1. Apt, K. R., Blair, H. A., & Walker, A. (1987). Towards a theory of declarative knowledge. In J. Minker (Ed.), Foundations of deductive databases and logic programming [Min87] (pp. 89–148). Los Altos: Morgan Kaufmann. This influential paper identifies the notion of stratification as an effective approach to embedding negation in logic programming, both computationally and cognitively. It develops its general theory and fixpoint semantics, and specializes SLD-resolution to it.
2. Apt, K. R., & van Emden, M. H. (1982). Contributions to the theory of logic programming. Journal of the ACM, 29(3), 841–862. This paper develops the characterization of the model semantics of logic programs consisting of Horn clauses (i.e., pure Prolog) as the least fixpoint of a continuous operator. It also observes that some forms of finite-failure (but not all) correspond to its greatest fixpoint.
3. Burnett, M., Atwood, J., Djang, R. W., Reichwein, J., Gottfried, H., & Yang, S. (2001). Forms/3: A first-order visual language to explore the boundaries of the spreadsheet paradigm. Journal of functional programming, 11(2), 155–206. This paper describes Forms/3, a conservative extension of the traditional spreadsheet with procedural abstractions such as recursion, data abstractions such as graphical values, and graphic time-based output. As it does so, it strives to maintain the usability characteristics that have made the spreadsheet popular with end-users.
4. Bonner, A. J. (1991). Hypothetical reasoning in deductive databases. PhD thesis, Rutgers University. This dissertation explores a principled way to extend deductive databases with hypothetical reasoning. It does so by allowing the body of a clause to mention “embedded clauses”. This adds significantly to the expressive power of the language, a fact that is thoroughly analyzed in the context of complexity theory. The model theory of this extension is investigated in [BM90] while the key insight was already present in [BMV89].
5. Bonner, A. J. (1994). Hypothetical reasoning with intuitionistic logic. In R. Demolombe & T. Imielinski (Eds.), Non-standard queries and answers (Studies in logic and computation, chapter 8, pp. 187–219). Oxford: Oxford University Press. This paper develops the author’s dissertation [Bon91] by focusing on forms of hypothetical reasoning that only add temporary facts in a deductive database and create new constants dynamically. It explores its proof-theory, its model theory, and the computational complexity of the extended language.