- Author:
- Arcot Kuppuswamy Rajasekar,
- Director:
- Jack Minker
The field of logic programming emerged in the early seventies and has since been an area of active research. But, most of the work done in this area has been confined to Horn (definite) programs and its generalizations, so much so that the term 'logic program' in the literature is used synonymously with Horn programs. In this thesis, we provide a departure from the framework of definite programs by extending the theoretical results of Horn programs to disjunctive (indefinite) programs.
The heart of the thesis is the definition of a fixpoint operator which provides a consistent semantics for disjunctive programs. The power of this operator is demonstrated by its ability to characterize existing theories of negation and by its motivation of a new theory of negation for disjunctive programs. The versatility of the operator is shown by its use in the development of two theories of stratification for general disjunctive programs. The operator is also the motivation behind the SLO-resolution proof procedure for disjunctive programs and is instrumental in proving its completeness. The theory underlying the fixpoint operator provides the framework for a model theoretic semantics for disjunctive programs.
Two declarative semantics, based on fixpoint theory and model theory, and two procedural semantics, SLI-resolution and SLO-resolution, are presented for answering positive queries in disjunctive programs. The semantics are shown to reduce to corresponding Horn semantics when applied to Horn programs.
Two theories of negation for disjunctive programs are also developed. First, a fixpoint characterization for the GCWA is provided and a rule of negation called SN-rule is described to provide a proof procedure for answering negative queries in disjunctive programs. Motivated by the fixpoint definition of the GCWA, a weaker theory of negation called the WGCWA is defined and a procedural rule called the NAFFD-rule is developed. The theories and rules of negation are shown to extend the negation semantics of Horn programs.
The declarative semantics of disjunctive programs is extended to general disjunctive programs. Non-monotonic fixpoint semantics and iterated model theoretic semantics are presented for stratified disjunctive programs. Theories of negation corresponding to these semantics are also developed.
Cited By
- (2019). Guide for authors, Discrete Applied Mathematics, 150:1-3, (I-IV), Online publication date: 1-Sep-2005.
- (2005). Guide for authors, Discrete Applied Mathematics, 147:2-3, (I-IV), Online publication date: 15-Apr-2005.
- (2019). Guide for authors, Discrete Applied Mathematics, 148:3, (I-IV), Online publication date: 15-Jun-2005.
- (2005). Guide for authors, Discrete Applied Mathematics, 148:1, (I-IV), Online publication date: 30-Apr-2005.
- (2019). Guide for authors, Discrete Applied Mathematics, 146:2, (I-IV), Online publication date: 1-Mar-2005.
- (2005). Guide for authors, Discrete Applied Mathematics, 146:1, (I-IV), Online publication date: 15-Feb-2005.
- (2019). Guide for authors, Discrete Applied Mathematics, 147:1, (I-IV), Online publication date: 1-Apr-2005.
- (2005). Guide for authors, Discrete Applied Mathematics, 145:2, (I-IV), Online publication date: 15-Jan-2005.
- (2019). Guide for authors, Discrete Applied Mathematics, 149:1-3, (I-IV), Online publication date: 1-Aug-2005.
- (2019). Guide for authors, Discrete Applied Mathematics, 146:3, (I-IV), Online publication date: 1-Mar-2005.
- (2005). Guide for authors, Discrete Applied Mathematics, 148:2, (I-IV), Online publication date: 15-May-2005.
- (2019). Guide for authors, Discrete Applied Mathematics, 151:1-3, (I-IV), Online publication date: 1-Oct-2005.
- Johnson C (2019). Top-Down Query Processing in First-Order Deductive Databases under the DWFS, Journal of Automated Reasoning, 32:2, (167-184), Online publication date: 1-Feb-2004.
- (2004). Guide for authors, Discrete Applied Mathematics, 144:1-2, (I-IV), Online publication date: 1-Nov-2004.
- (2019). Guide for authors, Discrete Applied Mathematics, 138:1-2, (I-IV), Online publication date: 1-Mar-2004.
- (2004). Guide for authors, Discrete Applied Mathematics, 138:3, (I-IV), Online publication date: 15-Apr-2004.
- (2018). Guide for authors, Discrete Optimization, 1:2, (233-235), Online publication date: 1-Nov-2004.
- (2019). Guide for authors, Discrete Applied Mathematics, 131:1, (I-IV), Online publication date: 1-Sep-2003.
- Dix J, Furbach U and Niemelä I Nonmonotonic reasoning Handbook of automated reasoning, (1241-1354)
- Bry F and Yahya A (2019). Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation, Journal of Automated Reasoning, 25:1, (35-82), Online publication date: 1-Jul-2000.
- Suchenek M (1997). Evaluation of Queries under Closed-World Assumption, Journal of Automated Reasoning, 18:3, (357-398), Online publication date: 1-Jun-1997.
- Johnson C (1997). Deduction Trees and the View Update Problem in Indefinite Deductive Databases, Journal of Automated Reasoning, 19:1, (31-85), Online publication date: 1-Aug-1997.
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