This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and modern equivariant moving frame a framework dubbed involutive frames. As an attestation fruitfulness our framework, we obtain new, constructive intuitive proof Lie-Tresse theorem (Fundamental basis theorem) first general upper bound on minimal number generating differential invariants for Li...

The concept of a Kleene algebra (sometimes also called lattice) was already generalized by the first author for non-distributive lattices under name pseudo-Kleene algebra. We extend these concepts to posets and show how (pseudo-)Kleene can be characterized identities implications assigned commutative meet-directoids. Moreover, we prove that Dedekind-MacNeille completion poset is finite Further,...

In this paper we consider parametric ideals and introduce a notion of comprehensive involutive system. This notion plays the same role in theory of involutive bases as the notion of comprehensive Gröbner system in theory of Gröbner bases. Given a parametric ideal, the space of parameters is decomposed into a finite set of cells. Each cell yields the corresponding involutive basis of the ideal f...

In this paper we present results of our computer experiments to study effectiveness of involutive criteria for avoiding useless prolongations in construction of polynomial Janet bases. These bases are typical representative of involutive bases. Though involutive bases are usually redundant as Gröbner ones, they can be used as well as the reduced Gröbner bases in whose theory Volker Weispfenning...

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...