## The meaning of negative premises in transition system specifications II (2004)

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Venue: | THE JOURNAL OF LOGIC AND ALGEBRAIC PROGRAMMING |

Citations: | 38 - 5 self |

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@MISC{Glabbeek04themeaning,

author = {R.J. van Glabbeek},

title = {The meaning of negative premises in transition system specifications II},

year = {2004}

}

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### Citations

1492 | The stable model semantics for logic programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...urely supported. My concept of well-supportedness can easily be seen to coincide with the one of Fages [5]. It is closely related to the earlier concept of stability, developed by Gelfond & Lifschitz =-=[7]-=- in logic programming, and adapted for TSSs by Bol & Groote [3]. Definition 7 (Stable transition relation). A transition relation T is stable for a TSS P if: T j= t a \Gamma! t 0 , there is a closed t... |

1286 | A structural approach to operational semantics
- Plotkin
- 1981
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Citation Context ...gative premises t 6 a \Gamma! were added in Groote [8]. The notion generalises the GSOS rule systems of [2] and constitutes the first formalisation of Plotkin's Structural Operational Semantics (SOS) =-=[10]-=- that is sufficiently general to cover most, if not all, of its applications. The premises t 6 a \Gamma! t 0 are added here, mainly for technical reasons. The following definition tells when a transit... |

960 |
Negation as failure
- Clark
- 1978
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Citation Context ...y impossible to infer t a \Gamma! t 0 , or t 6 a \Gamma! whenever for any term t 0 it is manifestly impossible to infer t a \Gamma! t 0 . This practice is sometimes referred to as negation as failure =-=[4]-=-. Definition 8 allows such an inference only if the impossibility to derive t a \Gamma! t 0 can be detected by examining all possible proofs that consist of one step only. This corresponds with the no... |

844 | The well-founded semantics for general logic programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ...n complete with support. In Bol & Groote [3] a method called reduction for associating a transition relation with a TSS was proposed, inspired by the well-founded models of Van Gelder, Ross & Schlipf =-=[6]-=- in logic programming. In the full version of this paper I show that this solution coincides with Solution 7. Solution 7 can therefore be regarded as a proof theoretical characterisation of the ideas ... |

254 |
On the declarative semantics of deductive databases and logic programs
- Przymusinski
- 1988
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Citation Context ...ratified \Gamma \Gamma + \Gamma + + \Gamma \Gamma 10 strictly stratified \Gamma \Gamma + \Gamma \Gamma \Gamma \Gamma \Gamma Evaluation of the solutions Solution 9 (stratified) stems from Przymusinski =-=[11]-=- and is the perhaps the best known solution in logic programming. A variant that only allows TSSs with a unique supported model is Solution 10 (strictly stratified), proposed by Groote [8]. Solution 1... |

242 | Logic programming and negation: a survey
- Apt, Bol
- 1994
(Show Context)
Citation Context ...ogramming jargon. However, I do not touch issues that are relevant in logic programming, but not manifestly so for transition system specifications. For these, and many more references, see Apt & Bol =-=[1]-=-. 2 Model theoretic solutions Solution 1 (Positive). A first and rather conservative answer to (1) and (2) is to take the class of positive TSSs as the meaningful ones, and associate with each positiv... |

221 | Unfounded Sets and Well-founded Semantics for General Logic - Gelder, Ross, et al. - 1989 |

194 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...available as Report STAN-CS-TN-95-16, 1995, and by ftp from boole.stanford.edu. The first systematic study of transition system specifications with negative premises appears in Bloom, Istrail & Meyer =-=[2]-=-. The concept of a (positive) TSS presented above was introduced in Groote & Vaandrager [9]; the negative premises t 6 a \Gamma! were added in Groote [8]. The notion generalises the GSOS rule systems ... |

189 | Structured operational semantics and bisimulation as a congruence - Groote, Vaandrager - 1992 |

135 | The well-founded semantics coincides with the threevalued stable semantics
- Przymusinski
- 1990
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Citation Context ...cater to this taste will be proposed in Section 3. 2.2 3-Valued solutions 3-valued interpretations of logical programs are considered, among others, in Van Gelder, Ross & Schlipf [6] and Przymusinski =-=[13]-=-. The same can be done for TSSs. The meaning of a TSS is then not given by a transition relation, i.e. a partition of T(Σ) × A × T(Σ) into the the transitions that hold and those that don’t, but a par... |

115 |
Transition system specifications with negative premises
- Groote
- 1993
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Citation Context ...ive premises appears in Bloom, Istrail & Meyer [2]. The concept of a (positive) TSS presented above was introduced in Groote & Vaandrager [9]; the negative premises t 6 a \Gamma! were added in Groote =-=[8]-=-. The notion generalises the GSOS rule systems of [2] and constitutes the first formalisation of Plotkin's Structural Operational Semantics (SOS) [10] that is sufficiently general to cover most, if no... |

108 | A congruence theorem for structured operational semantics with predicates and negative premises. Nordic Journal of Computing 2 (2), 274–302. A. Proof of Theorem 9 We show that the problem of deciding whether a universal two-counter machine diverges on inp - Verhoef - 1995 |

74 |
The meaning of negative premises in transition system specifications
- Bol, Groote
- 1996
(Show Context)
Citation Context ... 4. Solution 7 (well-founded, positive after reduction, complete) is essentially due to Van Gelder, Ross & Schlipf [6]. It is the most general solution without undesirable properties. In Bol & Groote =-=[3]-=-, where this solution has been adapted to TSSs, an example in the area of concurrency is given (the modelling of a priority operator in basic process algebra with abstraction) that can be handled with... |

54 | Ntyft/ntyxt rules reduce to ntree rules
- Fokkink, Glabbeek
- 1996
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Citation Context ...stance follows immediately from the definitions given here, whereas it would be nontrivial when starting from the original definitions. As a matter of fact, I needed this proposition in another paper =-=[8]-=-, and the search for it inspired me to write this one. 24sProposition 29 Let P and P ′ be TSSs over the same signature, such that P ⊢ N α ⇔ P ′ ⊢ N any closed action rule N α with only negative premis... |

53 | Bisimulation can’t be traced: Preliminary report - Bloom, Istrail, et al. - 1989 |

34 |
A fixpoint semantics for general logic programs compared with the well–supported and stable model semantics
- Fages
- 1991
(Show Context)
Citation Context ...l of P 4 is even the unique supported model of this TSS. My conclusion is that the criterion of being supported is too weak to be of any use in this context. This conclusion was also reached by Fages =-=[5]-=- in the setting of logic programming, who proposes to strengthen this criterion. Being supported can be rephrased as saying that a transition may only be present if there is a nonempty proof of its pr... |

14 | Transition system speci with negative premises. Theoretical Computer Science 118 - Groote - 1993 |