Browsing by Author "Morrill, Glyn"
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A categorial type logic
Morrill, Glyn (2014)
Article
Open AccessIn logical categorial grammar [23,11] syntactic structures are categorial proofs and semantic structures are intuitionistic proofs, and the syntaxsemantics interface comprises a homomorphism from syntactic proofs to ... 
A count invariant for Lambek calculus with additives and bracket modalities
Valentín Fernández Gallart, José Oriol; Serret, Daniel; Morrill, Glyn (SpringerVerlag Berlin Heidelberg, 2013)
Conference report
Restricted access  publisher's policyThe count invariance of van Benthem (1991) 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 ... 
A note on movement in logical grammar
Morrill, Glyn (2018)
Article
Open AccessIn this article, we make some brief remarks on overt and covert movement in logical grammar. With respect to covert movement (e.g. quantification), we observe how a treatment in terms of displacement calculus interacts ... 
A polynomialtime algorithm for the Lambek calculus with brackets of bounded order
Kanovich, Max; Kuznetsov, Stepan; Morrill, Glyn; Scedrov, Andre (Dagstuhl Publishing, 2017)
Conference report
Open AccessLambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomialtime algorithm for determining provability of bounded depth ... 
A reply to Kubota and Levine on gapping
Valentín Fernández Gallart, José Oriol; Morrill, Glyn (201702)
Article
Open AccessIn a series of papers Kubota and Levine give an account of gapping and determiner gapping in terms of hybrid type logical grammar, including anomalous scopal interactions with auxiliaries and negative quantifiers. We make ... 
Clausal proof nets and discontinuity
Morrill, Glyn (199403)
External research report
Open AccessWe consider the task of theorem proving in Lambek calculi and their generalisation to "multimodal residuation calculi". These form an integral part of categorial logic, a logic of signs stemming from categorial grammar, ... 
Computational coverage of TLG : the Montague test
Morrill, Glyn; Valentín Fernández Gallart, José Oriol (2015)
Conference report
Open AccessThis paper reports on the empirical coverage of Type Logical Grammar (TLG) and on how it has been computer implemented. We analyse the Montague fragment computationally and we proffer this task as a challenge to computational ... 
Computational coverage of TLG: displacement
Morrill, Glyn; Valentín Fernández Gallart, José Oriol (2015)
Conference report
Open AccessThis paper reports on the coverage of TLG of Morrill (1994) and Moortgat (1997), and on how it has been computer implemented. We computeranalyse examples of displacement: discontinuous idioms, quantification, (medial) ... 
Computational coverage of TLG: nonlinearity
Morrill, Glyn; Valentín Fernández Gallart, José Oriol (2015)
Conference report
Open AccessWe study nonlinear connectives (exponentials) in the context of Type Logical Grammar (TLG). We devise four conservative extensions of the displacement calculus with brackets, Db!, Db!?, Db!b and Db!b?r which contain the ... 
Computational coverage of type logical grammar: The Montague test
Morrill, Glyn; Valentín Fernández Gallart, José Oriol (2016)
Conference report
Open AccessIt is nearly half a century since Montague made his contributions to the field of logical semantics. In this time, computational linguistics has taken an almost entirely statistical turn and mainstream linguistics has ... 
Countinvariance including exponentials
Kuznetsov, Stepan; Morrill, Glyn; Valentín Fernández Gallart, José Oriol (Association for Computational Linguistics, 2017)
Conference lecture
Restricted access  publisher's policyWe define infinitary countinvariance for categorial logic, extending countinvariance for multiplicatives (van Benthem, 1991) and additives and bracket modalities (Valentín et al., 2013) to include exponentials. This ... 
Difference lists and difference bags for logic programming of categorial deduction
Llore, F. X.; Morrill, Glyn (19950101)
External research report
Open AccessWe show how difference lists can be used for systematically compiled linear clauses for Lambek categorial grammar and its generalisations, in analogy with standard Horn clauses for CF grammar. We also consider use of ... 
Discontinuity and piedpiping in categorial grammar
Morrill, Glyn (199306)
External research report
Open AccessDiscontinuity refers to the phenomena in many natural language constructions whereby signs differ markedly in their prosodic and semantic forms. As such it presents interesting demands on monostratal computational formalisms ... 
Displacement logic for anaphora
Morrill, Glyn; Valentín Fernández Gallart, José Oriol (201403)
Article
Open AccessThe displacement calculus of Morrill, Valentín and Fadda (2011) [25] aspires to replace the calculus of Lambek (1958) [13] as the foundation of categorial grammar by accommodating intercalation as well as concatenation ... 
Dutch word order and binding
Morrill, Glyn (200010)
External research report
Open AccessThis paper offers a typelogical account of Dutch word order with special reference to quantifier binding in subordinate clauses. 
Generalising discontinuity
Morrill, Glyn; Merenciano Saladrigas, Josep Maria (199601)
External research report
Open AccessThis paper makes two generalisations of categorial calculus of discontinuity. In the first we introduce unary modalities which mediate between continuous and discontinuous strings. In the second each of the modes of ... 
Geometry of language
Morrill, Glyn (199710)
External research report
Open AccessGirard (1987) introduced proof nets as a syntax of linear proofs which eliminates inessential rule ordering manifested by sequent calculus. Proof nets adapted to the Lambek calculus (Roorda 1991) fulfill a role in ... 
Geometry of language and linguistic circuitry
Morrill, Glyn (200303)
External research report
Open AccessWe illustrate the potential for geometry of language and linguistic circuitry under the rendering of the syntactic structures of Lambek categorial grammar as proof nets. This empirical application sees sentences as proof ... 
Grammar logicised: relativisation
Morrill, Glyn (20170401)
Article
Open AccessMany variants of categorial grammar assume an underlying logic which is associative and linear. In relation to left extraction, the former property is challenged by island domains, which involve nonassociativity, and the ... 
Higherorder linear logic programming of categorial deduction
Morrill, Glyn (199410)
External research report
Open AccessWe show how categorial deduction can be implemented in (higherorder) linear logic programming, thereby realising parsing as deduction for the associative and nonassociative Lambek calculi. This provides a method of ...