We introduce proof nets and sequent calculus for the multiplicative fragment of non-commutative logic, which is an extension of both linear logic and cyclic linear logic. The two main technical novelties are a third switching position for the non-commutative disjunction, and the structure of order variety.

In a previous article, the writer explored the geometric foundation of the generally covariant spinor calculus. This geometric reasoning can be extended quite naturally to include the Lie covariant differentiation of spinors. The formulas for the Lie covariant derivatives of spinors, adjoint spinors, and operators in spin space are deduced, and it is observed that the Lie covariant derivative of an operator in spin space must vanish when taken with respect to a Killing vector. The commutator of two Lie covariant (...) derivatives is calculated; it is noted that the result is consistent with the geometric interpretation of the Jacobi identity for vectors. Lie current conservation is seen to spring from the result that the operator of spinor affine covariant differentiation commutes with the operator of spinor Lie covariant differentiation with respect to a Killing vector. It is shown that differentiations of the spinor field defined geometrically are Lorentz-covariant. (shrink)

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.

T. 1-2. Statʹi po filosofīi.--t. 3. Statʹi obshchenauchnago kharaktera.

The interaction of the organism with the environment requires not only reactive, but also active behavior (i.e., search activity) which helps subject to meet the challenge of the uncertainty of the environment. A positive feedback between active behavior and immune system makes the selection process effective.

The Concept of Humanitarian Development of Ukraine till 2020: Religious Proposals to Plan-Prospectus.

For the current, turning point in the history of Ukraine characterized by the desire of ideologues of different confessions to speak from the standpoint of the global vision of the world, the inclusion in the public consciousness of the ideological function of religion, through which the religious interpretation of the relationship "man - the world" is revealed. To achieve this they seek, in particular, through the involvement in theological outlook of theological interpretations of the achievements of the combined science, which (...) supposedly only in such a way acquire perfection and true meaning. (shrink)

Topics in Cognitive Science, Volume 14, Issue 2, Page 414-425, April 2022.