Full Idea
Semantic rules can be presented in 'Tarski style', where the interpretation-plus-valuation is reduced to the same question for simpler formulas, or the 'Henkin-Hintikka style' in terms of games, or the 'Barwise-Etchemendy style' for computers.
Clarification
For 'interpretation' and 'valuation' see Idea 10283
Gist of Idea
There are three different standard presentations of semantics
Source
Wilfrid Hodges (First-Order Logic [2001], 1.3)
Book Reference
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.13
A Reaction
I haven't yet got the hang of the latter two, but I note them to map the territory.