We describe a BDI (Belief, Desire, Intention) approach and architecture for a conversational virtual companion embodied as a child’s Toy. Our aim is to support both structured conversation-based activities (e.g., story-telling, collaborative games) as well as more free-flowing, engaging dialogue with variation and some unpredictability. We argue that a goal-oriented approach to the agent’s conv...

We report our findings on the properties of Flagg and Friedman’s translation from Epistemic into Intuitionistic logic, which was proposed as the basis of a comprehensive proof method for the faithfulness of the Gödel translation. We focus on the propositional case and raise the issue of the admissibility of the translated necessitation rule. Then, we contribute to Flagg and Friedman’s program b...

Let C be the companion matrix of a monic polynomial p over a field F. We prove that if A is a matrix whose entries are rational functions of the coefficients of p over F and whose characteristic polynomial is p, then A has at least as many nonzero entries as C.

Recently we proposed to extend the matrix sign classical iteration to the approximation of the real eigenvalues of a companion matrix of a polynomial and consequently to the approximation of its real roots. In our present paper we advance this approach further by combining it with the alternative square root iteration for polynomials and also show a variation using repeated squaring in polynomi...

Let L(λ) = Inλ m + Am−1λm−1 + · · ·+ A1λ + A0 be an n× n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of CL when the matrices A0 and Pm−1 j=1 AjA ∗ j are nonsingular.

The standard way to solve polynomial eigenvalue problems P (λ)x = 0 is to convert the matrix polynomial P (λ) into a matrix pencil that preserves its spectral information– a process known as linearization. When P (λ) is palindromic, the eigenvalues, elementary divisors, and minimal indices of P (λ) have certain symmetries that can be lost when using the classical first and second Frobenius comp...

We propose a new analytic formula for evaluating the derivatives of a matrix exponential. In contrast to the diagonalization method, eigenvalues and eigenvectors do not appear explicitly in the derivation, although we show that a necessary and sufficient condition for the validity of the formula is that the matrix has distinct eigenvalues. The new formula expresses the derivatives of a matrix e...

This paper investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We rst develop matrix as well as Kripke style semantics for those logics. Then, by extending the Godel-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting...