# Logic programs with stable model semantics as a constraint programming paradigm

@article{Niemel1999LogicPW, title={Logic programs with stable model semantics as a constraint programming paradigm}, author={Ilkka Niemel{\"a}}, journal={Annals of Mathematics and Artificial Intelligence}, year={1999}, volume={25}, pages={241-273} }

Logic programming with the stable model semantics is put forward as a novel constraint programming paradigm. This paradigm is interesting because it bring advantages of logic programming based knowledge representation techniques to constraint programming and because implementation methods for the stable model semantics for ground (variable‐free) programs have advanced significantly in recent years. For a program with variables these methods need a grounding procedure for generating a variable…

## 848 Citations

### Two-Literal Logic Programs and Satisfiability Representation of Stable Models: A Comparison

- Computer ScienceCanadian Conference on AI
- 2002

It is shown that a 2-literal program can be translated to a SAT instance in polynomial time without using extra variables and reported and compared experimental results on solving a number of benchmarks by a stable model generator and by a SAT solver.

### Logic programming and cardinality constraints : theory and practice

- Computer Science
- 2009

This work defines an ASP language, cardinality constraint programs (CCP), a declarative formal semantics that is based on the stable model semantics of normal logic programs, and identifies a syntactic subclass of CCPs, namely omega-restricted programs, that are decidable even when function symbols are allowed.

### Predicate-calculus-based logics for modeling and solving search problems

- Computer ScienceTOCL
- 2006

This article proposes two logics based on predicate calculus as formalisms for encoding search problems and shows that the expressive power of these logics is given by the class NPMV.

### A New Semantics for Logic Programs Capturing and Extending the Stable Model Semantics

- Computer Science, Philosophy2012 IEEE 24th International Conference on Tools with Artificial Intelligence
- 2012

This paper introduces a new semantics for logic programs that is different from the known fixed point semantics, and gives a full characterization of the stable models of a logic program by means of the extensions of its CNF encoding verifying the simple discrimination condition.

### Template programs for Disjunctive Logic Programming: An operational semantics

- Computer ScienceAI Commun.
- 2006

This work extends Disjunctive Logic Programming, under stable model semantics, with the notion of "template" predicates, allowing to define reusable modules, to define new constructs and aggregates without any syntactic limitation.

### Characterizations of stable model semantics for logic programs with arbitrary constraint atoms

- Computer ScienceTheory and Practice of Logic Programming
- 2009

A succinct abstract representation of constraint atoms in which a constraint atom is represented compactly is introduced and provides a means to characterize dependencies of atoms in a program with constraint atoms, so that some standard characterizations and properties relying on these dependencies in the past for logic programs with ordinary atoms can be extended.

### Weight constraint programs with evaluable functions

- Computer ScienceAnnals of Mathematics and Artificial Intelligence
- 2011

This paper proposes an answer set semantics to these extended weight constraint programs and defines loop completion to characterize the semantics and implements a prototype system that competes well with the state-of-the-art ASP solvers.

### Answer Set Programming: A Declarative Approach to Solving Search Problems

- Computer ScienceJELIA
- 2006

The term answer set programming (ASP) was coined by Vladimir Lifschitz to name a new declarative programming paradigm that has its roots in stable model (answer set) semantics of logic programs [16]…

### A New Method for Computing Stable Models in Logic Programming

- Computer Science2018 IEEE 30th International Conference on Tools with Artificial Intelligence (ICTAI)
- 2018

A new method for searching stable models of logical programs based on a relatively new semantics that has not been exploited yet that has the advantage to use a Horn clause representation having the same size as the input logic program has constant spatial complexity.

## References

SHOWING 1-10 OF 38 REFERENCES

### Stable models and an alternative logic programming paradigm

- Computer ScienceThe Logic Programming Paradigm
- 1999

It is demonstrated that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics.

### Towards Constraint Satisfaction through Logic Programs and the Stable Model Semantics

- Computer Science
- 1997

In this work the paradigm for constraint satisfaction in logic programs with the stable model semantics is realized by developing an eecient procedure for computing the stable models of ground logic programs by introducing a strong pruning technique based on two deductive closures.

### Constraint logic programming

- Computer SciencePOPL '87
- 1987

A class of programming languages, the CLP languages, are defined, all of which share the same essential semantic properties, and are highly declarative and are soundly based within a unified framework of formal semantics.

### Efficient Implementation of the Well-founded and Stable Model Semantics

- Computer ScienceJICSLP
- 1996

The implementation has been tested extensively and compared with a state of the art implementation of the stable model semantics, the SLG system, and clearly outperforms SLG in tests involving ground programs.

### The well-founded semantics for general logic programs

- Computer ScienceJACM
- 1991

It is shown that the class of programs possessing a total well-founded model properly includes previously studied classes of "stratified" and "locally stratified" programs, and is compared with other proposals in the literature.

### Smodels - An Implementation of the Stable Model and Well-Founded Semantics for Normal LP

- Computer ScienceLPNMR
- 1997

The Smodels system is a C++ implementation of the well-founded and stable model semantics for range-restricted function-free normal programs and in tests involving ground programs it clearly outperforms SLG.

### Computation of Stable Models and Its Integration with Logical Query Processing

- Computer ScienceIEEE Trans. Knowl. Data Eng.
- 1996

An efficient implementation of goal-oriented effective query evaluation under the well-founded semantics that produces a residual program for subgoals that are relevant to a query, which contains facts for true instances and clauses with body literals for undefined instances.

### Eecient Implementation of the Well- Founded and Stable Model Seman- Tics

- Computer Science
- 1996

The implementation of the stable model semantics for ground programs is based on bottom-up back-tracking search and employs a powerful pruning method based on an approximation technique for stable models which is closely related to the well-founded semantics.

### Using Logic Programs with Stable Model Semantics to Solve Deadlock and Reachability Problems for 1-Safe Petri Nets

- Computer ScienceFundam. Informaticae
- 1999

In this work, it is shown that instead of using mixed integer programming, a constraint-based logic programming framework can be employed, and a linear-size translation from deadlock detection in prefixes into the problem of finding a stable model of a logic program is presented.

### Iterative Belief Revision in Extended Logic Programming

- Computer Science, PhilosophyTheor. Comput. Sci.
- 1996