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The recent series 5 of the Answer Set Programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions to clingo with difference and linear constraints over integersdoi:10.1017/s1471068417000242 fatcat:qpqpi4bkxzbutasqlgedjslb2q