We define proof nets for cyclic multiplicative linear logic as edge bi-coloured graphs. Our characterization is purely graph theoretical and works without further complication for proof nets with cuts, which are usually harder to handle in the non-commutative case. This also provides a new characterization of the proof nets for the Lambek calculus (with the empty sequence) which simply are a restriction on the formulas to be considered (which are asked to be intuitionistic).

This work is devoted to the relations between Lambek’s Syntactic Calculus and noncommutative variants of Girard’s Linear Logic; in particular the paper will consider: the geometrical representation of the laws of LC by means of proof-nets; the discovery - due to such a geometrical representation - of some laws of LC not yet considered; the discussion of possible linguistic uses of these new laws.

Hilbert's conference lectures during the year 1922, Neuebegründung der Mathematik. Erste Mitteilung and Die logischen Grundlagen der Mathematik (both are published in (Hilbert [1935] 1965) pp. 157-195), contain his first public presentation of an axiom system for propositional logic, or at least for a fragment of propositional logic, which is largely influenced by the study on logical woks of Frege and Russell during the previous years.The year 1922 is at the beginning of Hilbert's foundational program in its definitive form. The (...) final public presentation by Hilbert of an axiom system for propositional logic is contained in the 1934 book Grundlagen der Mathematik, I (Hilbert and Bernays [1934] 1968). Sequent .. (shrink)

Ch. 1. Metodologicheskie problemy sot︠s︡ialʹno-gumanitarnogo poznanii︠a︡ -- ch. 2. Metodologicheskie problemy istorii filosofii i ėstetiki.

A compact edition of Mr. Beck's excellent translation of the second Critique, slightly revised, together with a helpful short introduction and a bibliography.--V. C. C.

Open peer commentary on the article “Radical Constructivist Structural Design Education for Large Cohorts of Chinese Learners” by Christiane M. Herr. Upshot: Herr’s target article outlines a teaching approach that illustrates and explains how radical constructivism can be used to teach architectural design principles to a large cohort of students. Herr’s approach consists of a hybrid set of instructional activities whose implementation was supported by her establishment of a social climate in the classroom that encouraged the contributions of individuals in (...) the learning process. The activities included the integration of lectures with other teaching formats, the use of open‑ended problem solving tasks, and the use of small‑group projects. I will discuss each of these activities and offer a recommendation for future research. (shrink)