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## Modal Logic and Attribute Value Structures (1993)

Venue: | University of Amsterdam, ITLI |

Citations: | 33 - 9 self |

### Citations

854 |
M.: A New Introduction to Modal Logic
- Hughes, Cresswell
- 1996
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Citation Context ...formal proofs, formal provability (here denoted by `), maximal consistent sets of sentences (MCSs), and some very basic results of modal completeness theory. All the required material can be found in =-=-=-[11]. 4 From ` !sand ` deduce `s. 5 From ` deduce ` [l]. 6 The Henkin multiframe (of signature hL; Ai) is the pair H = hH; fR H l g l2L i, where H is the set of all maximal consistent sets of sente... |

293 |
Past, Present and Future
- Prior
- 1967
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Citation Context ...ore the following AVM: 2 6 6 4 subj " agr foo pred bar # 1 comp [subj 1 ] 3 7 7 5 This corresponds to the following L N w: hsubji(i ^ hagrifoo ^ hpredibar) ^ hcompihsubjii 7 For Prior's work cons=-=ult [20]-=-, for Bull's work [5]. For recent results on the subject see [7], [8], [2] or [3]. 16 In short, the nominal i is doing the work that 1 does in the AVM, and more generally, using a boxlabel superscript... |

139 | A logical semantics for feature structures
- Kasper, Rounds
- 1986
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Citation Context ...h AVSs. The denition subsumes the better known denitions of Attribute Value Structures found in the literature, and in particular those of Gazdar et al [10] [9], Johnson [12], and Kasper and Rounds [1=-=4]-=-. Moreover it's not too liberal. There are only two reasonably common further restrictions on the binary relations that it does not impose. Thesrst of these is acyclicity, which means that it is never... |

121 |
Attribute-Value Logic and the Theory of Grammar
- Johnson
- 1988
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Citation Context ... earlier are examples of such AVSs. The denition subsumes the better known denitions of Attribute Value Structures found in the literature, and in particular those of Gazdar et al [10] [9], Johnson [1=-=2]-=-, and Kasper and Rounds [14]. Moreover it's not too liberal. There are only two reasonably common further restrictions on the binary relations that it does not impose. Thesrst of these is acyclicity, ... |

97 |
Axioms for tense logic I
- Burgess
- 1982
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Citation Context ...is an MCS this means hfi hgi 62 h. Thus the straightforward Henkin method won't work, so we'll need to be more delicate. In the following pages I'll show in some detail how a method used by Burgess [=-=6]-=- for various tense logics can be adapted tost L KR . The method is an inductive process which builds something called a chronicle. As we shall see, given a chronicle with certain properties a suitable... |

84 |
Modal logic with names
- Gargov, Goranko
- 1993
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Citation Context ...1 ] 3 7 7 5 This corresponds to the following L N w: hsubji(i ^ hagrifoo ^ hpredibar) ^ hcompihsubjii 7 For Prior's work consult [20], for Bull's work [5]. For recent results on the subject see [7], [=-=8]-=-, [2] or [3]. 16 In short, the nominal i is doing the work that 1 does in the AVM, and more generally, using a boxlabel superscript amounts to conjoining a nominal. Thus L N allows a straightforward l... |

70 |
A complete logical calculus for record structures representing linguistic information
- Rounds, Kasper
- 1986
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Citation Context ...nd its semantics was a fruitful way of looking at puzzles involving disjunctive feature structures. However Kasper and Rounds proved relatively few results about L KR . They give some near the end of =-=[22-=-], but the bulk of this paper is devoted to dening the relevant languages and proving a completeness result for the negation free fragment of L. Incidentally, most of the results Kasper and Rounds giv... |

63 | Features and Values
- Karttunen
- 1984
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Citation Context ...te case takes one of the values nominative, genitive, or accusative, but it's not specied which. Another extension was to state negative partial dependencies: 1 The following examples are taken from [=-=13]. 7 -=-" number plural case [ dative] # In this AVM it's specied that case does not take the value dative. Now, it's certainly natural to demand full Boolean expressivity, and arguably it's linguistical... |

53 |
Modal environment for Boolean speculations
- Gargov, Passy, et al.
- 1987
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Citation Context ...subj 1 ] 3 7 7 5 This corresponds to the following L N w: hsubji(i ^ hagrifoo ^ hpredibar) ^ hcompihsubjii 7 For Prior's work consult [20], for Bull's work [5]. For recent results on the subject see [=-=7]-=-, [8], [2] or [3]. 16 In short, the nominal i is doing the work that 1 does in the AVM, and more generally, using a boxlabel superscript amounts to conjoining a nominal. Thus L N allows a straightforw... |

48 | The semantics of grammar formalisms seen as computer languages
- Pereira, Shieber
- 1984
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Citation Context ...AVS then thesrst two componentsshN; fR l g l2L i are an L indexed multiframe, while fQ g 2A supplies the interpretation of propositional variables. In short, a modal language 2 Pereira and Shieber [1=-=8-=-] seem to have been thesrst to note the usefulness of this distinction in the study of unication formalisms. The later work of Kasper and Rounds [14] was also very in uential. 8 with a L indexed colle... |

41 |
An Approach to tense logic
- Bull
- 1970
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Citation Context ... 2 6 6 4 subj " agr foo pred bar # 1 comp [subj 1 ] 3 7 7 5 This corresponds to the following L N w: hsubji(i ^ hagrifoo ^ hpredibar) ^ hcompihsubjii 7 For Prior's work consult [20], for Bull's w=-=ork [5]-=-. For recent results on the subject see [7], [8], [2] or [3]. 16 In short, the nominal i is doing the work that 1 does in the AVM, and more generally, using a boxlabel superscript amounts to conjoinin... |

19 |
Nominal Tense Logic and Other Sorted Intensional Frameworks
- Blackburn
- 1990
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Citation Context ...This corresponds to the following L N w: hsubji(i ^ hagrifoo ^ hpredibar) ^ hcompihsubjii 7 For Prior's work consult [20], for Bull's work [5]. For recent results on the subject see [7], [8], [2] or [=-=3]-=-. 16 In short, the nominal i is doing the work that 1 does in the AVM, and more generally, using a boxlabel superscript amounts to conjoining a nominal. Thus L N allows a straightforward linearisation... |

14 | A Logical Approach to Arabic Phonology
- Bird
- 1991
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Citation Context ...perty. Thus by the usual argument all these logics are decidable. There are only three papers which make use of modal languages with nominals for dealing with linguistic structure. Bird and Blackburn =-=[1-=-] use a modal language with nominals for talking about phonological information. The twist in this paper is that a number of dierent AVSs are pictured as being strung out along a time axis, and additi... |

8 |
Completeness theorems for logics of feature structures
- Moss
- 1991
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Citation Context ... attached any importance to it, and in particular don't make use of any of the standard tools and results of modal logic. In fact the only other logical investigation of L KR seems to be that of Moss =-=[17]-=-. This paper takes an essentially (Kripke) model theoretic stance towards L KR (and some other Attribute Value logics) and should be of interest to the readers of this paper. So, what is PATR-II? Basi... |

6 |
An Introduction to the Semantics of Uni Grammar Formalisms DYANA deliverable R3.2.A
- Reape
- 1991
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Citation Context ... is, the language is an attempt to capture Attribute Value style reasoning and temporal reasoning in a single framework. As in L N , the nominals are used to name nodes and enforce re-entrancy. Reape =-=[21]-=- uses a language similar to L N for talking about syntactic information. This language is then extended to a larger language containing polyadic modal operators to enable the set valued features and f... |

5 | The logic of uni - Rounds - 1990 |

3 |
Feature Logics, In Descriptions and The Logical Treatment of Grammar
- Keller
- 1991
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Citation Context ...e linguistically useful. Third, propositional dynamic logic | modal logic's big brother | beckons, and indeed those computational linguists who use functional uncertainty have already heeded the call =-=[15]-=-. However an adequate discussion of these topics is not possible here, and so I'll close the paper on a more general note. This investigation has shown that modal languages can arise quite naturally w... |

3 |
On the Logic of Category De
- Kracht
- 1989
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Citation Context ... modal operators; and the semantics they give to these features is just an ordinary Kripke semantics. Thesrst statement of the link between attributes and modalities seems to have been made by Kracht =-=[16]-=-. In this elegant paper he makes the link explicit and then explores issues of completeness and decidability for Gazdar et al's language. 14 3 Modal logic with nominals If there was no more to AVM not... |

3 |
Sorts in uni grammar and what they mean
- Pollard
- 1993
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Citation Context ... 0 2 Q then n = n 0 . The main reason for ignoring these demands is that by doing so we accommodate a generalisation that is beginning to emerge in computational linguistics, namely the use of sorts[=-=19-=-]. Sorts are essentially pieces of atomic information that need not obey these three restrictions. It seems sensible to dene basic notions in a manner that covers such natural generalisations, and thi... |

2 |
Semantic Considerations for Constraint based grammar Formalisms
- Ruhrberg
- 1991
(Show Context)
Citation Context ...e, for example, that none of the graphs drawn in this paper are AVSs under this denition, for in none of them is the atomic information 3rd realised anywhere. Finally, a chapter of Ruhrberg's thesis [=-=24]-=- examines modal languages with nominals. 19 4 Kasper Rounds logic As we have seen, multimodal languages with nominals correspond neatly to the AVM notation actually used by computational linguists. Ho... |

1 |
On the Complexity of Attribute Value Logics, to appear
- Blackburn, Spaan
- 1991
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Citation Context ...x methods for building satisfying models exist. The complexity of the satisability problem for various 11 Attribute Value logics (including L, L N and L KR ) has been analysed by Blackburn and Spaan [=-=4]-=-. The logics in L of interest in computational linguistics are rather simple to axiomatise. 3 Let'ssrst deal with minimal AV logic, that is, the logic of the class of all AVSs. As axioms we take some ... |

1 |
A logic for Category De
- Gazdar, Pullum
- 1987
(Show Context)
Citation Context ... graphs given earlier are examples of such AVSs. The denition subsumes the better known denitions of Attribute Value Structures found in the literature, and in particular those of Gazdar et al [10] [9=-=]-=-, Johnson [12], and Kasper and Rounds [14]. Moreover it's not too liberal. There are only two reasonably common further restrictions on the binary relations that it does not impose. Thesrst of these i... |