Dependence logic

Dependence logic is a logical formalism, created by <a href="/facts/Jouko_V%C3%A4%C3%A4n%C3%A4nen/okh0yBPv">Jouko Väänänen</a>, which adds dependence atoms to the language of <a href="/facts/First_Order_Logic/lcISqWIg">first-order logic</a>. A dependence atom is an expression of the form 
 
 
 
 =
 
 
 (
 
 t
 
 1
 
 
 …
 
 t
 
 n
 
 
 )
 
 
 {\displaystyle =\!\!(t_{1}\ldots t_{n})}
 
, where 
 
 
 
 
 t
 
 1
 
 
 …
 
 t
 
 n
 
 
 
 
 {\displaystyle t_{1}\ldots t_{n}}
 
 are terms, and corresponds to the statement that the value of 
 
 
 
 
 t
 
 n
 
 
 
 
 {\displaystyle t_{n}}
 
 is <a href="/facts/Functional_dependency/aLfwfUNk">functionally dependent</a> on the values of 
 
 
 
 
 t
 
 1
 
 
 ,
 …
 ,
 
 t
 
 n
 −
 1
 
 
 
 
 {\displaystyle t_{1},\ldots ,t_{n-1}}
 
. 
Dependence logic is a logic of imperfect information, like <a href="/facts/Branching_quantifier/MUVt3u7k"> branching quantifier logic</a> or <a href="/facts/Independence-friendly_logic/eknYWBtU">independence-friendly logic</a> (IF logic): in other words, its <a href="/facts/Game_semantics/FJSuV3un">game-theoretic semantics</a> can be obtained from that of first-order logic by restricting the availability of information to the players, thus allowing for non-linearly ordered patterns of dependence and independence between variables. However, dependence logic differs from these logics in that it separates the notions of dependence and independence from the notion of <a href="/facts/Quantification_(logic)/bgmvwxoo">quantification</a>.

Dependence logic open-in-new

Dependence logic