| Negation in Logic and Deductive Databases (1999) | |||||||||||||||
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| This thesis studies negation in logic and deductive databases. Among other things, two kinds of negation are discussed in detail: strong negation and nonmonotonic negation. In the logic part, we have constructed a first-order logic CF 0 of strong negation with bounded quantifiers. The logic is based on constructive logics, in particular, Thomason's logic CF. However, unlike constructive logic, quantifiers in our system as in Thomason's are static rather than dynamic. For the logic CF 0 , the usual Kripke formal semantics is defined but based on situations instead of conventional possible worlds. A sound and complete axiomatic system of CF 0 is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. CF 0 is proposed as the underlying logic for situation theory. Thus the connection between CF 0 and infon logic is briefly discussed. In the database part, based on the study of some main existing semant... | |||||||||||||||
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