Subregular Tree Transductions, Movement, Copies, Traces, and the Ban on Improper Movement

Extending prior work in Graf (2018, 2020, 2022c), I show that movement is tier-based strictly local (TSL) even if one analyzes it as a transformation, i.e. a tree transduction from derivation trees to output trees. I define input strictly local (ISL) tree-to-tree transductions with (lexical) TSL tests as a tier-based extension of ISL tree-to-tree transductions. TSL tests allow us to attach each mover to all its landing sites. In general, this class of transductions fails to attach each mover to its final landing site to the exclusion of all its intermediate landing sites, which is crucial for producing output trees with the correct string yield. The problem is avoided, though, if syntax enforces a variant of the Ban on Improper Movement. Subregular complexity thus provides a novel motivation for core restrictions on movement while also shedding new light on the choice between copies and traces in syntax

Modeling coupled thermohaline flow and reactive solute transport in discretely-fractured porous media

Tableau d’honneur de la Faculté des études supérieures et postdoctorales, 2005-2006Un modèle numérique tridimensionnel a été développé pour la simulation du système chimique quartz-eau couplé avec l’écoulement à densité et viscosité variable dans les milieux poreux discrètement fracturés. Le nouveau modèle simule aussi le transfert de chaleur dans les milieux poreux fracturés en supposant que l’expansion thermique du milieu est négligeable. Les propriétés du fluide, densité et viscosité, ainsi que les constantes chimiques (constant de taux de dissolution, constant d’équilibre, coefficient d’activité) sont calculées en fonction de la concentration des ions majeurs et de la température. Des paramètres de réaction et d’écoulement, comme la surface spécifique du minéral et la perméabilité sont mis jour à la fin de chaque pas de temps avec des taux de réaction explicitement calculés. Le modèle suppose que des changements de la porosite et des ouvertures de fractures n’ont pas d’impact sur l’emmagasinement spécifique. Des pas de temps adaptatifs sont utilisés pour accélérer et ralentir la simulation afin d’empêcher des résultats non physiques. Les nouveaux incréments de temps dépendent des changements maximum de la porosité et/ou de l’ouverture de fracture. Des taux de réaction au niveau temporel L+1 (schéma de pondération temporelle implicite) sont utilisés pour renouveler tous les paramètres du modèle afin de garantir la stabilité numérique. Le modèle a été vérifié avec des problèmes analytiques, numériques et physiques de l’écoulement à densité variable, transport réactif et transfert de chaleur dans les milieux poreux fracturés. La complexité de la formulation du modèle permet d’étudier des réactions chimiques et l’écoulement à densité variable d’une façon plus réaliste qu’auparavant possible. En premier lieu, cette étude adresse le phénomène de l’écoulement et du transport à densité variable dans les milieux poreux fracturés avec une seule fracture à inclinaison arbitraire. Une formulation mathématique générale du terme de flottabilité est dérivée qui tient compte de l’écoulement et du transport à densité variable dans des fractures de toute orientation. Des simulations de l’écoulement et du transport à densité variable dans une seule fracture implanté dans une matrice poreuse ont été effectuées. Les simulations montrent que l’écoulement à densité variable dans une fracture cause la convection dans la matrice poreuse et que la fracture à perméabilité élevée agit comme barrière pour la convection. Le nouveau modèle a été appliqué afin de simuler des exemples, comme le mouvement horizontal d’un panache de fluide chaud dans un milieu fracturé chimiquement réactif. Le transport thermohalin (double-diffusif) influence non seulement l’écoulement à densité variable mais aussi les réactions chimiques. L’écoulement à convection libre dépend du contraste de densité entre le fluide (panache chaud ou de l’eau salée froide) et le fluide de référence. Dans l’exemple, des contrastes de densité sont généralement faibles et des fractures n’agissent pas comme des chemins préférés mais contribuent à la dispersion transverse du panache. Des zones chaudes correspondent aux régions de dissolution de quartz tandis que dans les zones froides, la silice mobile précipite. La concentration de silice est inversement proportionnelle à la salinité dans les régions à salinité élevée et directement proportionnelle à la température dans les régions à salinité faible. Le système est le plus sensible aux inexactitudes de température. Ceci est parce que la température influence non seulement la cinétique de dissolution (équation d’Arrhenius), mais aussi la solubilité de quartz.A three-dimensional numerical model is developed that couples the quartz-water chemical system with variable-density, variable-viscosity flow in fractured porous media. The new model also solves for heat transfer in fractured porous media, under the assumption of negligible thermal expansion of the rock. The fluid properties density and viscosity as well as chemistry constants (dissolution rate constant, equilibrium constant and activity coefficient) are calculated as a function of the concentrations of major ions and of temperature. Reaction and flow parameters, such as mineral surface area and permeability, are updated at the end of each time step with explicitly calculated reaction rates. The impact of porosity and aperture changes on specific storage is neglected. Adaptive time stepping is used to accelerate and slow down the simulation process in order to prevent physically unrealistic results. New time increments depend on maximum changes in matrix porosity and/or fracture aperture. Reaction rates at time level L+1 (implicit time weighting scheme) are used to renew all model parameters to ensure numerical stability. The model is verified against existing analytical, numerical and physical benchmark problems of variable-density flow, reactive solute transport and heat transfer in fractured porous media. The complexity of the model formulation allows chemical reactions and variable-density flow to be studied in a more realistic way than previously possible. The present study first addresses the phenomenon of variable-density flow and transport in fractured porous media, where a single fracture of an arbitrary incline can occur. A general mathematical formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulations of variable-density flow and solute transport are conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the highpermeability fracture acts as a barrier for convection. The new model was applied to simulate illustrative examples, such as the horizontal movement of a hot plume in a chemically reactive fractured medium. Thermohaline (double-diffusive) transport impacts both buoyancy-driven flow and chemical reactions. Free convective flow depends on the density contrast between the fluid (hot brine or cool saltwater) and the reference fluid. In the example, density contrasts are generally small and fractures do not act like preferential pathways but contribute to transverse dispersion of the plume. Hot zones correspond to areas of quartz dissolution while in cooler zones, precipitation of imported silica prevails. The silica concentration is inversely proportional to salinity in high-salinity regions and directly proportional to temperature in low-salinity regions. The system is the most sensitive to temperature inaccuracy. This is because temperature impacts both the dissolution kinetics (Arrhenius equation) and the quartz solubility

Grammar Size and Quantitative Restrictions on Movement

Recently is has been proved that every Minimalist grammar can be converted into a strongly equivalent single movement normal form such that every phrase moves at most once in every derivation. The normal form conversion greatly simplifies the formalism and reduces the complexity of movement dependencies, but it also runs the risk of greatly increasing the size of the grammar. I show that no such blow-up obtains with linguistically plausible grammars that respect common constraints on movement. This establishes not only the cost-free nature of this normal form for realistic grammars, but also that the known restrictions on movement greatly reduce the range of licit movement configurations relative to what unconstrained Minimalist grammars are capable of. Moreover, this work constitutes a first step towards a quantitatively grounded view of movement

Curbing Feature Coding: Strictly Local Feature Assignment

Graf (2017) warns that every syntactic formalism faces a severe overgeneration problem because of the hidden power of subcategorization. Any constraint definable in monadic second-order logic can be compiled into the category system so that it is indirectly enforced as part of subcategorization. Not only does this kind of feature coding deprive syntactic proposals of their empirical bite, it also undermines computational efforts to limit syntactic formalisms via subregular complexity. This paper presents a subregular solution to feature coding. Instead of features being a cheap resource that comes for free, features must be assigned by a transduction. In particular, category features must be assigned by an input strictly local (ISL) tree-to-tree transduction, defined here for the first time. The restriction to ISL transductions correctly rules out various deviant category systems

Typological Implications of Tier-Based Strictly Local Movement

Earlier work has shown that movement, which forms the backbone of Minimalist syntax, belongs in the subregular class of TSL-2 dependencies over trees. The central idea is that movement, albeit unbounded, boils down to local mother-daughter dependencies on a specific substructure called a tree tier. This reveals interesting parallels between syntax and phonology, but it also looks very different from the standard view of movement. One may wonder, then, whether the TSL-2 characterization is linguistically natural. I argue that this is indeed the case because TSL-2 furnishes a unified analysis of a variety of phenomena: multiple wh-movement, expletive constructions, the that-trace effect and the anti-that-trace effect, islands, and wh-agreement. In addition, TSL-2 explains the absence of many logically feasible yet unattested phenomena. Far from a mere mathematical curiosity, TSL-2 is a conceptually pleasing and empirically fertile characterization of movement

Comparing Incomparable Frameworks: A Model Theoretic Approach to Phonology

In previous work, we used techniques from mathematical logic and model theory to study and compare two phonological theories, SPE and Government Phonology. The surprising result was that Government Phonology corresponds to a very weak fragment of SPE, yet it can attain the full expressivity of the latter through more powerful mechanisms of feature spreading. An issue that we didn\u27t elaborate on, however, is the question of what this increase in expressivity buys us in terms of empirical coverage, which we pick up in this paper. Again making good use of our model theoretic techniques, we investigate two phonological phenomena --- Sanskrit n-retroflexion and primary stress assignment in Creek and Cairene Arabic --- and show how much power feature spreading has to be granted in any descriptively adequate account which does not invoke additional technical machinery. These technical results are accompanied by reflections on the relation between empirically minded theory comparisons and the model theoretic approach

Diagnosing Movement via the Absence of C-command Relations

In this paper, we propose a new diagnostic for movement. It has been argued in the computational linguistics literature that some constraints can be formalized by path constraints on the sequence of their c-commanders (Graf and Shafiei 2019), and that some constraints can be formalized by the tree configuration they appear in (Graf and Heinz 2015). It holds that path constraints are a special case of tree constraints. We make the observation that path constraints cannot account for phenomena that have been argued to involve movement of the element requiring licensing, namely for ATB-extraction and parasitic gaps. However, the reverse does not hold: adjuncts islands and freezing effects, which also involve movement, can be formalized by path constraints. We thus propose the following one-way generalization: Whenever a phenomenon cannot be captured by path constraints, and can be captured by tree constraints, this phenomenon involves movement. We contend that this is not surprising given the fact that constraints on the well-formedness of the Move operation cannot be captured by path constraints, and rather must be captured by tree constraints (Graf 2018)

Multiple Wh-Movement is not Special: The Subregular Complexity of Persistent Features in Minimalist Grammars

Minimalist grammars have been criticized for their inability to analyze successive cyclic movement and multiple wh-movement in a manner that is faithful to the Minimalist literature. Persistent features have been proposed in the literature as a potential remedy (Stabler 2011, Laszakovits 2018). We show that not all persistent features are alike. The persistent features involved in multiple wh-movement do not increase subregular complexity, making this phenomenon appear very natural from the perspective of MGs. The persistent features in successive-cyclic movement, on the other hand, change the subregular nature of movement, favoring an alternative treatment along the lines of Kobele (2006

C-Command Dependencies as TSL String Constraints

We provide a general framework for analyzing c-command based dependencies in syntax, e.g. binding and NPI licensing, from a subregular perspective. C-command relations are represented as strings computed from Minimalist derivation trees, and syntactic dependencies are shown to be input-output tier-based strictly local over such strings. The complexity of many syntactic phenomena thus is comparable to dependencies in phonology and morphology