We present the results of our ALMA Cycle 0 observations, using HCN/HCO+/HNC J=4-3 lines, of six nearby luminous infrared galaxies with various energetic contributions from active galactic nuclei (AGNs) estimated from previous infrared spectroscopy. These lines are very effective for probing the physical properties of high-density molecular gas around the hidden energy sources in the nuclear regions of these galaxies. We find that HCN to HCO+ J=4-3 flux ratios tend to be higher in AGN-important galaxies than in starburst-dominated regions, as was seen at the J=1-0 transition, while there is no clear difference in the HCN-to-HNC J=4-3 flux ratios among observed sources. A galaxy with a starburst-type infrared spectral shape and very large molecular line widths shows a high HCN-to-HCO+ J=4-3 flux ratio, which could be due to turbulence-induced heating. We propose that enhanced HCN J=4-3 emission relative to HCO+ J=4-3 could be used to detect more energetic activity than normal starbursts, including deeply buried AGNs, in dusty galaxy populations.