VINCENT F . HENDRICKS Modal Operator Theory

Formal treatments of epistemology and epistemological issues have come a great way in recent years. Valuable results have been produced by Bayesians, in formal learning theory (also known as computational epistemology in [Kelly 96] and epistemic logic. While the first to formal approaches concentrate on learning and knowledge acquisition issues, the latter concentrate on axiomatics and validity. Then there is also mainstream epistemology, which seeks necessary and sufficient conditions for the possession of knowledge by presenting ‘intuitive’ examples and counterexamples. All these various approaches have proceeded largely in isolation from one another. This seems to be the state of epistemology today. What we have dubbed modal operator theory (MOT) [Hendricks 01], [Hendricks & Pedersen 00a] is a paradigm obtained by mixing epistemic, tense and alethic logic with a few concepts drawn from computational epistemology. The paradigm can then be used to study the acquistion and validity of knowledge observing the apparata and insights of the formal and mainstream epistemologies. Now modal logic has grown into a mature field of research with a wide range of applications in both philosophy, linguistics and computer science. Nevertheless approximately 30 years ago, Dana Scott in his famous article ‘Advice on Modal Logic’ pointed out a problem for the entire modal logic endeavor, which still to this day largely holds true: