The term 'universal logic' has also been used by some logicians (e.g. Richard Sylvan and Ross Brady) to refer to a new type of (weak) relevant logic.
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Three model-theoretic directions for universal logic have been explored to some depth: abstract model theory axiomatized by Jon Barwise, a topological / categorical approach based on sketches (sometimes called categorical model theory), and yet another categorical approach based on Goguen and Burstall's notion of institution.
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