Traditionally most programming languages have priority of AND higher than priority of OR so that expression “a OR b AND c” is treated as “a OR (b AND c)”. Following that idea search engines and query/addressing languages (css,xpath,sql,…) used the same prioritization. Wasn’t it mistake ?
When dealing with large enough data, that prioritization is inconvenient because it makes it impossible to create reusable query context without use of parentheses. It is more convenient to create context by using AND and then union results within that context by using OR. It is even more convenient if space is used as AND operator and comma is used as OR operator.
Examples:
When searching the internet for airline tickets to bahamas in november or december it would be more convenient to type “airline ticket bahamas november,december” instead of “airline ticket bahamas november”, “airline ticket bahamas december” or “airline ticket bahamas (november,december)”
In CSS if we need to set style red of 2 elements, we have to do that: body.app1 div.d1 td.phone span.area, body.app1 div.d1 td.fax span.area{color:red} essentially duplicating prefix body.app1 div.d1 and suffix span.area
If priority of OR was higher than AND we would write this in CSS: body.app1 div.d1 td.phone,td.fax span.area{color:red}
Of course, this idea can be developed into having 2 operators OR one with higher priority than AND and one with lower, for example ‘,’ is higher, ‘;’ is lower, but in many cases languages don’t have spare symbols to extend that way and also existing priority of “,” where it’s used is low.
Considering the fact that the background of OR and AND is from mathematical logic where they have well defined precedence, you can not violate that precedence in your design without confusing a VAST majority of the users.