The Logic of Knights, Knaves, Normals and Mutes

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...

Beyond Knights and Knaves

In the classic knights and knaves problem, there are n people in a room each of whom is a knight or a knave. Knights always tell the truth while knaves always lie. Everyone in the room knows each other’s identity. You are allowed to ask questions of the form “Person i, is person j a knight?” and you are told that there are more knights than knaves. What is the fewest number of questions you can...

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...

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...