An abstract logic 〈A, C〉 consists of a finitary algebraA and a closure systemC onA. C induces two other closure systems onA, CP andCI, by projective and inductive generation respectively. The various relations amongC, CP andCI are determined. The special case thatC is the standard equational closure system on monadic terms is studied in detail. The behavior of Boolean logics with respect to projective and inductive generation is determined.
KeywordsMathematical Logic Closure System Boolean Logic Inductive Generation Computational Linguistic
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