Editing Computability logic (section)

==Language== 
[[File:Operators_of_computability_logic.png|thumb|Operators of computability logic: names, symbols and readings]] The full language of CoL extends the language of classical [[first-order logic]]. Its logical vocabulary has several sorts of [[Logical conjunction|conjunction]]s, [[disjunction]]s, [[Quantifier (logic)|quantifier]]s, [[Implication (disambiguation)#Logic|implications]], [[negation]]s and so called recurrence operators. This collection includes  all connectives and quantifiers of classical logic. The language also has two sorts of nonlogical atoms: ''elementary'' and ''general''. Elementary atoms, which are nothing but the atoms of classical logic, represent ''elementary problems'', i.e., games with no moves that are automatically won by the machine when true and lost when false. General atoms, on the other hand, can be interpreted as any games, elementary or non-elementary. Both semantically and syntactically, classical logic is nothing but the fragment of CoL obtained by forbidding general atoms in its language, and forbidding all operators other than ¬, ∧, ∨, →, ∀, ∃.

Japaridze has repeatedly pointed out that the language of CoL is open-ended, and may undergo further extensions. Due to the expressiveness of this language, advances in CoL, such as constructing axiomatizations or building CoL-based applied theories, have usually been limited to one or another proper fragment of the language.