True Quantified Boolean Formula

A True Quantified Boolean Formula (TQBF) is central in theoretical computer science and AI, representing the decision problem for a logical expression built from Boolean variables subject to quantifiers, such as "for all" (∀) and "there exists" (∃). This becomes significant in AI, particularly in automated theorem proving and formal verification, as TQBF is PSPACE-complete, thus embodying problems that can be solved using polynomial space. In AI, TQBF problems are crucial in modeling decision-making scenarios that require verifying multiple layers of conditions, conducive to developing and testing algorithms in game theory and complex decision systems.

Coined during the mid-20th century, the term "quantified Boolean formula" gained traction in the 1970s with the formalization of complexity classes, particularly when computational theorists recognized its importance in delineating PSPACE-complete problems.

Stephen Cook, noted for his foundational work on computational complexity, and his contemporaries such as Richard Karp, were instrumental in framing the discussion of NP-completeness and PSPACE-completeness, lending significant theoretical underpinning to problems like TQBF, thereby influencing various AI domains.