The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way that the strengths of either paradigm will be retained. Current state-of-the-art research, however, fails by far to achieve this ultimate goal. As one of the main obstacles to be overcome we perceive the question how symbolic knowledge can be encoded by means of connectionist systems: Satisfactory answers to this will naturally lead the way to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page

Some Epistemic Extensions of G\"odel Fuzzy Logic

In this paper, we introduce some epistemic extensions of G\"odel fuzzy logic whose Kripke-based semantics have fuzzy values for both propositions and accessibility relations such that soundness and completeness hold. We adopt belief as our epistemic operator, then survey some fuzzy implications to justify our semantics for belief is appropriate. We give a fuzzy version of traditional muddy children problem and apply it to show that axioms of positive and negative introspections and Truth are not necessarily valid in our basic epistemic fuzzy models. In the sequel, we propose a derivation system $K_F$ as a fuzzy version of classical epistemic logic $K$. Next, we establish some other epistemic-fuzzy derivation systems $B_F, T_F, B_F^n$ and $T_F^n$ which are extensions of $K_F$, and prove that all of these derivation systems are sound and complete with respect to appropriate classes of Kripke-based models