What does a logo including a frame (see example below) express? In other words, what meaning/feeling does it carry?
The main meaning is to simulate a label.
The labels began to be used in commercial activity to describe the name and content of containers and packages more easily. Over time, beyond its basic identification function, the labels became decorative objects with the intention of enhancing the image of the product and being more attractive to the consumer.
The advantage of a logo-label is that in some cases it allows its variation of position in space.
Conceptually several meanings can be highlighted, direct or indirect and most of them related to the label resemblance:
The framing, mainly in monochrome logos, and the similarity with an ancient product label leads to the retro/vintage quality.
It's a consequence and extension of the previous concept
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The resemblance to the stamping made through a stamp and the blow when done gives a feeling of strength, firmness and decision.
Specially when the frame is large enough and wraps the content with a wide margin
When designing, the use of an enveloping frame is a too recurrent resource sometimes used when the logo can not be resolved as a unique element in the space.
Formerly the black frame was placed in postal items to inform about a death