On the Algebraic Structure of Lewis Carroll's Logic -- Behind the Looking Glass: A Mathematical Perspective
Year: 2026
Type: preprint
Abstract: Charles Ludwidge Dodgeson, better known by his literary pen name `Lewis Carroll', has a number of well known and cherished literary works to his credit, for example "Alice in Wonderland" and "Through the Looking Glass". Apart from this he is known to have a strong professional interest in mathematics and logic with an inclination towards an educational and recreational perspective. In this work we consider the algebraic structure behind Lewis Carroll's approach to classical logic and his logical puzzles. Starting with the arithmetic of $0$ and $1$, we develop the connections between Boolean-valued functions, sets and predicates, which we refer to as the "entangled trinity". This provides a common setting in which Carroll's approach and Boole's perspective can be understood. Particular attention is given to what is meant by "the conclusion" of a logical problem. We suggest a precise interpretation of a complete conclusion in terms of largest lower bounds involving only the predicates to be retained, thereby sharpening Carroll's approach. The role of natural language in choosing a suitable universe and identifying these predicates is discussed through a variety of examples. Finally, we present computerised solution methods, including the use of Boolean satisfiability solvers for larger puzzles.
Source: arXiv (Cornell University)
Authors: Franz, Sebastian, Picard, Rainer
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223663421