  We analyze the gravitational instability (GI) of a locally isothermal
inclined disk around one component of a binary system. Such a disk can undergo
global Kozai-Lidov (KL) cycles if the initial disk tilt is above the critical
KL angle (of about 40 degrees). During these cycles, an initially circular disk
exchanges its inclination for eccentricity, and vice versa. Self-gravity may
suppress the cycles under some circumstances. However, with hydrodynamic
simulations including self-gravity we show that for a sufficiently high initial
disk tilts and for certain disk masses, disks can undergo KL oscillations and
fragment due to GI, even when the Toomre Q value for an equivalent undisturbed
disk is well within the stable regime (Q > 2). We suggest that KL triggered
disk fragmentation provides a mechanism for the efficient formation of giant
planets in binary systems and may enhance fragmentation of disks in massive
black hole binaries.
