We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a self-dual logic; constructible duality. We develop a self-dual model by considering an interval of worlds in an intuitionistic Kripke model. The duality arises through how we judge truth and falsity. Truth is judged forward in the Kripk...

In this note, by using the concept of Bipolar-valued fuzzy set, the notion of bipolar-valued fuzzy BCK/BCI-algebra is introduced. Moreover, the notions of (strong) negative s-cut (strong) positive t-cut are introduced and the relationship between these notions and crisp subalgebras are studied.

This paper analyzes the action δ of a Lie algebra X by derivations on a C*–algebra A. This action satisfies an “almost inner” property which ensures affiliation of the generators of the derivations δ with A, and is expressed in terms of corresponding pseudo–resolvents. In particular, for an abelian Lie algebra X acting on a primitive C*–algebra A, it is shown that there is a central extension o...

In this paper we use continuous family of multisections of the moduli space of pseudo holomorphic discs to partially improve the construction of Lagrangian Floer cohomology of [13] in the case of R coefficient. Namely we associate cyclically symmetric filtered A∞ algebra to every relatively spin Lagrangian submanifold. We use the same trick to construct a local rigid analytic family of filtered...

In the late 1980s, Graeme Segal axiomatized conformal field theory in terms of a cobordism category. In that same preprint he outlined a more symmetric trace approach, which was recently rigorized in terms of pseudo algebras over a 2-theory. In this paper, we treat the cobordism approach in the pseudo algebra context. We introduce a new algebraic structure on a bicategory, called a pseudo 2-alg...

An implementation of the algebra of pseudo diierential operators in the computer algebra system AXIOM is described. In several examples the application of the package to typical computations in the theory of integrable systems is demonstrated. Nature of physical problem: Generation of integrable systems solvable by the Inverse Scattering Method and determination of conservation laws Method of s...

This article provides a complete description of the differential Gerstenhaber algebras of all nilpotent complex structures on any real six-dimensional nilpotent algebra. As an application, we classify all pseudo-Kählerian complex structures on six-dimensional nilpotent algebras such that the differential Gerstenhaber algebra of its complex structure is quasi-isomorphic to that of its symplectic...

The notion of pseudo-valuations (valuations) on a BCC-algebra is introduced by using the Buşneag’s model ([1–3]), and a pseudo-metric is induced by a pseudo-valuation on BCC-algebras. Conditions for a real-valued function to be an BCK-pseudo-valuation are provided. The fact that the binary operation in BCC-algebras is uniformly continuous is provided based on the notion of (pseudo) valuation.