121 research outputs found
Higher-order Linear Logic Programming of Categorial Deduction
We show how categorial deduction can be implemented in higher-order (linear)
logic programming, thereby realising parsing as deduction for the associative
and non-associative Lambek calculi. This provides a method of solution to the
parsing problem of Lambek categorial grammar applicable to a variety of its
extensions.Comment: 8 pages LaTeX, uses eaclap.sty, to appear EACL9
Geometry of language and linguistic circuitry
We 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 nets and words as partial proof nets, and well-formedness/meaningfulness as a global harmony of categorial syntactic connection. The global cohesion coincides with a dynamic connectivity remaniscent of circuits, but whereas circuits are just generalisations of formulas, our syntactic structures are much more sublime objects: proofs.Postprint (published version
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
A note on movement in logical grammar
In 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 with normal modalities for intensionality to allow a
coding in logical grammar of the distinction between weak and strong
quantifiers (i.e. those that may or may not scope nonlocally such as
a and every respectively). With respect to overt movement (e.g. relativisation), we observe how displacement calculus can support a
coding of a linear filler-gap dependency similar to that employed in
lambda grammars, but we argue that this general approach does not
extend to either the multiplicity nor the island-sensitivity of parasitic
gaps, for which we advocate instead treatment in terms of a bracket-conditioned contraction subexponential.Peer ReviewedPostprint (published version
Grammar logicised: relativisation
Many 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 latter property is challenged by parasitic gaps, which involve nonlinearity. We present a version of type logical grammar including ‘structural inhibition’ for nonassociativity and ‘structural facilitation’ for nonlinearity and we give an account of relativisation including islands and parasitic gaps and their interaction.Peer ReviewedPostprint (published version
Parsing/theorem-proving for logical grammar CatLog3
CatLog3 is a 7000 line Prolog parser/theorem-prover for logical categorial grammar. In such logical categorial grammar syntax is universal and grammar is reduced to logic: an expression is grammatical if and only if an associated logical statement is a theorem of a fixed calculus. Since the syntactic component is invariant, being the logic of the calculus, logical categorial grammar is purely lexicalist and a particular language model is defined by just a lexical dictionary. The foundational logic of continuity was established by Lambek (Am Math Mon 65:154–170, 1958) (the Lambek calculus) while a corresponding extension including also logic of discontinuity was established by Morrill and ValentÃn (Linguist Anal 36(1–4):167–192, 2010) (the displacement calculus). CatLog3 implements a logic including as primitive connectives the continuous (concatenation) and discontinuous (intercalation) connectives of the displacement calculus, additives, 1st order quantifiers, normal modalities, bracket modalities, and universal and existential subexponentials. In this paper we review the rules of inference for these primitive connectives and their linguistic applications, and we survey the principles of Andreoli’s focusing, and of a generalisation of van Benthem’s count-invariance, on the basis of which CatLog3 is implemented.Peer ReviewedPostprint (author's final draft
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
Geometry of language
Girard (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 categorial grammar analogous to that of phrase structure trees in
CFG so that categorial proof nets have a central part to play in
computational syntax and semantics; in particular they allow a
reinterpretation of the "problem" of spurious ambiguity as an
opportunity for parallelism. This article aims to make three
contributions: i) provide a tutorial overview of categorial proof
nets, ii) apply and provide motivation for proof nets by showing how
a partial execution eschews the need for semantic evaluation in
language processing, and iii) analyse the intrinsic geometry of
partially commutative proof nets for the kinds of discontinuity
attested in language, offering proof nets for the in situ binder
type-constructor Q(., ., .) of Moortgat (1991/6).Postprint (published version
- …