Note: setting a list-style using a shorthand property later in the cascade will override more explicit settings from earlier on. e.g. the second example if used after the first will reset values (back to default) from the first even though they're not declared.

If you only require to override one part of a setting the has been set using shorthand earlier in the cascade you should use a longhand list-style property as this will only affect that particular property.

Example:
ul {
list-style-type: disc;
}

Note:
ul {
list-style: none;
}

will set both <list-style-type> and <list-style-image> to none

Note: <li> items will inherit list-style values from their <ol> and <ul> parent elements and setting the list style on a <ul> or an <ol> is the recommended way to control the overall lists, then descendant selectors (specificity) will enable you to target individual <li> elements if required.
Example:
ol ol li {list-style: disc;}
ul li {list-style: square;}

... more to follow ....