This is the 9847th most frequent Spanish word.
basar
To base or establish something on.
Here, 'basar' is used reflexively as 'basarse', meaning 'to be founded or based upon something'. The verb is conjugated to agree with the subject, 'mis decisiones', and introduces the basis of the decisions, 'en la lógica'.
Mis decisiones siempre se basan en la lógica.
My decisions are always based on logic.
In this sentence, 'basar' is used transitively, meaning 'to establish or found something upon a basis'. The verb is conjugated for the subject, 'el arquitecto', and the object 'su diseño' is the thing being based on 'en la cultura local'.
El arquitecto basa su diseño en la cultura local.
The architect bases his design on the local culture.
Here, 'basar' appears in an infinitive form within an impersonal construction with 'es importante'. It denotes the necessity for foundational ethical principles in actions.