A Kripke Semantics for the Logic of Gelfand Quantales

Gelfand quantales are complete unital quantales with an involution, *, satisfying the property that for any element a, if a b a for all b, then a a* a = a. A Hilbert-style axiom system is given for a propositional logic, called Gelfand Logic, which is sound and complete with respect to Gelfand quantales. A Kripke semantics is presented for which the soundness and completeness of Gelfand logic is shown. The completeness theorem relies on a Stone style representation theorem for complete lattices. A Rasiowa/Sikorski style semantic tableau system is also presented with the property that if all branches of a tableau are closed, then the formula in question is a theorem of Gelfand Logic. An open branch in a completed tableaux guarantees the existence of an Kripke model in which the formula is not valid; hence it is not a theorem of Gelfand Logic.     

Zwei Wege am Ödipuskomplex vorbei

Two pathological constellations are presented that prevent from resolving the Oedipal complex. Both have in common the poor resilience of the negative Oedipal constellation. In the first version, a rivalry with the father is avoided, acknowledgement and idealization do not take place, but the father’s position is taken over in a regressive surreptitious way. The second way to avoid resolving the Oedipal constellation is based on narcissistic omnipotence. During Oedipal development the child – owing to the behaviour of the parent of the other sex – becomes convinced to be himself the preferred partner of father or mother. This development is illustrated by a case study.