Francisco Salto

Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered.

It is an intimate experience for us to think, to understand and to perceive things as being identical to themselves, and to suppose, consequently, that things are truly “what” they are. Something is always conceived as itself. The given is given full of itself in all its modifications. For instance, I can think or perceive partially some lips, I can see them almost in their whole or in some of their aspects, or just see them disappear. But it does not seem to be possible to think or to perceive a given as almost itself, as an aspect or as part of itself. It is the aim of this work to study the assumptions and conditions for the original position of sameness in experience, just as it occurs in the synthesis of the datum singular and distinct. The polarization of single tone (einstimmig) intentional rays in an αvτó already contains the aporiae peculiar to the experience of the identical, whose revelation shall lead us, on the one hand, to one of the nuclei of the analysis of passive synthesis, and, on the other hand, to point up how critical revision of the numerical or extensional model of self-identity is for the unity of meaning. Then, it will be a question of pointing out the reasons why in a phenomenology of identity, the renunciation of the phenomenological legitimacy of the αvτó as a guarantee for the different positions of identity must be observed. DOI: 10.1007/978-94-011-3464-4_13

Etude de l'extension par la negation semi-intuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type Routley-Meyer pour le systeme d'Urquhart (CI) en tant que celle-la ne fournit que des theories consistantes pour la completude de celui-ci