We present the results of multi-year gamma-ray observations by the AGILE
satellite of the black hole binary system Cygnus X-1. In a previous
investigation we focused on gamma-ray observations of Cygnus X-1 in the hard
state during the period mid-2007/2009. Here we present the results of the
gamma-ray monitoring of Cygnus X-1 during the period 2010/mid-2012 carried out
for which includes a remarkably prolonged `soft state' phase (June 2010 -- May
2011). Previous 1--10 MeV observations of Cyg X-1 in this state hinted at a
possible existence of a non-thermal particle component with substantial
modifications of the Comptonized emission from the inner accretion disk. Our
AGILE data, averaged over the mid-2010/mid-2011 soft state of Cygnus X-1,
provide a significant upper limit for gamma-ray emission above 100 MeV of
F_soft < 20 x 10^{-8} ph/cm^2/s, excluding the existence of prominent
non-thermal emission above 100 MeV during the soft state of Cygnus X-1. We
discuss theoretical implications of our findings in the context of high-energy
emission models of black hole accretion. We also discuss possible gamma-ray
flares detected by AGILE. In addition to a previously reported episode observed
by AGILE in October 2009 during the hard state, we report a weak but important
candidate for enhanced emission which occurred at the end of June 2010
(2010-06-30 10:00 - 2010-07-02 10:00 UT) exactly in coincidence with a
hard-to-soft state transition and before an anomalous radio flare. An appendix
summarizes all previous high-energy observations and possible detections of
Cygnus X-1 above 1 MeV.Comment: 16 pages, 12 figures, 1 table, accepted for publication in Ap
