Lincoln gave his second inaugural address on March 4, 1865. The North was winning, but had not yet won, the Civil War.
Logos is one of the three pillars of classical logic. It focuses on facts and statistics, whereas pathos focuses on emotions, and ethos focuses on establishing character and credibility.
While Lincoln's address leans heavily on pathos, or emotional appeal, he does also appeal to facts. For example, he briefly recounts the history of the past four years. He noted that four years ago the South was attempting to dissolve the United States without going to war. He also notes that the South was willing to go to war to dissolve the union, while the North was equally willing to fight to protect the union. Lincoln couches all of this in emotional language, but the facts he outlines are true.
Lincoln also offers a statistic, stating that one-eighth of the nation consisted of black ("colored") slaves when the war began. He notes that the slaves were concentrated in one part of the country. He states as fact that a key reason for the war was the Southern desire to perpetrate and extend slavery.
Lincoln spends much of the speech referring to God and makes an emotional plea for an end to the war in a way that ensures northern victory and healing for the nation. He includes logos as part of his appeal, but he frequently intertwines it with pathos.