  In this paper we use continuous family of multisections of the moduli space
of pseudo holomorphic discs to partially improve, in the case of real
coefficient, the construction of Lagrangian Floer cohomology of which the
author developed jointly with Oh-Ohta-Ono. Namely we associate cyclically
symmetric filtered A infinity algebra to every relatively spin Lagrangian
submanifold. We use the same trick to construct a local rigid analytic family
of filtered A infinity structure associated to a (family of) Lagrangian
submanifolds. We include the study of homological algebra of pseudo-isotopy of
cyclic (filtered) A infinity algebra.
