Book Chapter10.1007/3-540-63255-7_23
Programs with Universally Quantified Embedded Implications
Vyacheslav Petukhin
- 28 Jul 1997
- pp 310-324
5
TL;DR: For this class of logic programs with the new nonmonotonic operator, the standard model semantics for stratified programs, the stable model semantics, the well-founded semantics are defined and main properties of above semantics for normal logic programs hold as well for programs with implications.
read more
Abstract: We suggest to consider the class of logic programs with the new nonmonotonic operator which we call universally quantified embedded implication. By such implications we mean formulas of the form ∀x1⋯∀xl(P1 & ⋯ & Pm → Q1 & ⋯ & Qn). The main subject of the paper is lifting notions and theorems, related to normal logic programs, to programs with universally quantified embedded implications. For this class of programs we define the standard model semantics for stratified programs, the stable model semantics, the well-founded semantics. We show that main properties of above semantics for normal logic programs hold as well for programs with implications. Besides, we investigate the possibilities of reducing programs with implications to normal logic programs. Finally we define a calculus corresponding to SLDNF-calculus [9] and prove theorem of its soundness.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
From Clarity to Efficiency for Distributed Algorithms
TL;DR: A very high-level language for clear description of distributed algorithms and optimizations necessary for generating efficient implementations of logic quantifications and new optimizations are presented that automatically transform complex synchronization conditions into incremental updates of necessary auxiliary values as messages are sent and received.
32
From Clarity to Efficiency for Distributed Algorithms
TL;DR: In this paper, the authors describe a high-level language for describing distributed algorithms and optimizations necessary for generating efficient implementations, and present new optimizations that automatically transform complex synchronization conditions into incremental updates of necessary auxiliary values as messages are sent and received.
24
Logic programming and negation : a survey
Krzysztof R. Apt,Roland N. Bol +1 more
- 01 Jan 1994
TL;DR: A survey of negation in logic programs can be found in this paper, where the authors concentrate on the proof-theoretic and model theoretic issues and the relationships between them.
10
Integrating the Completion and the Well Founded Semantics
Mauricio Osorio,Bharat Jayaraman +1 more
- 05 Oct 1998
TL;DR: A new semantics is introduced, called CWFS, which is as powerful in inferring positive literals and as powerful as WFS in inferrings negative literals, and helps to understand the relationship among COMP, WFS, and STABLE.
3
From clarity to efficiency for distributed algorithms
Yanhong A. Liu,Scott D. Stoller,Bo Lin,Michael Gorbovitski +3 more
- 19 Oct 2012
TL;DR: A very high-level language for clear description of distributed algorithms and optimizations necessary for generating efficient implementations of logic quantifications and new optimizations are presented that automatically transform complex synchronization conditions into incremental updates of necessary auxiliary values as messages are sent and received.
References
Towards a theory of declarative knowledge
Krzysztof R. Apt,Howard A. Blair,Adrian Walker +2 more
- 01 Aug 1988
TL;DR: This work proves the consistency of Clark's completion for stratified programs and attempts to clarify the sources of some previously reported difficulties with negation in logic programming.
•Book
The Gödel Programming Language
Patricia M. Hill,John W. Lloyd +1 more
- 05 Apr 1994
TL;DR: Part 1 Overview of Goedel: introduction types formulas equality and numbers modules various data types control input/output meta-programming example programs and description of polymorphic many-sorted logic.
Logic Programming and Negation: A Survey.
Krzysztof R. Apt,Roland N. Bol +1 more
TL;DR: A survey of negation in logic programs can be found in this article, where the authors concentrate on the proof-theoretic and model theoretic issues and the relationships between them.