We define infinitary count-invariance for categorial logic, extending count-invariance for multip... more We define infinitary count-invariance for categorial logic, extending count-invariance for multiplicatives (van Benthem, 1991) and additives and bracket modalities (Valentín et al., 2013) to include exponentials. This provides an e↵ective tool for pruning proof search in categorial parsing/theorem-proving.
The Lambek calculus L provides a foundation for categorial grammar in the form of a logic of conc... more The Lambek calculus L provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus D, a generalization of Lambek calculus, which preserves the good proof-theoretic properties of the latter while embracing discontinuiity and subsuming L. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability
Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'... more Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'B AQB'AQB Fig. 4. BDLC discontinuous logical links A polar type tree is the result of unfolding a polar type up to its atomic leaves according to the ...
El proyecto Preparación Automatizada de Documentos, PrADo, se inició a partir del interés de los ... more El proyecto Preparación Automatizada de Documentos, PrADo, se inició a partir del interés de los dos grupos investigadores, de la Universitat Pompeu Fabra y de la Universitat Autònoma de Barcelona, en el procesamiento de textos reales no restringidos y en el establecimiento de métodos de procesamiento estables y eficientes para las lenguas habladas en Cataluña, el catalán y el castellano. Ver en el apéndice C la lista de investigadores de cada grupo.
We present here a general-purpose spell and grammar error detection architecture for Catalan unre... more We present here a general-purpose spell and grammar error detection architecture for Catalan unrestricted text. This architecture is based on a previous existing shallow morphosyntactic parser, which had to be adapted in order to successfully handle ill-formed input. The goal of this research is to obtain an architecture that can be used for developing morphosyntactic error checkers for both native and non-native speakers. We briefly present how we are currently customizing such an architecture in two different projects, as well as a means for annotating and exploiting error corpora (which ultimately condition the implementation of error checkers). We conclude with some remarks and future work.
The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, s... more The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus1 ([7], [4] and [8]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation (·)♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.
Proceedings of Logical Aspects of Computational Linguistics
The literature on categorial type logic includes proposals for semantically inactive additives, q... more The literature on categorial type logic includes proposals for semantically inactive additives, quantifiers, and modalities Morrill (1994[17]), Hepple (1990[2]), Moortgat (1997[9]), but to our knowledge there has been no proposal for semantically inactive multiplicatives. In this paper we formulate such a proposal (thus filling a gap in the typology of categorial connectives) in the context of the displacement calculus Morrill et al. (2011[16]), and we give a formulation of words as types whereby for every expression w there is a corresponding type W(w). We show how this machinary can treat the syntax and semantics of collocations involving apparently contentless words such as expletives, particle verbs, and (discontinuous) idioms. In addition, we give an account in these terms of the only known examples treated by Hybrid Type Logical Grammar (HTLG henceforth; Kubota and Levine 2012[4]) beyond the scope of unaugmented displacement calculus: gapping of particle verbs and discontinuous idioms.
The count invariance of van Benthem (1991[16]) is that for a sequent to be a theorem of the Lambe... more The count invariance of van Benthem (1991[16]) is that for a sequent to be a theorem of the Lambek calculus, for each atom, the number of positive occurrences equals the number of negative occurrences. (The same is true for multiplicative linear logic.) The count invariance provides for extensive pruning of the sequent proof search space. In this paper we generalize count invariance to categorial grammar (or linear logic) with additives and bracket modalities. We define by mutual recursion two counts, minimum count and maximum count, and we prove that if a multiplicative-additive sequent is a theorem, then for every atom, the minimum count is less than or equal to zero and the maximum count is greater than or equal to zero; in the case of a purely multiplicative sequent, minimum count and maximum count coincide in such a way as to together reconstitute the van Benthem count criterion. We then define in the same way a bracket count providing a count check for bracket modalities. This allows for efficient pruning of the sequent proof search space in parsing categorial grammar with additives and bracket modalities.
The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, s... more The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus 1 ([6], [3] and [7]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation (·) ♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD. 1 In [4] and [7], the term displacement calculus is used instead of Discontinous Lambek Calculus as in [6] and [9].
We show here the viability of a rapid deployment of a new language pair within the METIS architec... more We show here the viability of a rapid deployment of a new language pair within the METIS architecture. Contrarily to other SMT or EBMT systems, the METIS architecture allows us to forgo parallel texts, which for many language pairs, such as Catalan-English are hard to obtain. In this experiment, we have successfully built a Catalan-English prototype by simply plugging a POS tagger for Catalan and a bilingual Catalan-English dictionary to the English generation part of the system already developed for other language pairs.
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concat... more The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus, a generalization of Lambek calculus, which preserves its good proof-theoretic properties while embracing discontinuiity and subsuming it. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability
Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'... more Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'B AQB'AQB Fig. 4. BDLC discontinuous logical links A polar type tree is the result of unfolding a polar type up to its atomic leaves according to the ...
In type logical categorial grammar the analysis of an expression is a resource-conscious proof. A... more In type logical categorial grammar the analysis of an expression is a resource-conscious proof. Anaphora represents a particular challenge to this approach in that the antecedent resource is multiplied in the semantics. This duplication, which corresponds logically to the structural rule of contraction, may be treated lexically or syntactically. Furthermore, anaphora is subject to constraints, which Chomsky (1981)[1] formulated as Binding Principles A, B, and C. In this paper we consider English anaphora in categorial grammar including reference to the binding principles. We invoke displacement calculus, modal categorial calculus, categorial calculus with limited contraction, and entertain addition of negation as failure.
We define infinitary count-invariance for categorial logic, extending count-invariance for multip... more We define infinitary count-invariance for categorial logic, extending count-invariance for multiplicatives (van Benthem, 1991) and additives and bracket modalities (Valentín et al., 2013) to include exponentials. This provides an e↵ective tool for pruning proof search in categorial parsing/theorem-proving.
The Lambek calculus L provides a foundation for categorial grammar in the form of a logic of conc... more The Lambek calculus L provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus D, a generalization of Lambek calculus, which preserves the good proof-theoretic properties of the latter while embracing discontinuiity and subsuming L. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability
Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'... more Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'B AQB'AQB Fig. 4. BDLC discontinuous logical links A polar type tree is the result of unfolding a polar type up to its atomic leaves according to the ...
El proyecto Preparación Automatizada de Documentos, PrADo, se inició a partir del interés de los ... more El proyecto Preparación Automatizada de Documentos, PrADo, se inició a partir del interés de los dos grupos investigadores, de la Universitat Pompeu Fabra y de la Universitat Autònoma de Barcelona, en el procesamiento de textos reales no restringidos y en el establecimiento de métodos de procesamiento estables y eficientes para las lenguas habladas en Cataluña, el catalán y el castellano. Ver en el apéndice C la lista de investigadores de cada grupo.
We present here a general-purpose spell and grammar error detection architecture for Catalan unre... more We present here a general-purpose spell and grammar error detection architecture for Catalan unrestricted text. This architecture is based on a previous existing shallow morphosyntactic parser, which had to be adapted in order to successfully handle ill-formed input. The goal of this research is to obtain an architecture that can be used for developing morphosyntactic error checkers for both native and non-native speakers. We briefly present how we are currently customizing such an architecture in two different projects, as well as a means for annotating and exploiting error corpora (which ultimately condition the implementation of error checkers). We conclude with some remarks and future work.
The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, s... more The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus1 ([7], [4] and [8]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation (·)♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.
Proceedings of Logical Aspects of Computational Linguistics
The literature on categorial type logic includes proposals for semantically inactive additives, q... more The literature on categorial type logic includes proposals for semantically inactive additives, quantifiers, and modalities Morrill (1994[17]), Hepple (1990[2]), Moortgat (1997[9]), but to our knowledge there has been no proposal for semantically inactive multiplicatives. In this paper we formulate such a proposal (thus filling a gap in the typology of categorial connectives) in the context of the displacement calculus Morrill et al. (2011[16]), and we give a formulation of words as types whereby for every expression w there is a corresponding type W(w). We show how this machinary can treat the syntax and semantics of collocations involving apparently contentless words such as expletives, particle verbs, and (discontinuous) idioms. In addition, we give an account in these terms of the only known examples treated by Hybrid Type Logical Grammar (HTLG henceforth; Kubota and Levine 2012[4]) beyond the scope of unaugmented displacement calculus: gapping of particle verbs and discontinuous idioms.
The count invariance of van Benthem (1991[16]) is that for a sequent to be a theorem of the Lambe... more The count invariance of van Benthem (1991[16]) is that for a sequent to be a theorem of the Lambek calculus, for each atom, the number of positive occurrences equals the number of negative occurrences. (The same is true for multiplicative linear logic.) The count invariance provides for extensive pruning of the sequent proof search space. In this paper we generalize count invariance to categorial grammar (or linear logic) with additives and bracket modalities. We define by mutual recursion two counts, minimum count and maximum count, and we prove that if a multiplicative-additive sequent is a theorem, then for every atom, the minimum count is less than or equal to zero and the maximum count is greater than or equal to zero; in the case of a purely multiplicative sequent, minimum count and maximum count coincide in such a way as to together reconstitute the van Benthem count criterion. We then define in the same way a bracket count providing a count check for bracket modalities. This allows for efficient pruning of the sequent proof search space in parsing categorial grammar with additives and bracket modalities.
The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, s... more The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus 1 ([6], [3] and [7]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation (·) ♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD. 1 In [4] and [7], the term displacement calculus is used instead of Discontinous Lambek Calculus as in [6] and [9].
We show here the viability of a rapid deployment of a new language pair within the METIS architec... more We show here the viability of a rapid deployment of a new language pair within the METIS architecture. Contrarily to other SMT or EBMT systems, the METIS architecture allows us to forgo parallel texts, which for many language pairs, such as Catalan-English are hard to obtain. In this experiment, we have successfully built a Catalan-English prototype by simply plugging a POS tagger for Catalan and a bilingual Catalan-English dictionary to the English generation part of the system already developed for other language pairs.
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concat... more The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus, a generalization of Lambek calculus, which preserves its good proof-theoretic properties while embracing discontinuiity and subsuming it. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability
Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'... more Dutch Grammar and Processing: A Case Study in TLG 277 A [C' A [C BB* C] B' C] B B'B AQB'AQB Fig. 4. BDLC discontinuous logical links A polar type tree is the result of unfolding a polar type up to its atomic leaves according to the ...
In type logical categorial grammar the analysis of an expression is a resource-conscious proof. A... more In type logical categorial grammar the analysis of an expression is a resource-conscious proof. Anaphora represents a particular challenge to this approach in that the antecedent resource is multiplied in the semantics. This duplication, which corresponds logically to the structural rule of contraction, may be treated lexically or syntactically. Furthermore, anaphora is subject to constraints, which Chomsky (1981)[1] formulated as Binding Principles A, B, and C. In this paper we consider English anaphora in categorial grammar including reference to the binding principles. We invoke displacement calculus, modal categorial calculus, categorial calculus with limited contraction, and entertain addition of negation as failure.
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Papers by Oriol Valentín
This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus1 ([7], [4] and [8]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD.
More concretely, we present a faithful embedding translation (·)♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.
This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus1 ([7], [4] and [8]), which like sL has no structural rules, is also equivalent to an ω-sorted multimodal calculus mD.
More concretely, we present a faithful embedding translation (·)♯ between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.