Proving infinitary formulas. Issue 5 (14th October 2016) - HARRISON, AMELIA; LIFSCHITZ, VLADIMIR; MICHAEL, JULIAN
Abstract: The infinitary propositional logic of here-and-there is important for the theory of answer set programming in view of its relation to strongly equivalent transformations of logic programs. We know a formal system axiomatizing this logic exists, but a proof in that system may include infinitely many formulas. In this note we describe a relationship between the validity of infinitary formulas in the logic of here-and-there and the provability of formulas in some finite deductive systems. This relationship allows us to use finite proofs to justify the validity of infinitary formulas.