Joshi, A., Kulick, S.: Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy 20 (1997) 637--667  Home/Search   Document Details and Download   Summary   Related Articles   Check

....[8] The second task will be formalised by the notion of the grid of a CG. 47 Configuring Categorial Grammars Relation to partial proof trees The unfolding encoding can be regarded as a constraint formalisation of the context free fragment of the partial proof tree system of Joshi and Kulick [17]. Partial proof trees (PPTs) essentially are unfoldings that, besides plugging (called application by Joshi and Kulick) support two other operations, stretching and interpolation, which increase the generative capacity of PPTs beyond context freeness. In order to remain in the realm of mildly ....

....tree, it is not at all obvious how it could provide for hypotheticals in the first place. One possibility would be to adapt compilation techniques [15] to the present framework. Another interesting direction would be to explore the connections between the unfolding encoding and partial proof trees [17], in which hypothetical reasoning is possible through the stretching operation. 68 Parallelism A final proposal for further work concerns the general architecture of the processing itself: The current model is linear; it first generates the starting trees and then for each of these starting ....

Arivind K. Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20(6):637--667, 1997.

....system. Furthermore, we point out some possible directions to recast the deductive solution into a Tree Adjoining Grammar system. In particular, we suggest to compare the proof system developed for Multimodal Categorial Grammar (Moot Puite, 1999) with the Partial Proof Trees proposed in (Joshi Kulick, 1997). Introduction In this paper we discuss how polarity effects can be derived from controlled lexical items. Polarity Items (PIs) are linguistic expressions which depend on the polarity of their context for grammaticality (Ladusaw, 1979) Moreover, both in the syntactic and semantic traditions ....

....between the two families would be productive for both approaches. In this paper we suggest some possible lines of research which could be worked out to recast the deductive implementation of PIs into TAG. In order to reduce the gap between the two systems we consider the works carried out in (Joshi Kulick, 1997) and (Joshi et al. 1999) which build a bridge between TAG and MMCG. In the former paper, categorial grammar proofs are used as building blocks resulting in a middle ground system known as PPTS. In the latter, the comparison is extended to the structural modalities which characterize MMCG. 1. ....

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JOSHI A. & KULICK S. (1997). Partial proof trees as building blocks for categorial grammar. Linguistics and Philosophy, 20, 637--667.

.... by a mixed deductive system type deduction is used to project intra clausal structure (much as in Categorial Grammar cf. in particular Morrill 185 1994, Oehrle 1995) but there is in addition inference defined over databases as units for projecting inter clausal (adjunct) structure (cf. Joshi and Kulick 1995 for a simple composite type deduction system) The background methodology assumed is that of Labelled Deductive Systems (Gabbay forthcoming) According to this methodology, mixed logical systems can be defined, allowing systematically related phenomena to be defined together while keeping their ....

Joshi, A. & Kulick, S. (1995). 'Partial proof trees as building blocks for a categorial grammar' in Morrill, G. & Oehrle, R. (eds.) Proceedings of Formal Grammar Conference, Barcelona July 1995.

.... (V is(b; a b ) Pa(a b ) D ) where: i) a(x) ffly(V is(x; y) Pat(y) ii) b = x(Nu(x) V is(x; a x ) Pa(a x ) iii) a b = ffly(V is(b; y) Pat(y) 4 Conclusion This LDS NL model relates to categorial analyses manipulating labelled type deduction (eg Morrill 1994, Oehrle 1995, Joshi Kulick 1995), though it is unlike these in addressing issues of underspecificity, and in its explicitly procedural perspective. It is close to semantic accounts of underspecificity (Alshawi Crouch 1992, Reyle 1993, Farkas forthcoming) though unlike these formalisms, the process of resolving dependencies is ....

Joshi, A. & Kulick S. 1995. 'Partial proof trees as building blocks for a categorial grammar ' in Morrill, G. & Oehrle, R. (eds.) Proceedings of the Formal Grammar Conference, Barcelona July 1995.

....of LFG, and various members of the family of Tree Adjoining Grammars. These systems can be simulated (at least partially) in the framework of labeled type logical deduction, in a way that may reveal underlying points of similarity and sharpen understanding of points of essential difference. See [Joshi Kulick 95] for an exploration of this perspective. 7 Categorial parsing as deduction In this section we turn to the computational study of categorial type logics, and discuss some aspects of their algorithmic proof theory, under the slogan Parsing as Deduction a slogan which in the type logical ....

Joshi, A. & S. Kulick (1995), `Partial proof trees as building blocks for a categorial grammar`. In [Morrill & Oehrle], 138--149.

.... and so called non constituent coordination upon lexical word order are also captured (see Dowty 1988 and Steedman 1985, Steedman 1990) There is no equivalent of type raising in standard TAG (although Karttunen 1989 and Rambow 1994 use structural equivalents of type raising, and Sarkar and Joshi 1996 capture coordination using related rules for abstraction or contraction over the verb anchoring initial trees) However, type raised categories are as immediately compatible with TAG under present assumptions as any other, and as we have seen they capture constructions like (37) without any ....

.... rules for abstraction or contraction over the verb anchoring initial trees) However, type raised categories are as immediately compatible with TAG under present assumptions as any other, and as we have seen they capture constructions like (37) without any additional apparatus at all (see also Joshi and Kulick 1996). This suggests that the tangled trees in Sarkar and Joshi s analysis of coordination via contraction could similarly be factored into an untangled tree like predicate argument structural component and a purely categorial component, using CCGTAG trees. The inclusion of type raised CCGTAG ....

Joshi, Aravind, and Seth Kulick. 1996. Partial Proof Trees as Building Blocks for a Categorial Grammar. Linguistics and Philosophy. (to appear).

....ones really go beyond the usual type logical approach. The syntactic analysis within such a paradigm consists in combining these modules into a complete proof net by a uniform set of plugging rules. This approach is related to the Partial Proof Trees as building blocks of a categorial grammar of Joshi and Kulick (1995), the main difference being the emphasis put on the geometric notion of Proof Net as in our first attempt (Lecomte and Retore 1995) Our main motivation is to obtain a general logical model in which it would be possible to embed other calculi like Lambek grammars on one side and Lexicalised Tree ....

Joshi, Aravind and Kulick, Seth. 1995. "Partial proof trees as building blocks for a categorial grammar". In G. V. Morrill and R. Oehrle, Formal Grammar, FoLLI, 138--149.

....There is some extent of a parallel here with formalisms allowing partial descriptions of lambda expressions, such as the Constraint Language over Lambda Structures of (Egg et al. 1998) used for underspecified semantics, which allows lambda bindings specified via dominance relations. 5 See (Joshi et al. 1997; Henderson, 1992) for other work connecting categorial formalisms (namely, the Lambek calculus and CCG, respectively) to tree oriented formalisms. Y Z is a Y missing Z somewhere and a type X#(Y Z) infixes its string to the position of the missing Z. Thus, a word w with type X#(Y Z) c.f. the ....

Joshi, A. & Kulick, S. 1997. `Partial proof trees as building blocks for a categorial grammar. ' Linguistics and Philosophy.

....components of formulae that would be associated as types with the lexical items in a typelogical grammar ( Mor 94] Proof nets are obtained by combining these modules by a uniform set of plugging rules. There are other approaches, based on Partiel Proof Trees as building blocks in a grammar ( Jos 95] our approach differs from them mainly by the emphasis put on the geometric notion of Proof Net (cf [Lec 95] Our main motivation is to obtain a very general and logical model in which it would be possible to embed other calculi like the Lambek grammars on one side and the Lexicalized Tree ....

Joshi, A. & Kulick, S.: 1995, Partial Proof Trees as Building Blocks for a Categorial Grammar, in Morrill & Oehrle (eds) Formal Grammar, Proceedings of the Conference of the European Summer School in Logic, Language and Information, Barcelona.

....We discuss in detail how the properties of Prolog are used for the implementation. 1 Introduction In this paper, we present some implementational aspects of a categorial grammar based on partial proof trees. The formal and linguistic aspects of such a system (PPTS) have been discussed by (Joshi and Kulick 1997). A prototype version of this system has been implemented in Prolog (Nadathur and Miller 1988) a logic programming language that supports higher order abstract syntax , an approach to representing syntax that allows for an elegant and declarative implementation of variable abstrac 0 We would ....

....complexity too much beyond that of CFGs, while still achieving polynomial parsability (i.e. the class of mildly context sensitive grammar formalisms (Joshi et al. 1990) Thus, EDL and FRD together lead from CFGs to LTAGs, with significant formal, linguistic, and computational properties. See (Joshi and Kulick 1997) for a thorough investigation of the consequences of incorporating these notions into a categorial grammar, leading to the system based on PPTs. We first give an overview in x2 of PPTS and its inference rules, followed by some illustrative examples in x3. x4 will detail some key aspects of ....

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Joshi, Aravind K., and Seth Kulick. 1997. Partial Proof Trees as Building Blocks for a Categorial Grammar. Linguistics and Philosophy. To appear.

....alone does not encode the syntactic environment in which it would be used in. A part of the proof tree needs to be specified to determine the ordering of the arguments. Thus the history of the derivation alone does not encode the dependency structure of the input. In the system described by Joshi and Kulick [1997], the primitive objects are partial proof trees that are formed from the categorial grammar categories by proof building operations. These proof trees, like LTAG trees, encode the possible orderings of the arguments in each syntactic environments they would be used in. In such a system the history ....

Aravind Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 1997. To appear.

....Bob NP likes (NP S) NP [NP] NP S) Hazel NP passionately [ NP S) NP S) NP S) NP S) NP S) S Fig. 1. Sample Partial Proof Tree Derivation 2 Partial Proof Trees When viewed from the context of categorial grammar, LTAG can be seen as a system of partial proof trees (PPTs) see [2] for details) The key idea is that instead of associating a type with each lexical item, we associate one or more partial proof trees, and each tree is obtained by unfolding the arguments of the type. The basic PPTs then serve as the building blocks of the grammar, and complex proof trees are ....

....simultaneously. Technically, however, they are two independent compositions and must occur in sequence, although it does not matter which order they occur in. Here we use the order of (A) stretching into (B) and (B) stretching into (C) 5 This suggestion had already been made previously in [2]. An alternative is to allow the verb and the NP argument to be co anchors of the tree. We leave this option aside for now. Aravind K. Joshi, Seth Kulick, and Natasha Kurtonina laten S NP S S (S NP S) S NP S] S S 1 S (S NP S) S [S] Piet S (S NP S) S NP S] S S (S NP S) ....

Aravind K. Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20:637--667, 1997.

....in the second logic, this allows for a semantic representation with terms embedded inside terms. We show that by allowing such terms to be moved to the outermost position, then compositionality can be maintained in the hybrid logic. There has recently been work by various authors (e. g, [2, 3, 5]) suggesting that a categorial grammar derivation can be reconceptualized by using a hybrid logic. One logic is used for unfolding a categorial type, resulting in what might be considered a partial derivation or a proofnet, depending on one s preference. A second logic is used to combine these ....

....computes using these representations. In this paper we address several issues related to the semantic compo1 [NP] S likes (NP S) NP [NP] NP S) Mary NP John NP Figure 1: Partial Proof Trees for John, likes, Mary sition of such a hybrid logic in the context of the system discussed by [2, 3]. Figure 1 illustrates a a simple case, for the sentence John likes Mary. The verb is unfolded into a partial proof with two unfilled assumptions, for the two NPs. Semantically, this can of course be seen as the usual lambda term (1) 1) obj: subj: like 0 subj obj) Each of the NPs is ....

Aravind K. Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20:637--667, 1997.

....and Hybrid Logic LTAG is a tree rewriting system and therefore deals with structural, and not string, adjacency. Being lexicalized, a structure is associated with each lexical item. When viewed from the context of categorial grammar, LTAG can be seen as a system of partial proof trees (PPTs) see [3] for more details than can be discussed here) The key idea is that instead of associating a type with each lexical item, we associate one or more partial proof trees, and each tree is obtained by unfolding the arguments of the 2 These considerations also hold for the CCG categorial system of ....

....which is locally discharged. This is a case of non peripheral extraction, a classic example of the use of a Permutation modality in categorial grammar. We show that hybridization of the inference allows us to avoid the use of the structural modality, and in general, it has been shown elsewhere ([3, 4]) that this approach allows the use of structural modalities to be in some cases eliminated and in other cases localized. The sequents in (3) model the derivation of the first part of the meets tree. For space reasons, we are not discussing the latter part of the tree with the use of who. The ....

Aravind K. Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20:637--667, 1997.

....LTAG are incorporated into a system of categorial inference (Partial Proof Tree System) namely, the extended domain of locality and consequent factoring of recursion from the domain of dependencies. In the categorial framework this leads to the use of a hybrid logic. It has been shown elsewhere ([2, 3]) that this approach allows the use of structural modalities to be in some cases eliminated and in other cases localized. In this paper we extend this argument, showing how the cross serial dependencies are derived without the need for such modalities. We give a brief description of the Partial ....

....of the logics for creating and combining the partial proof trees (PPTs) Section 1.4 then illustrates how this same idea is then used for the Dutch cross serial dependencies case. 1. 2 Partial Proof Trees When viewed from the context of categorial grammar, LTAG can be seen as a system of PPTs (see [2] for more detail than can be discussed here) The key idea is that instead of associating a type with each lexical item, we associate one or more partial proof trees, and each tree is obtained by unfolding the arguments of the type. Only arguments are unfolded not arguments of arguments. The ....

Aravind K. Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20:637--667, 1997.

....[NP] Bob NP likes (NP S) NP [NP] NP S) Hazel NP passionately [ NP S) NP S) NP S) NP S) NP S) S Fig. 1. Sample Partial Proof Tree Derivation 2 Partial Proof Trees When viewed from the context of categorial grammar, LTAG can be seen as a system of partial proof trees (PPTs) see [2] for details) The key idea is that instead of associating a type with each lexical item, we associate one or more partial proof trees, and each tree is obtained by unfolding the arguments of the type. The basic PPTs then serve as the building blocks of the grammar, and complex proof trees are ....

....There are some technical problems with this option, which we cannot discuss here. Note also that the simulation of verb raising in the tree for Jan zag is not necessary to derive the cross serial dependencies, although we have kept it here. 5 This suggestion had already been made previously in [2]. An alternative is to allow the verb and the NP argument to be co anchors of the tree. We leave this option aside for now. An LTAG Perspective on Categorial Inference 13 f. Jan s v 1 ) s (cut of d,e) 13) tree for Piet v 2 a. P iet s ) s=ff b. s=ff ff ) s c. P iet s ff ) s (cut of a,b) d. ....

Aravind K. Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20:637--667, 1997.

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Joshi, A., Kulick, S.: Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy 20 (1997) 637--667

No context found.

Aravind Joshi and Seth Kulick. Partial proof trees as building blocks for a categorial grammar. Linguistics and Philosophy, 20:637-667, 1997.

No context found.

Joshi, A. & S. Kulick (1995), `Partial proof trees as building blocks for a categorial grammar`. In [Morrill & Oehrle], 138--149.

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