Unlike the discovery of strictly logical truths, which are the heart of all things and thus do not rely on anything more foundational than themselves, thinking of storytelling concepts is often prompted by experience, though even this cannot be understood apart from reason. There is nothing logically necessary, other than a few basic aspects, that a story must have. It can have heroes and villains or just one protagonist. It can delve into comedy, horror, drama, or action. It might or might not combine genres and subgenres. In an experiential vacuum, there is little to nothing to specifically inspire a story, even when logical axioms and their ramifications could be discovered and perfectly understood in an absence of sensory experiences. Without something to prompt a storyteller to think of a particular fictional narrative, whether a personal experience or another story was the muse, it would be highly difficult to realize how truths, ideas, and events can all come together to form precise stories (yes, logical truths and philophical concepts can inspire art as well, but logical truths alone would likely not bring someone to think of events in narratives as opposed to necessary truths).
One kind of art can even inspire new works in different mediums, as is exemplified in the way the first Alien movie inspired the game Metroid, down to the name of Samus Aran's franchise nemesis Ridley being named after director Ridley Scott, whose film Alien will be mentioned again shortly. Both feature female protagonists in a hostile science fiction world at a time when it would have been even more groundbreaking to defy the norm of male protagonists in entertainment. Both feature extraterrestrial creatures the heroine must defeat (or in the case of Alien, one extraterrestrial creature). Of course, they have their differences, even as the similarities extend to the Weyland Corporation and the Galactic Federation respectively trying to capture, study, and experiment upon the titular alien of each franchise.
The influence of those who worked on Alien does not stop with Metroid! Far from it. Lovecraft's writings, the artwork of H.R. Giger (who also was involved with the creature and set design of Alien), and the film Eyes Wide Shut all inspired the erotic cosmic horror game Lust for Darkness, which combines the eldritch horror of Lovecraftian fiction with sexually evocative environments and even one of the lines from Eyes Wide Shut--just in a very different context. Cosmic horror is here used as to emphasize the destructiveness of hedonism, which takes this horror subgenre in an unconventional direction while still holding onto some of the norms of Lovecraftian fiction. It is unfortunate that the production values and gameplay do not live up to the absolutely genius philosophical narrative that the game explores.
Many other examples can be found, such as how Tolkien's Lord of the Rings provoked George R.R. Martin to write his A Song of Ice and Fire books to correct the simplicity of the former. There is the way the psychological horror video game series Silent Hill inspired Stranger Things, with the Otherworld of the former (an alternate dimension where ordinary laws of physics do not apply) pushing the Duffer brothers to conceive of the Upside Down for the latter. It is not always art, though, that inspires art. Author Stephen King says he has found inspiration for some of his most renowned works in random personal experiences throughout his life, such as how his stay at a hotel in Colorado gave him ideas for The Shining. Lovecraft himself, whose works inspired Stephen King (stories like It definitely veer into cosmic horror territory at points), was inspired by a dream to write the short story The Call of Cthulhu.
Strictly logical truths and personal experiences, though of the two, only the first can be known without prompting from the latter, can inspire incredible artistic narratives that reflect at least something of reality; it is impossible for fiction to ever escape the necessary truths of logical axioms, as that which is truly logically necessary cannot even be contradicted within fiction--it is logically impossible! For many aspects of entertainment, it would nonetheless be very difficult or impossible to think of the ideas without experience providing psychological material to draw from. Sometimes these experiences are encounters with someone else's art, and sometimes they are introspective or sensory experiences that have nothing to do with entertainment. Either way, there is even now, after so many works of entertainment in various mediums that have been responses to other works of entertainment, a plethora of ways to combine themes, genres, and narrative structures to make them original in the sense of novelty, and sometimes this originality is ironically sparked by familiarity with other art.