'logically-decided' originates from the combination of 'logical' and 'decide', where 'logical' is derived from the Greek word 'logikos', meaning 'pertaining to reason', and 'decide' comes from the Latin 'decidere', meaning 'to cut off'.

'logikos' transformed into the Latin 'logicus', and eventually became the modern English word 'logical'. 'Decidere' transformed into the Old French 'decider', and eventually became the modern English word 'decide'.

Initially, 'logical' meant 'pertaining to reason', and 'decide' meant 'to cut off', but over time they evolved into their current meanings of 'based on logic' and 'to make a choice', respectively.