# OData logical operators in Azure AI Search - and, or, not

OData filter expressions in Azure AI Search are Boolean expressions that evaluate to true or false. You can write a complex filter by writing a series of simpler filters and composing them using the logical operators from Boolean algebra:

• and: A binary operator that evaluates to true if both its left and right sub-expressions evaluate to true.
• or: A binary operator that evaluates to true if either one of its left or right sub-expressions evaluates to true.
• not: A unary operator that evaluates to true if its sub-expression evaluates to false, and vice-versa.

These, together with the collection operators any and all, allow you to construct filters that can express very complex search criteria.

## Syntax

The following EBNF (Extended Backus-Naur Form) defines the grammar of an OData expression that uses the logical operators.

logical_expression ::=
boolean_expression ('and' | 'or') boolean_expression
| 'not' boolean_expression


An interactive syntax diagram is also available:

There are two forms of logical expressions: binary (and/or), where there are two sub-expressions, and unary (not), where there is only one. The sub-expressions can be Boolean expressions of any kind:

• Fields or range variables of type Edm.Boolean
• Functions that return values of type Edm.Boolean, such as geo.intersects or search.ismatch
• Comparison expressions, such as rating gt 4
• Collection expressions, such as Rooms/any(room: room/Type eq 'Deluxe Room')
• The Boolean literals true or false.
• Other logical expressions constructed using and, or, and not.

Important

There are some situations where not all kinds of sub-expression can be used with and/or, particularly inside lambda expressions. See OData collection operators in Azure AI Search for details.

### Logical operators and null

Most Boolean expressions such as functions and comparisons cannot produce null values, and the logical operators cannot be applied to the null literal directly (for example, x and null is not allowed). However, Boolean fields can be null, so you need to be aware of how the and, or, and not operators behave in the presence of null. This is summarized in the following table, where b is a field of type Edm.Boolean:

Expression Result when b is null
b false
not b true
b eq true false
b eq false false
b eq null true
b ne true true
b ne false true
b ne null false
b and true false
b and false false
b or true true
b or false false

When a Boolean field b appears by itself in a filter expression, it behaves as if it had been written b eq true, so if b is null, the expression evaluates to false. Similarly, not b behaves like not (b eq true), so it evaluates to true. In this way, null fields behave the same as false. This is consistent with how they behave when combined with other expressions using and and or, as shown in the table above. Despite this, a direct comparison to false (b eq false) will still evaluate to false. In other words, null is not equal to false, even though it behaves like it in Boolean expressions.

## Examples

Match documents where the rating field is between 3 and 5, inclusive:

    rating ge 3 and rating le 5


Match documents where all elements of the ratings field are less than 3 or greater than 5:

    ratings/all(r: r lt 3 or r gt 5)


Match documents where the location field is within the given polygon, and the document does not contain the term "public".

    geo.intersects(location, geography'POLYGON((-122.031577 47.578581, -122.031577 47.678581, -122.131577 47.678581, -122.031577 47.578581))') and not search.ismatch('public')


Match documents for hotels in Vancouver, Canada where there is a deluxe room with a base rate less than 160:

    Address/City eq 'Vancouver' and Address/Country eq 'Canada' and Rooms/any(room: room/Type eq 'Deluxe Room' and room/BaseRate lt 160)