## Forward and Backward Chaining in Linear Logic (0)

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Citations: | 5 - 2 self |

### BibTeX

@MISC{Harland_forwardand,

author = {James Harland and David Pym and Michael Winikoff},

title = {Forward and Backward Chaining in Linear Logic},

year = {}

}

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### Abstract

. Logic programming languages based on linear logic are of both theoretical and practical interest, particulaly because such languages can be seen as providing a logical basis for programs which execute within a dynamic environment. Most linear logic programming languages are implemented using standard resolution or backward chaining techniques. However, there are many applications in which the combination of such techniques with forward chaining ones are desirable. We develop a proof-theoretic foundation for a system which combines both forms of reasoning in linear logic. 1 Introduction Backward chaining is a standard technique in automated deduction, particularly in logic programming systems, often taking the form of a version of Robinson's resolution rule [18]. The fundamental question is to determine whether or not a given formula follows from a given set of formul, and there are various techniques which can be used to guide the search for a proof. An instance of this approach is...

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710 | The semantics of predicate logic as a programming language
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(Show Context)
Citation Context ...e program is then given by the least fixed pointsof this operator. It is interesting to note that this forward chaining system is traditionally used to provide a fixpoint semantics for SLD-resolution =-=[3]-=-, a backward-chaining system. It should be noted that a key property of the modus ponens rule in intuitionistic logic is that it preserves equivalence: � � � � � � � � �. This strong property greatly ... |

692 |
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(Show Context)
Citation Context ...good basis for backward chaining, other systems for inference in intuitionistic logic provide forward chaining capabilities. Hilbert-type systems are the oldest and perhaps best-known of such systems =-=[10]-=-. Such systems allow different logics to be specified by different sets of axioms whilst maintaining modus ponens as the sole means of inference. Another technical expression of forward chaining in in... |

567 | Untersuchungen über das logische Schließen - Gentzen - 1935 |

375 | Uniform proofs as a foundation for logic programming
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(Show Context)
Citation Context ... a given set of formulæ, and there are various techniques which can be used to guide the search for a proof. An instance of this approach is the analysis of logic programming in intuitionisitic logic =-=[13]-=-. The standard such analysis is that of Miller et al. [13], based around the notion of uniform proofs. These are defined in terms of the sequent calculus, which is well-known to be suited for analyses... |

332 | Logic programming with focusing proofs in linear logic
- Andreoli
- 1992
(Show Context)
Citation Context ...ackward-chaining. With more recent interest in logic programming languages based on linear logic [6], the natural extension of these backward chaining techniques to linear logic has been much studied =-=[1, 2, 4, 9, 17]-=-; generally, it follows a similar pattern to intuitionistic logic. The details of the analysis are more intricate than in intuitionistic logic, and there are a number of points of diversion amongst th... |

302 | Logic programming in a fragment of intuitionistic linear logic
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- 1994
(Show Context)
Citation Context ...ackward-chaining. With more recent interest in logic programming languages based on linear logic [6], the natural extension of these backward chaining techniques to linear logic has been much studied =-=[1, 2, 4, 9, 17]-=-; generally, it follows a similar pattern to intuitionistic logic. The details of the analysis are more intricate than in intuitionistic logic, and there are a number of points of diversion amongst th... |

207 | Linear Objects: logical processes with built-in inheritance
- Andreoli, Pareschi
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(Show Context)
Citation Context ...ackward-chaining. With more recent interest in logic programming languages based on linear logic [6], the natural extension of these backward chaining techniques to linear logic has been much studied =-=[1, 2, 4, 9, 17]-=-; generally, it follows a similar pattern to intuitionistic logic. The details of the analysis are more intricate than in intuitionistic logic, and there are a number of points of diversion amongst th... |

69 | A Uniform Proof-Theoretic Investigation of Linear Logic Programming
- Harland, Pym
- 1994
(Show Context)
Citation Context |

61 | Higher-Order Horn Clauses - Nadathur, Miller |

54 | The Aditi deductive database system
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(Show Context)
Citation Context ...� � � � �. This strong property greatly simplifies the analysis of this rule of inference. A combination of both backward and forward chaining may be found in deductive database systems such as Aditi =-=[20]-=-. In such systems, which are based on variants of Prolog, forward chaining is generally used in order to compute all answers to a query using efficient join algorithms and other techniques from relati... |

40 | Programming in lygon: An overview - Harland, Pym, et al. - 1996 |

29 | On bunched predicate logic - Pym - 1999 |

21 | A Logical Analysis of Modules - Miller - 1989 |

14 | A proof-theoretic analysis of goal-directed provability
- Harland
- 1994
(Show Context)
Citation Context ...etermine a program È such that È� Î È and È � �. The key technical question is then to find the appropriate rules for �. This procedure is reminiscent of interpolation results, in particular those of =-=[7]-=-, in which it is shown that for any uniform proof of È��, there is a program È such that È� Î È and È � �, where the latter proof is considerably simpler than the original one. In particular, È can be... |

11 | The Art of Prolog, 2nd ed - Sterling - 1994 |

9 | Structural Operational Semantics (lecture notes - Plotkin - 1981 |

6 | On proof normalisation - Galmiche, Perrier - 1994 |

4 |
On Proof Normalization
- Galmiche, Perrier
- 1994
(Show Context)
Citation Context |