arXiv subjects

Oriol Valentín

Publications and source records attributed to Oriol Valentín.

6 recordsLinked to original sources

arXiv2026

Logical Computational Linguistics

In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type logical grammar, and adds new ideas and material. Chains of statistical dependencies of less than one hundred per cent confidence tend monotonically to zero. Chains of logical dependencies of any length maintain one hundred per cent confidence end to end. We aspire to enable perfect syntactic and semantic processing in life-critical NLP applications.

cs.CL↗

arXiv2017

Models for the Displacement Calculus

The displacement calculus $\mathbf{D}$ is a conservative extension of the Lambek calculus $\mathbf{L1}$ (with empty antecedents allowed in sequents). $\mathbf{L1}$ can be said to be the logic of concatenation, while $\mathbf{D}$ can be said to be the logic of concatenation and intercalation. In many senses, it can be claimed that $\mathbf{D}$ mimics $\mathbf{L1}$ in 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 $\mathbf{D}$ and prove some completeness results; strikingly, we see that these results and proofs are natural extensions of the corresponding ones for $\mathbf{L1}$.

cs.LO↗

arXiv2017

Computational Coverage of TLG: Nonlinearity

We study nonlinear connectives (exponentials) in the context of Type Logical Grammar (TLG). We devise four conservative extensions of the displacement calculus with brackets, DbC, DbCM, DbCb and DbCbMr which contain the universal and existential exponential modalities of linear logic (LL). These modalities do not exhibit the same structural properties as in LL, which in TLG are especially adapted for linguistic purposes. The universal modality ! for TLG allows only the commutative and contraction rules, but not weakening, whereas the existential modality ? allows the so-called (intuitionistic) Mingle rule, which derives a restricted version of weakening. We provide a Curry-Howard labelling for both exponential connectives. As it turns out, controlled contraction by ! gives a way to account for the so-called parasitic gaps, and controlled Mingle ? iteration, in particular iterated coordination. Finally, the four calculi are proved to be Cut-Free, and decidability is proved for a linguistically sufficient special case of DbCbMr (and hence DbCb).

cs.LO↗

arXiv2015

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.

cs.LO↗

arXiv2013

The Hidden Structural Rules of the Discontinuous Lambek Calculus

The sequent calculus sL for the Lambek calculus L (lambek 58) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus (Morrill and Valentín), which like sL has no structural rules, is also equivalent to an omega-sorted multimodal calculus mD. More concretely, we present a faithful embedding translation between mD and hD in such a way that it can be said that hD absorbs the structural rules of mD.

cs.LO↗

arXiv2010

Displacement Calculus

The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus, a generalization of Lambek calculus, which preserves its good proof-theoretic properties while embracing discontinuiity and subsuming it. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability

cs.CL↗