficient support for high-precision spatial-temporal processing, optimizing ISAC resource utilization, and enabling effective multi-modal sensing performance. Addressing key challenges such as efficient data management and connect-compute resource utilization, 6G- DISAC stands to revolutionize applications in diverse sectors including transportation, healthcare, and industrial automation. Our study encapsulates the project vision, methodologies, and potential impact, marking a significant stride towards a more connected and intelligent world.