… theories’ hierarchy. … hierarchical counterparts of some of the usual modal logics, such as
K4, KD4 and S4. Then we will introduce a natural provability interpretation for these new logics …

… in "Hierarchical recta-logics for beliefs and provability: how we can do without modal logics
"… Thus, for instance, we study logics of provability with the goal of providing foundations to the …

… provability logics for such pairs of theories. We also show that there are some provability
logics … , in the last section the polymodal provability logics for natural recursive progressions of …

… The indexing and degree-restriction extends to the proofs of these corollaries, eg in the
proof of Corollary 2, we define Uj as {A :deg(A) < j and (3B)(deg(B) < j, A -. B ea, and B 0 cj)}. …

… formal provability we know that the provability logic GL describes exactly all provable structural
… interpretation is that the resulting provability hierarchies run in phase with the arithmetical …

… -theoretic analog of this problem, the question of classifying arithmetical sentences by
hierarchies of iterated re ection principles, was first considered by Turing in [19]. To the best of my …

… logics that go well beyond the family of logics addressed by Nute. We consider logics that …
statements of definite or defeasible proof, as well as logics with different notions of failure-to…

… In expressing the proof theory we consider only propositional rules. Rules containing free …
is provable defeasibly we have two choices: (1) We show that q is already definitely provable; …

… We define the analogue of the analytical hierarchy for finite sets. The language L2 is the
language of second-order arithmetic; it consists of two symbols for constants: O,1, two symbols …

… the way the constructible hierarchy grows by examining its l~ … the usual L~ hiei'archy by a
new hierarchy I~. We define Jo,÷ l … The main difference between the two hierarchies is that Ja …