Modal logic, an extension of classical logic, investigates the modes of truth such as necessity and possibility. Its development has been closely intertwined with advances in proof theory, a field ...

What seem to be Kurt Gödel's first notes on logic, an exercise notebook of 84 pages, contains formal proofs in higher-order arithmetic and set theory. The choice of these topics is clearly suggested ...

We present a dynamic approach to Peirce's original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic ...

A mathematical problem more than 300 years old gets a formal proof with the help of computer formal verification. A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler ...

Quantified Boolean Formulas (QBF) extend classical Boolean logic by incorporating quantifiers over Boolean variables, thereby enabling the expression of problems in the PSPACE complexity class. The ...

Computer-assisted of mathematical proofs are not new. For example, computers were used to confirm the so-called 'four color theorem.' In a short release, 'Proof by computer,' the American Mathematical ...

A team led by mathematician Thomas Hales has delivered a formal proof of the Kepler Conjecture, which is the definitive resolution of a problem that had gone unsolved for more than 300 years. The ...