Morrill, G. (1994), Type Logical Grammar, Kluwer, Dordrecht. 3  Home/Search   Document Not in Database   Summary   Related Articles   Check

....make our proofs a bit more readable, we will typically use lexical word as structural variables. A structure term is then a tree of words. The natural deduction calculus for MMCL tells us how to combine proofs from an initial set of lexical assignments to produce phrases of different types. See [21] for a more detailed explanation and many linguistic applications of the Fitch style natural deduction calculus presented below. In the logical rules below X,Y,Z range over structure terms, A, B, C range over formulas and x, y are structural variables not occurring elsewhere in the proof. ....

G. Morrill. Type Logical Grammar. Dordrecht:Kluwer, 1994.

....a relational database, for example, requires an explicit recursive semantic composition process. This is why our deeper semantics in Prolog closely parallels that which a categori d analysis would furnish, i. e: using function application and composition over lambda forms, per treatments such as [11, 12] and using a semantic theory such as DRT [7] Such an approach allows one to compose a semantics in a principled manner and to interpret with respect to the domain model. Nevertheless, to this point, in an interface to a project and program scheduling system, we have attempted only to render ....

Morrill, Glyn. 1994. Type Logical Grammar. Dordrecht: Kluwer Academic.

....accounts for Weak Crossover violations. As mentioned above, binding to hypothetical antecedents is not restricted to quantification. Another obvious case in point is wh movement. There are several proposals for a type logical treatment of this complex around in the literature (see for instance [14, 17]) Despite the di#erences in detail, they share the assumption that a hypothesis is put into the base position of wh movement that is later discharged and bound by the operator. So we correctly predict the same patterns concerning the interaction of binding and scope and with respect to ....

....of cross sentential dynamic binding is thus essentially the same as for sentence internal binding. Other quantifiers like every man can be prevented from taking discourse scope by the same multimodal mechanisms that block them from outscoping and in coordinate structures (see for instance [17]) 7 Incremental Interpretation This treatment of cross sentential anaphora is compatible with the intuitive requirement that discourse interpretation works incrementally. Note that in all compositional theories of dynamic semantics, the meaning of a sentence includes someone lex q(N,I, ....

Morrill, G.: Type Logical Grammar. Kluwer (1994)

....99 as part of the workshop on Resource Logics and Minimalist Grammars (C.Retore E. Stabler, organizers) 1 In this paper we propose a formal approach to lexical information in the perspective of the recent extensions of Non commutative Linear Logic [1, 2, 3, 4] Following type logical grammars [17, 16] lexical items are treated as complex signs in which the phonological, syntactical and semantic dimensions are simultaneously considered and processed. We intend to show that the formal elegance and the appealing inferential properties of a type logical approach to the lexicon are nicely expressed ....

.... perspective we will treat head affixation (lexical or syntactic) where the affix may be a particle such as ri that, occurring before e.g. the transitive verb vedere (to see) produces the compound transitive verb rivedere (to see again) or a clitic, such 2 Following type logical grammars (e.g. [17] a lexical item is associated to three relevant types of information, that flow in parallel: phon, cat, sem , where phon is the phonological dimension, cat is the logical type and sem is the corresponding lambda term that introduces the semantic interpretation. Here however we will consider the ....

Morrill, G. (1994), Type Logical Grammar, Dordrecht, Kluwer.

....linguistic inference which is fine grained enough to give an adequate account of the forms of ellipsis that show up in coordinate constructions and comparatives. I present a unified account of Gapping in coordinate constructions and Subdeletion in clausal comparatives, improving on earlier work of Morrill (1994) and Moortgat (1991) In multimodal categorial type logic, a number of unimodal logics (Lambek systems) are combined into one system (cf. Moortgat 1994; Moortgat Oehrle 1994; Morrill 1994) Thus, families of type constructors with different resource management properties live together. Because ....

.... Gapping in coordinate constructions and Subdeletion in clausal comparatives, improving on earlier work of Morrill (1994) and Moortgat (1991) In multimodal categorial type logic, a number of unimodal logics (Lambek systems) are combined into one system (cf. Moortgat 1994; Moortgat Oehrle 1994; Morrill 1994). Thus, families of type constructors with different resource management properties live together. Because the individual resource management properties of the constituting unimodal logics are preserved, but at the same time the component logics interact with each other, the result is a system ....

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Morrill, Glyn (1994) Type Logical Grammar. Categorial Logic of Signs. Kluwer, Dordrecht.

....Fortunately, we can refer the interested reader to a number of monographs that deal with logical and linguistic aspects of the type logical approach in a more spacious manner. For the general logical background, Language in Action ( van Benthem 91,95] is essential reading. Type Logical Grammar ( Morrill 94a] situates the type logical approach within the framework of Montague s Universal Grammar and presents detailed linguistic analyses for a substantive fragment of syntactic and semantic phenomena in the grammar of English. Type Logical Semantics ( Carpenter 96] offers a general introduction to ....

....adjunction. In order to force the formation of the verb cluster, the type language has to be further refined. See [Moortgat Oehrle 94] for discussion, and 4.2 for the required logical vocabulary. For a second illustration, we take up the discussion of in situ binding of 3. It is shown in [Morrill 94a] that the connective q(A, B, C) can be defined in a multimodal system with three communicating modes: a (associative regime) n (non associative regime) and w (wrapping) The crucial interaction principle is given in (22) The deconstruction of Ex 4.5 partially answers the question raised in ....

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Morrill, G. (1994), Type Logical Grammar. Categorial Logic of Signs. Kluwer, Dordrecht.

....some systems in which variables do not occur. Binding in situ A central problem in the revival of the categorial grammar tradition since the 1980 s has been the search for an adequate formulation of general operations of extraction and infixation (Bach [1, 2] Moortgat [10, 11, 12] Morrill [14, 15]) We present the multimodal structural normalization approach of [12] after reviewing some of the steps that led up to this proposal. extraction and infixation operators. An initial attempt to tackle these issues in deductive terms can be found n Moortgat [10] where one finds extraction and ....

Morrill, G. (1994), Type Logical Grammar. Categorial Logic of Signs. Kluwer, Dordrecht.

....to LCG s which massively overgenerated strings, when compared to the natural languages they were intended to model. More recently, some linguists have augmented this classical calculus with various modalities to represent some of the more complex linguistic processes in a more constrained fashion [4, 11, 17, 18]. On the more formal side of computational linguistics, the weak equivalence of LCG s and CFG s has now been properly established [7, 19] renewing concern about efficient parsing algorithms for the Lambek calculus and about the theoretical complexity of parsing for it and related substructural ....

Morrill, G., 1994. Type-Logical Grammar. Kluwer, Dordrecht.

....platform for solving a number of syntactic phenomena which are traditionally regarded as an adequacy criterion for grammar formalisms. The list of such phenomena includes non constituent coordination, right and left node raising and peripheral extraction in relative clause constructions, see Morrill 1992, Steedman 1990. Nevertheless, there still remain constructions which, from the perspective of the Lambek calculus L, are still intractable such as, for example, topicalization or non peripheral extraction in relative clauses. The fundamental reason for the incapability of L is the directionality ....

Morrill, G. 1992. Type-logical Grammar. Research Institute for Language and Speech, Rijksuniversiteit Utrecht.

....and for the representation of the denotation of an utterance it does not matter in which order the arguments were found. In other words: bracketing can be omitted in the prosodics dimension, order is irrelevant for predicate argument structure. In sign based Categorial Grammar (Moortgat 1992, Morrill 1994), every lexical entry is represented by a sign that contains two dimensions: prosody and denotational semantics. The sign, the basic element of the framework, looks as follows: 20) h C : P) i where C = combinatorics; denotational semantics; P = prosody The combinatorics is the category as ....

....is not correct also. We want to be able to make a selection, and only use those values that apply in a given context. 5.4 The Calculus We will not go into detail about all the varieties of functional application that occur in the literature. For that we refer the reader to (Moortgat 1992) and (Morrill 1994) on Lambek style Categorial Grammar. What we claim with respect to functional application of a functor to an adjacent argument, may be generalized to any form of adjacent or non adjacent argument resolution. In order to have a complete calculus, we not only need to have rules for functional ....

Morrill, Glyn V. 1994. Type-logical Grammar. Dordrecht: Kluwer Academic Publishers.

.... problem which cannot be reduced to positing referential uses of indefinites cf. Farkas 1981, Abusch 1994) Various computational and formal systems have tackled this ambiguity problem, either, as is familiar, by positing processes of restructuring or storage (Montague 1974, Cooper 1983, May 1985, Morrill 1994, Pereira 1990) or by building underspecified structures including unscoped or partially scoped representations of quantified NPs (Alshawi Crouch 1992, Reyle 1993, Pereira Pollack 1991) In all of these cases, there is implicit recognition that the determination of scope choice is not ....

.... ; DONE: Ty(t) Form( Nu(b) 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 ....

Morrill, G. 1994. Type-logical Grammar . Kluwer.

.... both at the level of context (anaphora resolution) and also at the level of structure (wh gap binding) The approach is an extension of the parsing as deduction methodology familiar in both computational linguistics [Pereira Warren 1980] and categorial grammar [Moortgat 1988, Hepple 1990, Morrill 1994] Inference is defined over declarative units each of which consists This research was in part supported by the UK Engineering and Physical Sciences Research Council under grant reference GR K67397, A Labelled Deduction System for Natural Language Understanding and by the Economic and Social ....

.... 1994] or as part of the construction algorithm [Gabbay Kempson 1992, Doerre et al. 1996] ii) The directional operators are retained but additional operators are defined such as permutation, associativity or more recently infixing operations which locally remove their effect [Moortgat 1988, Morrill 1994] iii) Additional inference postulates are added to the axioms that define a basic set of combinatorial operators, which have the effect of mapping one string sequence into another [Steedman 1993] iv) Combinatorial processes over units larger than individual typed expressions can be defined, ....

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Morrill, G. 1994. Type-logical Grammar. Kluwer.

....A task may spawn new (sub)tasks. The goal of the entire procedure is the satisfaction of the top level task with goal type t, at the last word of a string. The steps involved in the satisfaction of such tasks include steps of type deduction (modus ponens) but, unlike categorial grammars (eg [Mor94]) such familiar deductive steps form but one type of transition from task state to task state. At the conclusion of a successful parse the satisfied tasks can be seen to label a (parse) tree. 2 Data Structures The object of our parser is the compilation of logical formulas. This determines the ....

....as a mechanism of upward feature percolation. Like categorial grammar analyses, the basic mode of combination is type deduction, and wh expressions are defined to ensure the combination of the content projected by the wh expression with expressions with which it is not contiguous (cf eg [Moo88] [Mor94]) However unlike categorial grammar accounts, this is not defined through some suitable type assignment, and no semantic mode of combination is defined between the wh expression and its sister expressions in the string. Seen in the most general terms, the account we have proposed presents the ....

Morrill, G. 1994. Type-Logical Grammar. Kluwer, Dordrecht.

....phenomena begin to exceed the natural coverage of a formalism, more powerful mechanisms are typically introduced. 2 Multimodal Categorial Grammar The general paradigm of multimodal categorial grammars was introduced by Moortgat [1994] following earlier multimodal developments by Hepple [1990] Morrill [1991, 1994], and Moortgat and Oehrle [1994] The fundamental idea underlying these systems is that languages allow many different modes of combination for linguistic expressions (which have often been called resources in the literature, following common usage in linear logic) In addition to Lambek s [1958, ....

....concatenation, several additional mechanisms have been proposed. For instance, commutative operations have been applied to free word order languages [Hepple 1990; Moortgat and Oehrle 1994] wrapping and infixing have been used to deal with scoping and unbounded dependencies [Moortgat 1991; Morrill 1994, 1995] and to deal with gapping and ellipsis [Solias 1992] In some systems, unary modes of combination have been used to deal with permuting for unbounded dependencies [Morrill 1994] islands and locality constraints [Hepple 1990; Morrill 1990, 1994] for encoding syntactic features [Kraak ....

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Morrill, G. 1994. Type-Logical Grammar. Kluwer Academic Publishers, Dordrecht.

....is to associate 2 Alain Lecomte, Christian Retor# with each lexical item one or more modules which encode(s) its syntactic behaviour. The simplest of these modules are obtained by unfolding the components of formulae that would be the type(s) of the lexical items in a type logical grammar # la Morrill (1994), while the more sophisticated 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 ....

G. V. Morrill. 1994 , Type Logical Grammar. Dordrecht and Hingham: Kluwer.

....Fortunately, we can refer the interested reader to a number of monographs that deal with logical and linguistic aspects of the type logical approach in a more spacious manner. For the general logical background, Language in Action ( van Benthem 91,95] is essential reading. Type Logical Grammar ( Morrill 94a] situates the type logical approach within the framework of Montague s Universal Grammar and presents detailed linguistic analyses for a substantive fragment of syntactic and semantic phenomena in the grammar of English. Type Logical Semantics ( Carpenter 96] offers a general introduction to ....

....head adjunction. In order to force the formation of the verb cluster, the type language has to be further refined. See [Moortgat Oehrle 94] for discussion, and x4.2 for the required logical vocabulary. For a second illustration, we take up the discussion of in situ binding of x3. It is shown in [Morrill 94a] that the connective q(A; B; C) can be defined in a multimodal system with three communicating modes: a (associative regime) n (non associative regime) and w (wrapping) The crucial interaction principle is given in (22) The deconstruction of Ex 4.5 partially answers the question raised in x3: ....

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Morrill, G. (1994), Type Logical Grammar. Categorial Logic of Signs. Kluwer, Dordrecht.

....the IGPL, Vol. 5 No. 5, pp. 647 671 1997 c # Oxford University Press 648 Parsing Natural Language using LDS: A Prototype structure (wh gap binding) The approach is an extension of the parsing as deduction methodology familiar in both computational linguistics [37] and categorial grammar [29, 16, 33]. Inference is defined over declarative units each of which consists of a pair: a type logical formula and an algebraic label . The label has two constituents, namely the formula s semantic interpretation and a list containing any extra control specifications on the step of inference to be ....

.... restrictions either within the prosodic algebra directly [35] or as part of the construction algorithm [11, 8] ii) The directional operators are retained but additional operators are defined such as permutation, associativity or more recently infixing operations which locally remove their e#ect [29, 33]. iii) Additional inference postulates are added to the axioms that define a basic set of combinatorial operators, which have the e#ect of mapping one string sequence into another [43] iv) Combinatorial processes over units larger than individual typed expressions can be defined, giving a ....

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Morrill, G. 1994. Type-logical Grammar. Kluwer.

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COLING 14. 1095-9 Morrill, G. (1994). Type-logical Grammar. Kluwer.

....as a functor over a functor over e.g. commutable N: R (S 4N) We will argue that the latter approach probably offers most prospects for treatments including domains which are semi islandlike. One way of increasing the discriminatory power of basic Lambek calculus is to add universal modality (Morrill 1989, 1990). Where certain functors are of category B= A, inducing a modal domain on their argument, a higher order functor C= D=E) can only exercise a dependency into the modal domain if E itself is modalised, i.e. is of the form E 0 . For such effects to be made to work however each lexical category ....

....S 12, 13 En 15. Mary likes Fred and John dislikes Bill : S 11, 14 En 16. Mary likes Fred and John dislikes Bill : S 15 E Figure 10: Derivation of Mary likes Fred and John dislikes Bill VP (S(VPffl4N) rather than simply VP S, where VP is ( NnS) For use of the disjunction see Morrill (1990, 1992) which explains how the semantics is conditioned to the different syntactic categories. The approach adopted here resolves a puzzle in a common British English dialect which allows the object or accusative relative pronoun whom to bind downstairs subject nominative positions, but ....

Morrill, Glyn: 1992a, `Type-Logical Grammar', working paper, OTS, Utrecht, and report de reserca LSI--92--5--R, Departament de Llenguatges i Sistemes Inform`atics, Universitat, Polit`ecnics de Catalunya. Monograph to appear in 36 the series Studies in Language, Logic and Information, Kluwer, Dordrecht.

....categorial logic, is the last word in lexicalism. Consequence is fixed model theoretically and rules of formation are only used in proof theoretic calculi (of which there can be many kinds) of the formalism. For substantive background to this approach see Moortgat (1988b) van Benthem (1991) and Morrill (1992). The aim of the present paper is to demonstrate application of the framework developed more theoretically in these references to the formal specification of a significant fragment. This is after all the point of a grammar This work was supported by a scholarship for estancies temporales de ....

....(see Dos, en 1990a) This scheme originated with the modalities ( of course ) and (why not ) of linear logic. Drawing on this, Morrill, et al. 1990) and Barry et al. 1991) propose permutation structural modalities for medial relativisation. An approach to the interpretation is offered in Morrill (1992, Chaper VI) and pursued in Venema (1992) but logic of structural modalities in general is not yet a resolved issue. Here we choose a simpler approach, proceeding with a binary operator proposed by Moortgat (1988b) 29) If A and B are category formulas, A B is a category formula; 30) t ....

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Morrill, G. (1992), Type-Logical Grammar, Report de Recerca, Departament de Llenguatges i Sistemes Informtics, Universitat Politcnica de Catalunya and Working Paper, OTS, Rijksuniversiteit Utrecht. Research monograph to appear in the series Studies in Language, Logic and Information, Kluwer Academic Publishers, Dordrecht.

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Morrill, G. (1994), Type Logical Grammar, Kluwer, Dordrecht. 3

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G. Morrill. Type Logical Grammar. Dordrecht:Kluwer, 1994.

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Morrill, Type-logical grammar. Kluwer.

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Morrill, G., Type Logical Grammar, Kluwer, Dordrecht, 1994

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Morrill, G., Type Logical Grammar, Kluwer, Dordrecht, 1994

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