# Clausal Logic and Logic Programming in Algebraic Domains

@article{Rounds2001ClausalLA, title={Clausal Logic and Logic Programming in Algebraic Domains}, author={William C. Rounds and Guo-Qiang Zhang}, journal={Inf. Comput.}, year={2001}, volume={171}, pages={183-200} }

We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for defaultâ€¦Â

## 46 Citations

Domain-theoretic Semantics for Disjunctive Logic Programs

- Computer Science
- 2007

This paper proposes a resolution-style semantics for GL programs which bears the same kind of relation to extended disjunctive logic programs as SLD resolution bears to SLDNF resolution in the non-disjunctive case, and provides an operational semantics based on nondeterministic state transitions.

Formal Concept Analysis and Resolution in Algebraic Domains

- Computer Science, PhilosophyArXiv
- 2003

It is shown how to identify the notion of formal concept in the domain theoretic setting and it is shown that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis.

Resolution and Logic Programming in Algebraic Domains: Negation and Defaults

- Computer Science
- 2002

This work extends the framework to include reasoning with negative information, i.e. the implicit or explicit absence of bits of information, to lead to a form of default reasoning which is strongly related to logic programming with answer sets or stable models.

Formal Concept Analysis and Resolution on Algebraic Domains - Preliminary Report

- Computer Science, Philosophy
- 2003

It is shown how to identify the notion of formal concept in the domain theoretic setting and it is shown that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis.

Generalized metrics and uniquely determined logic programs

- Computer ScienceTheor. Comput. Sci.
- 2003

Semantics of logic programs with aggregates

- Computer Science
- 2004

A framework admits arbitrary aggregate relations in the bodies of rules which follows a denotational approach in which a semantics is defined as a (set of) fixpoint(s) of an operator associated with a program.

Default Reasoning over Domains and Concept Hierarchies

- Computer ScienceKI
- 2004

A default reasoning paradigm for conceptual knowledge which is in accordance with mainstream developments in nonmonotonic reasoning is obtained and it is shown that the hierarchically structured knowledge on which programming in this paradigm can be done, arises very naturally from formal concept analysis.

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