I picked up Dependence Logic: A New Approach to Independence Friendly Logic by Jouko Väänänen. I figure I’ll write up a review when I am finished with the book, but there is one chief difference between Dependence Logic and Independence Friendly Logic that needs to be mentioned. On pages 44-47 when describing the difference between Dependence Logic and Independence Friendly Logic Väänänen says, The backslashed quantifier, ∃xn{xi0,…,xim-1}φ, introduced in ref. [20], with the intuitive meaning: […]

# Category: game theory

## The Monty Hall Problem

[check out my more recent Monty Redux for, perhaps, a clearer exposition] The Monty Hall Problem illustrates an unusual phenomenon of changing probabilities based upon someone else’s knowledge. On the game-show Let’s Make a Deal the host, Monty Hall, asks the contestant to choose one of three possibilities – Door One, Two or Three – with one door leading to a prize and the other two leading to goats. After the contestant selects a door, […]

## The Logic of Biological Relativity [draft]

How can we represent biological relativity in logical notation? Organism a is adapting relative to organism b Aab Organism b is adapting relative to a Aba Organisms a and b are adapting relative to each other Aab & Aba This schema is unsatisfactory because it describes the situation from an indeterminate outside perspective: a and b are said to be adapting relative to each other without regard to the observer describing the situation. Relativity applies […]

## The Logic of Relativity [draft]

How can we represent relativity in logical notation? a is moving relative to b Mab b is moving relative to a Mba a and b are moving relative to each other Mab & Mba This schema is unsatisfactory because it describes the situation from an indeterminate outside perspective: a and b are moving relative to each other without regard to the observer describing the situation. Relativity applies to all the perspectives in question (with special […]