Learn Spanish (Latin America): No creo que la conclusión sea lógica. - I don't believe the conclusion is logical.

Because the sentence starts with no creo que (I don't believe that). Denying a belief or expressing doubt triggers the subjunctive mood in Spanish. Since you are stating you don't believe it, you must use the subjunctive sea. If it were an affirmative belief like creo que (I believe that), you would use the indicative es.

If I wanted to say 'I believe the conclusion is logical', how would the sentence change?

You would say Creo que la conclusión es lógica. By changing it to an affirmative belief (creo que), you remove the element of doubt. This means you must switch the verb from the subjunctive sea back to the normal indicative es.

Why do we use a form of ser (sea) here instead of estar (esté)?

We use ser because being logical is an inherent characteristic of the conclusion. Estar is used for temporary states, conditions, or locations. A conclusion is either logical or not by its very nature, so it requires ser.

Why does the word lógica have an accent mark?