# User:IssaRice/Logical induction notation

Term | Notation | Type | Definition | Notes |
---|---|---|---|---|

-combination | Function application of an -combination uses square brackets instead of parentheses. Why? As far as I can tell, this is because each coefficient is in so is itself a function. This means we have two senses of "application": we can pick out the specific coefficient we want (square brackets), or we can apply each coefficient to return something (parentheses). | |||

Holdings from against (a -combination) | ||||

Trading strategy | ||||

Feature | or equivalently or equivalently |

Example of a 5-strategy given on p. 18 of the paper:

Since the coefficients ( and ) are in , this is an -combination. Let's call this 5-strategy . We can pick out the coefficient for the term like . But since each coefficient is a feature (which is a function), we can also apply each coefficient to some valuation sequence , like this:

Now each coefficient is a real number, so is an -combination. Note that since is a function that takes a sentence or the number and is a valuation sequence (*not* a sentence or number), there appears to be a type error in writing . What is going on is that we aren't evaluating at ; rather, we are evaluating *each coefficient* of , to convert the range of from to .

To summarize the types:

- in other words

If , then

and

and

I think but the former notation seems to be preferred in the paper.