SECOND ORDER QUANTIFIER ELIMINATION

* the need for a representational language strong enough to express domain knowledge of a particular application, and the need for a logical formalism general enough to unify several reasoning facilities relevant to the application, on the one hand, and * the need to enable computationally feasible reasoning facilities, on the other hand. Second-order logics are very expressive and allow us to represent domain knowledge with ease, but there is a high price to pay for the expressiveness. Most second-order logics are incomplete and highly undecidable. It is the quantifiers which bind relation symbols that make second-order logics computationally unfriendly. It is therefore desirable to eliminate these second-order quantifiers, when this is mathematically possible, and often it is. If second-order quantifiers are eliminable we want to know under which conditions, we want to understand the principles and we want to develop methods for second-order quantifier elimination. This book provides the first comprehensive, systematic and uniform account of the state-of-the-art of second-order quantifier elimination in classical and non-classical logics. It covers the foundations, it discusses in detail existing second-order quantifier elimination methods, and it presents numerous examples of applications and non-standard uses in different areas. These include