A logic of implications in algebra and coalgebra
This paper rephrases previous work by Rosu that develops a sound and complete calculus for abstract logics in which models are objects in abstract categories, sentences are epimorphisms in the respective categories, and satisfaction is given by (categorical) injectivity. Both Birkhoff calculus for conditional equations in universal algebra and Gumm calculus for coalgebra appear as instances of the abstract calculus developed here. However important potential applications are not discussed, most notably in the area of partial algebra, which may rise doubts about the real value of this work.
scientific article; zbMATH DE number 5652288