## Structures, Languages and Translations: the Structural Approach to Feature Logic (1994)

Venue: | Constraints, Language and Computation |

Citations: | 17 - 2 self |

### BibTeX

@INPROCEEDINGS{Blackburn94structures,languages,

author = {Patrick Blackburn},

title = {Structures, Languages and Translations: the Structural Approach to Feature Logic},

booktitle = {Constraints, Language and Computation},

year = {1994},

pages = {1--27},

publisher = {Academic Press}

}

### OpenURL

### Abstract

This paper discusses an approach to feature logic called the structural approach. The method consists in first viewing feature structures as models (or relational structures) in the standard model theoretic sense, and then going on to consider various languages that can be interpeted on these structures and the way these languages are interrelated. It will be shown that the structural approach offers...

### Citations

710 |
An Introduction to Modal Logic
- Hughes, Cresswell
- 1972
(Show Context)
Citation Context ... 9n 0 (nR l n 0 & M j= [n 0 ]) If M j= [n] then we say that M satises at n, or is true in M at n. For further technical details about modal logic the reader should consult Hughes and Cresswell [21]. The basic logical theory of L is easy to establish using standard modal techniques. Completeness results for some linguistically interesting classes of feature structure (including the ccc-extension... |

330 | The Logic of Typed Feature Structures
- CARPENTER
- 1992
(Show Context)
Citation Context ...: the entire language may contain non-monotonic descriptions, so one should not use the entire language. But what are the monotonic fragments? Some answers have been given in recent work by Carpenter =-=[14-=-], who shows how to incorporate negated path equations into a variant of (otherwise negation free) Kasper Rounds logic and retain monotonicity. A second approach to the problem is to work with a diere... |

255 | A correspondence theory for terminological logics: Preliminary report
- Schild
- 1991
(Show Context)
Citation Context ...r the enriched versions of L and L N are still decidable, but enriching L KR in this fashion results in undecidability. Finally, in the neighbouringseld of knowledge representation formalisms, Schild =-=[42]-=- has used modal logic as a tool for investigating the computational complexity of various systems for terminological reasoning. 2.4 Propositional Dynamic Logic Propositional Dynamic Logic (PDL) is an ... |

181 |
Present and Future
- Satellites, Past
- 1982
(Show Context)
Citation Context ... to allow re-entrancy to be encoded, and unlike the Kasper Rounds path equality this extension has been considered in the modal literature; in fact it traces back to work in tense logic done by Prior =-=[36]-=- and Bull [13] in the late sixties. The basic idea is to add new atomic symbols, called nominals, to L. These new symbols are interpreted standardly except for one thing: we insist that nominals are t... |

163 | Information-based syntax and semantics, Volume 1: Fundamentals - Pollard, Sag - 1987 |

127 | A logical semantics for feature structures
- Kasper, William
- 1986
(Show Context)
Citation Context ...s as special cases most of the denitions of feature structure the reader is likely to encounter in the computational linguistics literature. For example, it covers the denition of Kasper and Rounds [2=-=6, 39, 40-=-]. Kasper and Rounds dene feature structures to be certain kinds of automata; but recall that automata theory treats automata simply as certain kinds of decorated labeled graph. At the same time this ... |

73 |
Modal logic with names
- Gargov, Goranko
- 1993
(Show Context)
Citation Context ...y modal setting. The original paper on nominal modal languages is due to Gargov, Passy and Tinchev [16] and a more detailed investigation of such systems can be found in a paper by Gargov and Goranko =-=[18]-=-. Somewhat later, Blackburn [7, 8] proved a number of results concerning nominals in the setting of tense logic. There is also work of more direct relevance to feature logic. Ruhrberg [41] has investi... |

65 |
A Complete Logical Calculus for Record Structures Representing Linguistic Information
- Rounds, Kaspar
- 1986
(Show Context)
Citation Context ...s as special cases most of the denitions of feature structure the reader is likely to encounter in the computational linguistics literature. For example, it covers the denition of Kasper and Rounds [2=-=6, 39, 40-=-]. Kasper and Rounds dene feature structures to be certain kinds of automata; but recall that automata theory treats automata simply as certain kinds of decorated labeled graph. At the same time this ... |

62 |
An Essay in Combinatory Dynamic Logic
- Passy, Tinchev
- 1991
(Show Context)
Citation Context ... motivation for the introduction of nominals. On the other hand the satisability problem is 1 1 complete. Gargov and Passy [17] extend these results to deterministic systems, and Passy and Tinchev [3=-=3]-=- is an encyclopaedia of results in this area that is an obvious starting point for further investigations of feature logic. 2.5 Attribute Value Matrices In this section I shall discuss Attribute Value... |

57 | Features and Values
- Karttunen
- 1984
(Show Context)
Citation Context ...lowing the transition labeled case must be decorated with one of the items nominative, genitive or accusative, it's not specied which. Such fully Boolean expressive AVMs were introduced by Karttunen [=-=25]-=- in the early 1980s. Consider again the simple conjunctive AVM we started with. There is nothing about it that explicitly insists on the identity (or non-identity) of any of the satisfying nodes n, n ... |

43 |
Dynamic Logic, in Handbook of Philosophical Logic, ,2 edited by
- Harel
- 1984
(Show Context)
Citation Context ... for terminological reasoning. 2.4 Propositional Dynamic Logic Propositional Dynamic Logic (PDL) is an extension of modal logic that was devised for reasoning about program behaviour; consult Harel's =-=[20]-=- survey for a detailed account of thisseld. In this section we will see that PDL, and certain of its extensions, are natural constraint language for dealing with feature structures. We will consider t... |

42 | A modal perspective on computational complexity of attribute value grammars
- Blackburn, Spaan
- 1993
(Show Context)
Citation Context ...echniques. Completeness results for some linguistically interesting classes of feature structure (including the ccc-extensional structures) have been given by Blackburn [9], while Blackburn and Spaan =-=[10, 1-=-1] show that the satisability problem for L is NP-complete. This last result is mildly surprising; the complexity of the satisability problems for most well known modal languages are PSPACE-complete. ... |

42 | The semantics of -grammar formalisms seen as computer languages
- Pereira, Shieber
- 1984
(Show Context)
Citation Context ...al languages that are interpreted on feature structures. This distinction (absolutely fundamental to model theory) found its way into computational linguistics through the work of Pereira and Shieber =-=[34]-=-, became very in uential through the work of Kasper and Rounds [26, 39, 40], and underlies approaches such as those of Smolka [43, 44] and Johnson [22, 23]. One advantage the logical perspective confe... |

41 |
An Algorithm for Functional Uncertainty
- Kaplan, Maxwell
- 1988
(Show Context)
Citation Context ...y tosnd other ideas in the linguistic literature which go beyondsrst order expressive capabilities in more interesting ways. Consider the LFG concept of functional uncertainty (see Kaplan and Maxwell =-=[24-=-]). A functional uncertainty constraint with respect to an attribute R holds between two nodes x and y i y can be reached by somesnite sequence of R transitions from x. This isn't something that can b... |

35 |
An approach to tense logic
- Bull
- 1970
(Show Context)
Citation Context ...ntrancy to be encoded, and unlike the Kasper Rounds path equality this extension has been considered in the modal literature; in fact it traces back to work in tense logic done by Prior [36] and Bull =-=[13]-=- in the late sixties. The basic idea is to add new atomic symbols, called nominals, to L. These new symbols are interpreted standardly except for one thing: we insist that nominals are true at exactly... |

30 | Modal Logic and Attribute Value Structures
- Blackburn
- 1992
(Show Context)
Citation Context ...stablish using standard modal techniques. Completeness results for some linguistically interesting classes of feature structure (including the ccc-extensional structures) have been given by Blackburn =-=[-=-9], while Blackburn and Spaan [10, 11] show that the satisability problem for L is NP-complete. This last result is mildly surprising; the complexity of the satisability problems for most well known m... |

29 |
Deterministic propositional dynamic logic: Finite models, complexity, and completeness
- Ben-Ari, Halpern, et al.
- 1982
(Show Context)
Citation Context ...puter science interpretation, the restriction to partial functional structures means that one is working with deterministic programs. Deterministic PDL is well understood; Ben-Ari, Halpern and Pnueli =-=[2]-=- have proved its decidability, determined its complexity, given explicit satisfaction algorithms, and axiomatised its logic. Now, the mention in the previous paragraph of the words `transitive closure... |

29 | Category Structures
- Gazdar, Pullum, et al.
- 1988
(Show Context)
Citation Context ...ng with the set values of HPSG; the key idea is to make use of n-place modalities. Moss [31] has considered modal languages with a special `membership modality' to deal with set values. Gazdar et al. =-=[19-=-] introduce a `master modality' to L that enables recursive constraints to be imposed; this language has been investigated by Kracht [29] and Blackburn and Spaan [11], who also consider the eects of e... |

26 | Features and Formulae
- Johnson
- 1991
(Show Context)
Citation Context ...the number of unication formalisms is continually growing, while our understanding of their mutual interrelationships lags ever further behind. This problem has been raised in recent work by Johnson [=-=23]-=-, who complains of the proliferation of `custom built' constraint languages. Ac2 tually, the solution Johnson proposes, namely the translation of constraint formalisms into a fragment ofsrst order log... |

24 |
Attribute Value Logic and Theory of Grammar . CSLI Lecture Notes
- Johnson
- 1988
(Show Context)
Citation Context ...guistics through the work of Pereira and Shieber [34], became very in uential through the work of Kasper and Rounds [26, 39, 40], and underlies approaches such as those of Smolka [43, 44] and Johnson =-=[22, -=-23]. One advantage the logical perspective confers is a neat (and very general) account of unication: unication is possible whenever two feature descriptions andsare compatible. In the logical approa... |

19 |
Nominal Tense Logic and Other Sorted Intensional Frameworks
- Blackburn
- 1990
(Show Context)
Citation Context ...per on nominal modal languages is due to Gargov, Passy and Tinchev [16] and a more detailed investigation of such systems can be found in a paper by Gargov and Goranko [18]. Somewhat later, Blackburn =-=[7, 8]-=- proved a number of results concerning nominals in the setting of tense logic. There is also work of more direct relevance to feature logic. Ruhrberg [41] has investigated L N , Blackburn [9] has axio... |

16 |
Model-theoretic logics: Background and Aims
- Barwise
- 1985
(Show Context)
Citation Context ... become interesting objects of study. However instead of pursuing the parallels with model theoretic logic any further, I'll simply urge the reader urged to consult Barwise's lucid survey of thatseld =-=[1]-=-. His account will clarify the present paper's methodological orientation, and, as an added bonus, contains salutory warnings against the naive (and irritatingly prevalent) con ation of `logic' with `... |

12 |
Determinism and looping
- Gargov, Passy
- 1988
(Show Context)
Citation Context ...deed the problem of treating the intersection of programs was an important motivation for the introduction of nominals. On the other hand the satisability problem is 1 1 complete. Gargov and Passy [1=-=7]-=- extend these results to deterministic systems, and Passy and Tinchev [33] is an encyclopaedia of results in this area that is an obvious starting point for further investigations of feature logic. 2.... |

8 |
Tinko Tinchev. Modal environment for Boolean speculations
- Gargov, Passy
- 1987
(Show Context)
Citation Context ...tlining this work in the following section), but they have also proved important results in the purely modal setting. The original paper on nominal modal languages is due to Gargov, Passy and Tinchev =-=[16]-=- and a more detailed investigation of such systems can be found in a paper by Gargov and Goranko [18]. Somewhat later, Blackburn [7, 8] proved a number of results concerning nominals in the setting of... |

8 |
Completeness theorems for logics of feature structures
- Moss
- 1991
(Show Context)
Citation Context ...s interpret the negation free fragment of this language on certain ccc-extensional models. They give a number of axioms for this fragment, and show that its satisability problem is NP-complete. Moss [=-=31-=-] and Blackburn [9] have both axiomatised the full language and proved completeness results using very dierent techniques. Finally Blackburn and Spaan [10, 11] have proved a number of complexity resul... |

6 | Beginning Model Theory - Bridge - 1977 |

6 |
An Introduction to the Semantics of Uni Grammar Formalisms DYANA deliverable R3.2.A
- Reape
- 1991
(Show Context)
Citation Context ...se two systems, as will be discussed later. To conclude this section, I'll mention some other modal approaches to feature logics which go beyond the systems discussed above in interesting ways. Reape =-=[37]-=- has considered much richer languages with nominals for dealing with the set values of HPSG; the key idea is to make use of n-place modalities. Moss [31] has considered modal languages with a special ... |

6 |
Feature constraint logics for uni grammars
- Smolka
- 1992
(Show Context)
Citation Context ...nto computational linguistics through the work of Pereira and Shieber [34], became very in uential through the work of Kasper and Rounds [26, 39, 40], and underlies approaches such as those of Smolka =-=[43, -=-44] and Johnson [22, 23]. One advantage the logical perspective confers is a neat (and very general) account of unication: unication is possible whenever two feature descriptions andsare compatible. ... |

5 |
Model Theory for In Logic
- Keisler
- 1971
(Show Context)
Citation Context ...to variables i at least one formula from is true in M. Unsurprisingly, the move from L 1 to L!1! results in a big increase in expressive power; for a discussion of mathematical results see Keisler [2=-=7]-=-. However what is of most importance for the present discussion is that the extra expressive power is of a kind that is relevant to linguistics, and indeed to computational linguistics; both these sub... |

5 |
The logic of uni
- Rounds
- 1990
(Show Context)
Citation Context ...s as special cases most of the denitions of feature structure the reader is likely to encounter in the computational linguistics literature. For example, it covers the denition of Kasper and Rounds [2=-=6, 39, 40-=-]. Kasper and Rounds dene feature structures to be certain kinds of automata; but recall that automata theory treats automata simply as certain kinds of decorated labeled graph. At the same time this ... |

3 |
v.: 1984, Correspondence Theory, in Handbook of Philosophical Logic 2, edited by
- Benthem
(Show Context)
Citation Context ...gments of classical languages, and to use the highly developed techniques of classical logic to teach us about modal languages. An excellent overview of thisseld is given in a survey by van Benthem's =-=[5]-=-; a more technical account is provided by the same author's monograph [6]. Thesrst thing to note about this translation (a point van Benthem has repeatedly emphasized) is that it is essentially a reca... |

3 |
On the Complexity of Attribute Value Logics
- Blackburn, Spaan
- 1991
(Show Context)
Citation Context ...echniques. Completeness results for some linguistically interesting classes of feature structure (including the ccc-extensional structures) have been given by Blackburn [9], while Blackburn and Spaan =-=[10, 1-=-1] show that the satisability problem for L is NP-complete. This last result is mildly surprising; the complexity of the satisability problems for most well known modal languages are PSPACE-complete. ... |

3 |
Feature Logics, In Descriptions and The Logical Treatment of Grammar
- Keller
- 1991
(Show Context)
Citation Context ...' will turn out to be fragments of L!1! . I'll close this section by mentioning that my interest in innitary systems for linguistic applications has been strongly in uenced by Keller's recent thesis [=-=28-=-]. I will be discussing some of his work in a later section. 2.3 Modal Logic In this section we turn from the richness of innitary logic to the austerity of modal languages. We will discuss three moda... |

3 |
On the Logic of Category De
- Kracht
- 1989
(Show Context)
Citation Context ... KR , thus it 1 Thesrst person to have realised this, or at any rate, thesrst person to realise this and make use of modal techniques for investigating feature logic, seems to have been Marcus Kracht =-=[29]-=-. 11 only remains to give the semantic clause for the path equations. In what follows we assume without loss of generality that 0 62 L, and denote the identity relation on any set of nodes N by R 0 . ... |

2 |
Tense logic and standard logic, Logique et Analyse 20
- Benthem
- 1977
(Show Context)
Citation Context ...ly languages `tuned' for this viewpoint. The classic example of this occurring is the way tense operators naturally arise when temporal semantics for natural language is considered; see either [4] or =-=[3]-=- for an illuminating account of this. It is straightforward to extend ST to cover the richer syntax of both L KR and L N . Let'ssrst treat the language of Kasper and Rounds. To do this we need merely ... |

2 |
v.: 1983, The Logic of Time
- Benthem
(Show Context)
Citation Context ...ntains salutory warnings against the naive (and irritatingly prevalent) con ation of `logic' with `rst order logic'. Van Benthem's work on temporal logic, most notably in his book \The logic of Time&q=-=uot;[4]-=-, is a revealing demonstration of how to apply the structural approach to non-mathematical domains. Actually, for the purposes of the present discussion, it is the subtitle of this book which says it ... |

2 |
Semantic Considerations for Constraint based grammar Formalisms
- Ruhrberg
- 1991
(Show Context)
Citation Context ...and Goranko [18]. Somewhat later, Blackburn [7, 8] proved a number of results concerning nominals in the setting of tense logic. There is also work of more direct relevance to feature logic. Ruhrberg =-=[41-=-] has investigated L N , Blackburn [9] has axiomatised the L N logics of various classes of feature structure, and Blackburn and Spaan [10, 11] have investigated the complexity of the satisability pro... |

1 |
v.: 1986, Modal Logic and Classical Logic
- Benthem
(Show Context)
Citation Context ... of classical logic to teach us about modal languages. An excellent overview of thisseld is given in a survey by van Benthem's [5]; a more technical account is provided by the same author's monograph =-=[-=-6]. Thesrst thing to note about this translation (a point van Benthem has repeatedly emphasized) is that it is essentially a recasting of the satisability denition for L in more mundane form: as a `tr... |

1 |
Nominal Tense Logic, to appear in Notre Dame Journal of Formal Logic
- Blackburn
- 1989
(Show Context)
Citation Context ...per on nominal modal languages is due to Gargov, Passy and Tinchev [16] and a more detailed investigation of such systems can be found in a paper by Gargov and Goranko [18]. Somewhat later, Blackburn =-=[7, 8]-=- proved a number of results concerning nominals in the setting of tense logic. There is also work of more direct relevance to feature logic. Ruhrberg [41] has investigated L N , Blackburn [9] has axio... |

1 |
A logic for partially speci data structures
- Moshier, Rounds
- 1987
(Show Context)
Citation Context ...s logic and retain monotonicity. A second approach to the problem is to work with a dierent notion of negation over richer classes of semantic entities. This is the approach of of Moshier and Rounds [=-=30]-=-, who use intuitionistic negation. This is a very natural idea as the `growth of information' interpretation of intuitionistic logic meshes well with the `partial description' interpretation that unde... |

1 |
A Feature Logic with
- Smolka
- 1988
(Show Context)
Citation Context ...nto computational linguistics through the work of Pereira and Shieber [34], became very in uential through the work of Kasper and Rounds [26, 39, 40], and underlies approaches such as those of Smolka =-=[43, -=-44] and Johnson [22, 23]. One advantage the logical perspective confers is a neat (and very general) account of unication: unication is possible whenever two feature descriptions andsare compatible. ... |