It seems easy to accept that rationality involves many features that cannot be summarized in terms of some straightforward formula, such as binary consistency.  However, this recognition does not immediately lead to alternative characterizations that might be regarded as satisfactory, even though the inadequacies of the traditional assumptions of rational behavior standard used in economic theo...

Given the positive integers m,n, solving the well known symmetric Diophantine equation xm+kyn=zm+kwn, where k is a rational number, is a challenge. By computer calculations, we show that for all integers k from 1 to 500, the Diophantine equation x6+ky3=z6+kw3 has infinitely many nontrivial (y≠w) rational solutions. Clearly, the same result holds for positive integers k whose cube-free part is n...

this paper seeks to trace some of the roots and problems of the rational view of innovation. concentrating primarily upon product innovation, we point out that the eighteenth century notion of social progress in the light of reason has gradually given an enormous impetus to a rational view of product innovation in modern organizations. we summarize several decades of research into management of...

This paper aims to explore the role of questions in communication in a group of cooperative rational agents. Using epistemic representation of questions proposed in [6] we employ the framework of public announcement logic to explore the flow of information in the process of asking and replying questions in a group. We show that some of the erotetic notions we introduce nicely correspond to the ...

We show through a number of examples how it is possible to express beliefs of agents and communication among agents by employing a rst-order logic language with metalogical facilities. We argue that (i) such a language is suitable to characterise rational agents in diierent application areas, and (ii) the interplay between metalogical reasoning and diierent modalities of communications allows u...

creativity or uncreativity of the rational soul is one of the oldest problem of philosophy. ibn sina by giving some proofs has proven the creativity of the rational soul. fakhr ad-din ar razi has propsed several critics to each of the avecina’s argument. in this article, we are going to prove that, the origin of razi’s critics is his misunderstanding in ibn sina’s philosophical views in potenti...

Modelling real world problems using rational agents has been heavily investigated over the past two decades. BDI (Beliefs, Desires, and Intentions) Logic has been widely used to represent and reason about rational agency. However, in the real world, we often have to deal with different levels of confidence in the beliefs we hold, desires we have, and intentions that we commit to. This paper pro...

We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector fields. We estimate the number of sides of parallelograms in a free nilpotent group and point out a relation to the rank of rational series. 1 Int...