If you are referring to logs as a pod's sub-resource you can manage it with RBAC role.
To represent this in an RBAC role, use a slash to delimit the resource and subresource. To allow a subject to read both pods and pod logs, you would write:
- apiGroups: [""]
resources: ["pods", "pods/log"]
verbs: ["get", "list"]
Hence, to restrict access to pod's logs you just need NOT to include "pods/log" into resource list
Also, bear in mind, that rules are purely additive in kubernetes RBAC, so you will need to list all accessible resources, otherwise you won't be able to access them as well.
When the role is created, you'll need to link it to your user or service account within a
- kind: User