Integrated optical computing attracts increasing interest recently as Moore's law approaches the physical limitation. Among all the approaches of integrated optical computing, directed logic that takes the full advantage of integrated photonics and electronics has received lots of investigation since its first introduction in 2007. Meanwhile, as integrated photonics matures, it has become critical to develop automated methods for synthesizing optical devices for large-scale optical designs. In this paper, we propose a general electro-optic (EO) logic in a higher level to explore its potential in integrated computing. Compared to the directed logic, the EO logic leads to a briefer design with shorter optical paths and fewer components. Then a comprehensive gate library based on EO logic is summarized. At last, an And-Inverter Graphs (AIGs) based automated logic synthesis algorithm is described as an example to implement the EO logic, which offers an instruction for the design automation of high-speed integrated optical computing circuits.