56 research outputs found
Multiplicative-Additive Focusing for Parsing as Deduction
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar
may assign the same structural reading, resulting in redundancy in the parse
search space and inefficiency in parsing. Understanding the problem depends on
identifying the essential mathematical structure of derivations. This is
trivial in the case of context free grammar, where the parse structures are
ordered trees; in the case of categorial grammar, the parse structures are
proof nets. However, with respect to multiplicatives intrinsic proof nets have
not yet been given for displacement calculus, and proof nets for additives,
which have applications to polymorphism, are involved. Here we approach
multiplicative-additive spurious ambiguity by means of the proof-theoretic
technique of focalisation.Comment: In Proceedings WoF'15, arXiv:1511.0252
Computational coverage of type logical grammar: The Montague test
It 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 adopted an almost entirely non-formal methodology. But in a minority approach reaching back before the linguistic revolution, and to the origins of computing, type logical grammar (TLG) has continued championing the flags of symbolic computation and logical rigor in discrete grammar. In this paper, we aim to concretise a measure
of progress for computational grammar in the form of the Montague Test. This is the challenge of providing a computational cover grammar of the Montague fragment. We formulate this Montague Test and show how the challenge is met by the type logical parser/theorem-prover CatLog2.Peer ReviewedPostprint (published version
A reply to Kubota and Levine on gapping
In 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 three observations: i) under the counterpart assumptions that Kubota and Levine make, the existent displacement type logical grammar account of gapping already accounts for the scopal interactions, ii) Kubota and Levine overgenerate determiner-verb order permutations in determiner gapping conjuncts whereas the immediate adaptation of their proposal to displacement type logical grammar does not do so, and iii) Kubota and Levine do not capture simplex gapping as a special case of complex gapping, but require distinct lexical entries for the two cases; we show how a generalisation of displacement type logical grammar allows both simplex and discontinuous gapping under a single type assignmentPostprint (author's final draft
Models for the displacement calculus
The displacement calculus D is a conservative extension of the Lambek calculus L* (with empty antecedent allowed in sequents). L* can be said to be the logic of concatenation, while D can be said to be the logic of concatenation and intercalation. In many senses, it can be claimed that D mimics L*, namely that the proof theory, generative capacity and complexity of the former calculus are natural extensions of the latter calculus. In this paper, we strengthen this claim. We present the appropriate classes of models for D and prove its completeness results, and strikingly, we see that these results and proofs are natural extensions of the corresponding ones for L*.Peer ReviewedPostprint (published version
Spurious ambiguity and focalization
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on identifying the essential mathematical structure of derivations. This is trivial in the case of context free grammar, where the parse structures are ordered trees; in the case of type logical categorial grammar, the parse structures are proof nets. However, with respect to multiplicatives, intrinsic proof nets have not yet been given for displacement calculus, and proof nets for additives, which have applications to polymorphism, are not easy to characterize. In this context we approach here multiplicative-additive spurious ambiguity by means of the proof-theoretic technique of focalization.Peer ReviewedPostprint (published version
Semantically inactive multiplicatives and words as types
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.Peer ReviewedPostprint (author’s final draft
Theory of discontinuous Lambek calculus
Aquesta tesi s'emmarca dins del camp de la lingüÃstica matemà tica, concretament en la branca de la gramà tica lògica de tipus, disciplina Ãntimament relacionada amb la teoria de la demostració. En aquest treball es proposa un cà lcul o lògica substructural, anomenat cà lcul discontinu de lambek, que intenta tractar amb èxit el problema de la discontinuïtat, que és un fenomen molt estès en totes les llengües naturals. Al llarg del llibre s'analitzen i es demostren diverses propietats del cà lcul discontinu de Lambek, la qual cosa dóna fe de la seva bondat matemà tica. Finalment, mitjançant aquest cà lcul estudiem en detall una sèrie de fenòmens lingüÃstics de naturalesa discontÃnuaThis is a thesis in Mathematical Linguistics, namely in Proof Theory. Its main contribution is the conception of the Discontinuous Lambek calculus (D henceforth), an intuitionistic substructural logic. This calculus (or logic) tries to face the problem of discontinuity, which is pervasive in natural languages. In this work, several mathematical results on proof-theoretical aspects, soundness/completeness theorems and generative power are formulated and proved. This represents, we think, a remarkable achievement. Finally, the logic machinery developped through the book allows a study in depth of several discontinuous linguistic phenomena
Computational coverage of TLG : the Montague test
This 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 grammar: the Montague TestPeer ReviewedPostprint (author's final draft
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