  Let $(\mathcal{E},D(\mathcal{E}))$ be a quasi-regular semi-Dirichlet form and
$(X_t)_{t\geq0}$ be the associated Markov process. For $u\in
D(\mathcal{E})_{loc}$, denote $A_t^{[u]}:=\tilde{u}(X_{t})-\tilde{u}(X_{0})$
and $F^{[u]}_t:=\sum_{0<s\leq t}(\tilde u(X_{s})-\tilde u(X_{s-}))1_{\{|\tilde
u(X_{s})-\tilde u(X_{s-})|>1\}}$, where $\tilde{u}$ is a quasi-continuous
version of $u$. We show that there exist a unique locally square integrable
martingale additive functional $Y^{[u]}$ and a unique continuous local additive
functional $Z^{[u]}$ of zero quadratic variation such that
$$A_t^{[u]}=Y_t^{[u]}+Z_t^{[u]}+F_t^{[u]}.$$ Further, we define the stochastic
integral $\int_0^t\tilde v(X_{s-})dA_s^{[u]}$ for $v\in D(\mathcal{E})_{loc}$
and derive the related It\^{o}'s formula.
