In recent times there was an expanding use of logical equipment and important new advancements were spawned in different components of laptop technological know-how, starting from synthetic intelligence and software program engineering to agent-based structures and the semantic net. within the research and alertness of logical tools there's a stress among: * the necessity for a representational language powerful sufficient to precise area wisdom of a specific program, and the necessity for a logical formalism common sufficient to unify numerous reasoning amenities correct to the applying, at the one hand, and * the necessity to allow computationally possible reasoning amenities, nonetheless. Second-order logics are very expressive and make allowance us to symbolize area wisdom conveniently, yet there's a excessive expense to pay for the expressiveness. so much second-order logics are incomplete and hugely undecidable. it's the quantifiers which bind relation symbols that make second-order logics computationally unfriendly. it's as a result fascinating to put off those second-order quantifiers, while this is often mathematically attainable; and infrequently it really is. If second-order quantifiers are eliminable we wish to recognize less than which stipulations, we wish to comprehend the foundations and we wish to advance equipment for second-order quantifier removal. This publication offers the 1st finished, systematic and uniform account of the cutting-edge of second-order quantifier removal in classical and non-classical logics. It covers the principles, it discusses intimately current second-order quantifier removal tools, and it offers quite a few examples of purposes and non-standard makes use of in numerous components. those contain: * classical and non-classical logics, * correspondence and duality conception, * wisdom illustration and outline logics, * common-sense reasoning and approximate reasoning, * relational and deductive databases, and * complexity conception. The booklet is meant for somebody drawn to the idea and alertness of logics in laptop technological know-how and synthetic intelligence.
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