Beyond Knights and Knaves

The Logic of Knights, Knaves, Normals and Mutes

R. M. Smullyan wrote in his book about islands, knights and knaves. The knights always tell the truth and the knaves are always lying. Instead of say we shall examine the can say modal operator. We show the soundness and the completeness of this logic.

Proving Facts about "|"

We study the Knights and Knaves problem, and find that for a proper treatment via theorem-proving, an interaction with natural language processing research is helpful. In particular, we discuss Ohlbach's claim that first-order logic is not well suited to handling this problem. Then we provide another interpretation of the problem using indexicals, and axiomatize it so that the desired result fo...

Julian Le Grand (2003), Motivation, Agency, and Public Policy: Of Knights and Knaves, Pawns and Queens, Oxford: Oxford University Press, xii + 191 pp., 25.00, ISBN: S0-19-926699-9

Emergent bipartiteness in a society of knights and knaves

We propose a simple model of a social network based on so-called knights-and-knaves puzzles. The model describes the formation of networks between two classes of agents where links are formed by agents introducing their neighbors to others of their own class. We show that if the proportion of knights and knaves is within a certain range, the network self-organizes to a perfectly bipartite state...

Logicians Who Reason About Themselves

By treating belief as a modality and combining this with problems about constant truth tel lers and constant l iars (knights and knaves) we obtain some curious epistemic counterparts of undecidability results in metamathematics. Godel's second theorem gets reflected in a logician who cannot believe in his own consistency without becoming inconsistent. Lob's theorem reflects i t se l f in a vari...