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)

Summary Ideomotor apraxia is a cognitive disorder in which the patient loses the ability to accurately perform learned, skilled actions. This is despite normal limb power and coordination. It has long been known that left supramarginal gyrus lesions cause bilateral upper limb apraxia and it was proposed that this area stored a visualkinaesthetic image of the skilled action, which was translated elsewhere in the brain into the pre-requisite movement formula. We hypothesise that, rather than these two functions occurring separately, both (...) are complementary functions of chains of ‘‘mirror neurons’’ within the left inferior parietal lobe. We go on to propose that this neural mechanism in the supramarginal gyrus and its projection zones, which originally evolved to allow the creation of a direct map between vision and movement, was subsequently exapted to allow other sorts of cross-domain mapping and in particular those sorts of abstract re-conceptualisation, such as metaphor, that make mankind unique. (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.

Former research showed that up to 20–25 % of those who leave schools of type VIII are referred to nursery homes for chronic mental patients not due to medical problems but because of social ones. According to the authors’ opinion, such social practice has more positive than negative aspects. However, this issue requires extensive discussions. Organizing special post-diploma training courses of 16–24 hours on ethical-psychological aspects of referral various categories of patients to nursery homes for chronic mental patients also seems (...) to be reasonable. (shrink)

In the article the problem of transformation of the information received by the user on the Internet into his knowledge is investigated. The paper uses the main special scientific and logical research methods used in the social and humanitarian sciences. At the same time, the methods of systematic and value-worldview analysis of the phenomena of the spiritual world of a person are distinguished by the degree of significance, which allow us to study the problem of the dialectic of knowledge and (...) information on the Internet not in isolation, but in connection with the main phenomena of the spiritual life of people, taking into account the priority of value-worldview structures. The goal of the work is to find a priority factor that provides a higher degree of accuracy in the transformation of information from the Internet into human knowledge. It is shown that the nature of the world wide web to a certain extent complicates the process of translating information coming to a person into his knowledge. It is concluded that the condition for the transformation of information received by the user on the Internet is the cognitive activity of a person, due primarily to the development of its value and ideological sphere. If the cognizing person has sufficiently developed and stable value – ideological foundations of personality, he successfully realizes himself as a developing subject, an active participant in knowledge. On the contrary, insufficiently stable value-worldview sphere can lead to passive perception of information by the individual, adaptation to reality, simplification of personality. Information from the Internet in the most adequate form is transformed into a person’s knowledge on the basis of his own cognitive activity, in the presence of intellectual and volitional capabilities for verifying the information available on the Network. (shrink)

The problem of man and the environment has many aspects. I would like to discuss the scientific aspect of the problem.

The report brought to the section members’ notice issues consideration of the major tendencies of religious and aesthetic medium transformation laying the emphasis on the major factors of this transformation together with its socio-cultural basis. Based on the comparison of the processes taking place within Catholicism, Protestantism and Orthodoxy the report marks the concurrency of religious and aesthetic processes present within the named confessions which challenges the idea of absolute uniqueness of religious and aesthetic experience of the orthodox in Russia (...) nowadays. The syncretism in the first place and dialectical unity of fundamentalism and modernism in the second, can be considered as the leading tendencies of transformation of religious and aesthetic medium of modern Christianity. (shrink)