The computer has three fundamental analogies with the human being (senses, memory and intelligence), but the coming out of the data bases announced a new form of language: the computer language. The data bases not only set several new technical and social problems, but moreover are modifying the traditional form of social memory, supported by paper, by changing it in a memory based on electronic means. This situation creates new forms of representation of knowledge to which the author gave attention in previous contributions with his SENECA project, in which computer language tries to give a synthesis of oral and written languages, with their respective advantages.

An impossible world is a world which necessarily does not exist. Besides the paradigm of necessity, wich is logical necesslty, we must consider physical necessity and ethical necessity, both of wich can beexpressed in terms of logical necessity, in the way suggested by Montague. Accordingly, an impossible world can be logically impossible, physically impossible or ethically impossible, but in every case the impossibility can be reduced to logical impossibility, and in consequence an impossible world is irrational and cannot be understood by us. An illustration is taken from the incongruities of Kafka’s story in Di Verwandlung.

A Fuzzy-Set Theoretical Framework -resting on a paraconsistent infinite-valued logic- is sketched, wherein a thorough ontological-reduction program can be carried out. The framework includes formulae of the form “x comprises z in the time-interval e”. Reducing aggregates to sets thus handled is shown to escape usual objections. Likewise, systems generally can be regarded as aggregates, hence as (fuzzy) sets -the purported nonextensionality of systems objection being disposed of owing to our system’s recognizing infinitely many membership degrees. So do bodies, too, which enables us to find a solutionto Unger’s sorites concerning ordinary material bodies.

A system S has the “converse Ackermann property” (C.A.P.) if (A -> B) -> C is unprovable in S whenever C is a propositional variable. In this paper we define the fragments with the C.A.P. of some well-know propositional systems in the spectrum between the minimal and classical logic. In the first part we succesively study the implicative and positive fragments and the full calculi. In the second, we prove by a matrix method that each one of the systems has the C.A.P. Thus, we think the problem proposed in Anderson & Belnap (1975) § 8.12 has been solved.