Exploring the correlation between the density and the thermo-physical properties of the Al2O3-CaO-MgO-SiO2 quaternary slag system is a subject of great interest in the domain of high alumina slag systems. This work attempts to establish correlations between (a) molar volume/density with enthalpy of mixing and (b) molar volume/density with slag viscosity, for the quaternary slag systems. The former is targeted based on existing models to determine the slag density and enthalpy of mixing first and then to develop machine-learning models which can suitably extrapolate the enthalpy of mixing as a function of slag composition, temperature and density. The volume shrinkage and the exothermic enthalpy of mixing between the slag constituent components are correlated in the current work. The later part would involve the conjunction of two hybrid machine-learning models, one for predicting slag viscosity as a function of slag compositions and temperature, and the other which predicts slag viscosity with the incorporation of slag density. The work will facilitate the establishment of two novel quantitative relationships that could provide better insights into the blast furnace quaternary slag systems.