# Hybrid Probabilistic Logic Programs as Residuated Logic Programs

@article{Damsio2002HybridPL, title={Hybrid Probabilistic Logic Programs as Residuated Logic Programs}, author={Carlos Viegas Dam{\'a}sio and Lu{\'i}s Moniz Pereira}, journal={Studia Logica}, year={2002}, volume={72}, pages={113-138} }

In this paper we show the embedding of Hybrid Probabilistic Logic Programs into the rather general framework of Residuated Logic Programs, where the main results of (definite) logic programming are validly extrapolated, namely the extension of the immediate consequences operator of van Emden and Kowalski. The importance of this result is that for the first time a framework encompassing several quite distinct logic programming semantics is described, namely Generalized Annotated Logic Programs…

## 43 Citations

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- 2006

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- 2005

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- 2004

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- 2004

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## References

SHOWING 1-10 OF 29 REFERENCES

### Monotonic and Residuated Logic Programs

- Computer ScienceECSQARU
- 2001

This paper defines the rather general framework of Monotonic Logic Programs, where the main results of (definite) logic programming are validly extrapolated and the embedding of possibilistic logic programming is provided.

### Hybrid Probabilistic Programs: Algorithms and Complexity

- Computer ScienceUAI
- 1999

This paper classify HPPs into three classes called HPP1, HPP2 and HPPr, r > 3, and provides algorithms and complexity results for the problems of entailment, consistency and consistency.

### Theory of Generalized Annotated Logic Programming and its Applications

- Computer ScienceJ. Log. Program.
- 1992

### Multi-adjoint Logic Programming with Continuous Semantics

- Computer Science, MathematicsLPNMR
- 2001

The continuity of the immediate consequences operators is proved and the assumptions required to get continuity are further analysed.

### Towards Possibilistic Logic Programming

- PhilosophyICLP
- 1991

This paper proposes extensions of the possibilistic logic calculus where weighted formulas can be attached to a set of agents or which can be embedded inside another weighted formula, for the expression of mutual beliefs.

### Foundations of Logic Programming

- Computer ScienceSymbolic Computation
- 1987

This is the second edition of an account of the mathematical foundations of logic programming. Its purpose is to collect, in a unified and comprehensive manner, the basic theoretical results of the…

### On Fuzzy Logic III. Semantical completeness of some many-valued propositional calculi

- Computer ScienceMath. Log. Q.
- 1979

The case when the underlying lattice of B is a chain is investigated, viz. an abstract set of formulas, which poses the problem of axiomatizability of the 8-valued propositional calculus over P.

### Many-Valued Logics

- Philosophy, Computer Science
- 1992

This chapter discusses the method of Finitely Generated Trees in n-valued Logical Calculi of Propositional Calculus for Many-Valued Logics and some examples of fuzzy propositional calculus.