Negation in logic and deductive databases

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 rst-order logic CF0 of strong negation with bounded quanti ers. The logic is based on constructive logics, in particular, Thomason's logic CF. However, unlike constructive logic, quanti ers in our system as in Thomason's are static rather than dynamic. For the logicCF0, the usual Kripke formal semantics is de ned but based on situations instead of conventional possible worlds. A sound and complete axiomatic system of CF0 is established based on the axiomatic systems of constructive logics with strong negation and Thomason's completeness proof techniques. CF0 is proposed as the underlying logic for situation theory. Thus the connection between CF0 and infon logic is brie y discussed. In the database part, based on the study of some main existing semantic theories for logic programs with nonmonotonic negation, we have de ned a novel semantics of logic programs called quasi-stable semantics. An important observation is that a nonmonotonic negation such as is required for logic programs should be computed by a nonmonotonic, revision process. Only a process that allows one to withdraw by revising provisionally held negative information can hope to be adequate to model a non-monotonic negation. In light of this, we propose a model of negation that owes much to the stable semantics but allows, through a mechanism of consistencyrecovery, for just this withdrawal of previously assumed negative information. It has been proved that our new semantics maintains the desired features of both the well-founded semantics and the stable model semantics while overcoming their shortcomings. In addition, the quasi-stable semantics has been generalised to logic programs with both strong negation and nonmonotonic negation, giving rise to the quasi-answer set semantics. i Acknowledgments I should like to thank my supervisor, Peter Mott for his direction, supervision, criticism and encouragement throughout the whole process of my study. Without his valued help, I would have not studied at Leeds, let alone nish the thesis. Thanks also to my advisor, Professor Tony Cohn for his encouragement and instructive advice. There have been many other people giving me various kinds of timely help in one way or another in my life. I should like to thank them too. Finally I wish thank and acknowledge funding from an Overseas Research Students (ORS) Award (#ORS-95023007), a Tetley & Lupton Scholarship, a Leeds University Foundation Scholarship, and a departmental grant. ii