On Quantifying Literals in Boolean Logic and Its Applications to Explainable AI
This work provides incremental theoretical foundations for explainable AI by refining quantified Boolean logic.
The paper tackled the problem of extending quantified Boolean logic by introducing universal literal quantification and a novel semantics, and identified efficient classes of Boolean formulas and circuits for quantification, with literal quantification serving as a primitive refinement.
Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the decades. The existential quantification of literals (variable states) and its applications have also been studied in the literature. In this paper, we complement this by studying universal literal quantification and its applications, particularly to explainable AI. We also provide a novel semantics for quantification, discuss the interplay between variable/literal and existential/universal quantification. We further identify some classes of Boolean formulas and circuits on which quantification can be done efficiently. Literal quantification is more fine-grained than variable quantification as the latter can be defined in terms of the former. This leads to a refinement of quantified Boolean logic with literal quantification as its primitive.