By Sara Negri

This publication keeps from the place the authors' prior publication, Structural facts thought, ended. It provides an extension of the equipment of study of proofs in natural common sense to undemanding axiomatic structures and to what's often called philosophical common sense. A self-contained short advent to the evidence thought of natural common sense is integrated that serves either the mathematically and philosophically orientated reader. the tactic is equipped up steadily, with examples drawn from theories of order, lattice conception and user-friendly geometry. the purpose is, in all of the examples, to aid the reader grab the combinatorial behaviour of an axiom process, which generally ends up in decidability effects. The final half offers, as an program and extension of all that precedes it, a proof-theoretical method of the Kripke semantics of modal and similar logics, with plenty of new effects, supplying crucial examining for mathematical and philosophical logicians.