Papers by Diego Gabriel Krivochen
Biolinguistics, Mar 1, 2023
This paper examines Minimal Search, an operation that is at the core of current Minimalist inquir... more This paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered setformation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore, some problematic configurations for Minimal Search (namely, {XP, YP} and {X, Y}) are argued to be an artefact of these set-theoretic commitments. However, if unordered sets are given up as the format of structural descriptions in favour of directed graphs such that Merge(X, Y) creates an arc from X to Y, Minimal Search can be straightforwardly characterised as a sequential deterministic search algorithm: the total order required to define MS as a sequential search algorithm is provided by structure building.
Folia Linguistica, 2024
Generative syntax was built on the foundations of Immediate Constituent (IC) analysis, and IC met... more Generative syntax was built on the foundations of Immediate Constituent (IC) analysis, and IC methods and heuristics were an important tool in the early days of the generative enterprise. However, developments in the theory entailed a departure from some fundamental IC assumptions: we will argue that structural descriptions in contemporary generative grammar (transformational and non-transformational) define not constituents, but strictly ordered sequences closer to arrays. We therefore define and characterise IC approaches to syntax as opposed to what we will call Array-Based (AB) approaches. IC grammars define distributional generalisations, and proper containment and is-a relations between indexed distributionally defined categories. AB grammars, in contrast, define strictly ordered sequences of categories. In this paper we introduce and define the fundamental properties of IC grammar, and the changes in the generative theory that introduced arrays in phrase structure. We argue that it is crucial to distinguish between IC and AB grammars when evaluating the empirical adequacy of structural descriptions used in current syntactic theorising, as structures in AB and IC grammars represent different relations between expressions and may be better suited for different purposes.
John Benjamins Publishing Company eBooks, Dec 15, 2021
Evolutionary Linguistic Theory 5(2), 2024
In this paper we provide an introduction to a set of tools for syntactic analysis based on graph ... more In this paper we provide an introduction to a set of tools for syntactic analysis based on graph theory, and apply them to the study of some properties of English accusativus cum infinitivo constructions, more commonly known as 'raising to object' or' exceptional case marking' structures. We focus on puzzling extraction asymmetries between base-generated objects and ‘raised’ objects and on the interaction between raising to object and Right Wrap. We argue that a lexicalised derivational grammar with grammatical functions as primitives delivers empirically adequate analyses.
Aahus University Library eBooks, 2019
To appear in Oxford Handbook of Iconicity, 2024
In this paper we analyse the place of iconicity in the architecture of a generative grammar, in r... more In this paper we analyse the place of iconicity in the architecture of a generative grammar, in relation to the notion of diagrammatic iconicity. We will present the fundamental assumptions of current generative grammar about the relations between syntax, morpho-phonology, and semantics, and discuss the problems that arise when attempting to include a semiotic dimension in the generative architecture.
The Linguistic Review
Recent work on structure building and mapping in Minimalist syntax makes explicit reference to wo... more Recent work on structure building and mapping in Minimalist syntax makes explicit reference to workspaces; however, it is still an underexplored area. This paper is an attempt to (a) analyse the notion of ‘workspace’ as used in current Minimalist syntax and (b) provide a definition of ‘syntactic workspace’ that can help us capture interesting empirical phenomena. In doing this, we confront set-theoretic and graph-theoretic approaches to syntactic structure in terms of the operations that can affect syntactic objects and how their properties are related to the definition of workspace. We analyse the consequences of conceptualising ‘syntax’ as a set of operations that affect local regions of the workspace, defining directed graphs.
Borealis: An international journal of Hispanic linguistics, 2022
En este trabajo examinaremos análisis existentes de las oraciones de relativo
(principalmente re... more En este trabajo examinaremos análisis existentes de las oraciones de relativo
(principalmente restrictivas), y propondremos un análisis para las relativas españolas desde la perspectiva de una gramática de adjunción (TAG) lexicalizada. Presentaremos un panorama de las principales propuestas existentes y examinaremos las preguntas a las que todo análisis de las oraciones de relativo debe responder. La propuesta que desarrollamos aquí sintetiza las ventajas descriptivas y teóricas de los modelos existentes (el análisis de núcleo externo, el análisis de ascenso, y el análisis de correspondencia), y ofrece una solución a algunos de los principales problemas que
han sido observados anteriormente en la bibliografía. Nos ocuparemos de la configuración interna de las oraciones de relativo, de su posición estructural, y de la categoría de la expresión 'que' en español.
Frontiers in Psychology, 2019
This paper presents an experimental study investigating artificial grammar learning in monolingua... more This paper presents an experimental study investigating artificial grammar learning in monolingual and bilingual children, with and without dyslexia, using an original methodology. We administered a serial reaction time task, in the form of a modified Simon task, in which the sequence of the stimuli was manipulated according to the rules of a simple Lindenmayer grammar (more specifically, a Fibonacci grammar). By ensuring that the subjects focused on the correct response execution at the motor stage in presence of congruent or incongruent visual stimuli, we could meet the two fundamental criteria for implicit learning: the absence of an intention to learn and the lack of awareness at the level of resulting knowledge. The participants of our studies were four groups of 10-year-old children: 30 Italian monolingual typically developing children, 30 bilingual typically developing children with Italian L2, 24 Italian monolingual dyslexic children, and 24 bilingual dyslexic children with Italian L2. Participants were administered the modified Simon task developed according to the rules of the Fibonacci grammar and tested with respect to the implicit learning of three regularities: (i) a red is followed by a blue, (ii) a sequence of two blues is followed by a red, and (iii) a blue can be followed either by a red or by a blue. Results clearly support the hypothesis that learning took place, since participants of all groups became increasingly sensitive to the structure of the input, implicitly learning the sequence of the trials and thus appropriately predicting the occurrence of the relevant items, as manifested by faster reaction times in predictable trials. Moreover, group differences were found, with bilinguals being overall faster than monolinguals and dyslexics less accurate than controls. Finally, an advantage of bilingualism in dyslexia was found, with bilingual dyslexics performing consistently better than monolingual dyslexics and, in some conditions, at the level of the two control groups. These results are taken to suggest that bilingualism should be supported also among linguistically impaired individuals.
Isogloss, 2022
Spanish auxiliary sequences as in 'Juan puede haber tenido que estar empezando a trabajar hasta t... more Spanish auxiliary sequences as in 'Juan puede haber tenido que estar empezando a trabajar hasta tarde' 'Juan may have had to be starting to work until late', traditionally termed auxiliary chains, have two properties that are not naturally captured in phrasestructure approaches to syntax: (i) they follow no a priori fixed order; auxiliary permutations have different meanings, none of which is any more basic than any other (cf. 'Juan puede estar trabajando' 'Juan may be working' and 'Juan está pudiendo trabajar' 'Juan is currently able to work'); and (ii) the syntactic and semantic relations established within a chain go beyond strict monotonicity or cumulative influence; rather, they present different kinds of syntactic relations in distinct local domains. We show that an alternative to syntax grounded in a modification of the categorial grammar introduced in Ajdukiewicz (1935) that closely follows Montague (1973), Dowty (1978, 1979, 2003), and Schmerling (1983a, b, 2019) provides effective tools for subsuming Spanish auxiliary chains in an explicit and explanatory grammar.
This paper examines English sentences with go, up, or take as an apparent first conjunct, which w... more This paper examines English sentences with go, up, or take as an apparent first conjunct, which we term pivots, and demonstrates that they fail all tests for involving either true-or pseudo-coordination. Semantically, each generates a conventional implicature specific to it: Go and sentences implicate a lack of 7 concern on the part of the subject for consequences of the event expressed in 8 the apparent second conjunct, up and sentences implicate that the event expressed in the apparent second conjunct is both sudden and unexpected, and take and sentences, the most complex of the three types, implicate that the 11 subject plays an active role in coercion towards an accomplishment interpretation of the apparent second conjunct. Syntactically, pivot-and sequences are modifiers of the verb in the apparent second conjunct.
Studia Anglica Posnaniensia, 2019
This paper deals with the syntactic and semantic properties of a specific kind of anaphoric devic... more This paper deals with the syntactic and semantic properties of a specific kind of anaphoric device (AD) in English, instantiated by Prn+SELF lexical items (himself/herself/itself…; ‘SELF’ henceforth), which do not behave like anaphors in the sense of Binding Theory either syntactically or semantically. These devices have received the name of intensives in the grammatical literature (Leskosky 1972; Siemund 2000, among many others). We will look at the syntactic behaviour of so-called intensives in different syntactic contexts, and refine the classification of these ADs taking into consideration (a) how each type of intensive is derived, (b) the kinds of syntactic rules that can affect them, and (c) their meaning.
Revista Española de Lingüística, 2019
Borealis – An International Journal of Hispanic Linguistics, 2019
Chains of auxiliary verbs in Spanish allow for the reconceptualization of well-known grammatical ... more Chains of auxiliary verbs in Spanish allow for the reconceptualization of well-known grammatical problems under the light of understudied structures. In this paper we will deal with issues regarding the position of subjects in declarative and interrogative sentences featuring auxiliary chains. It will become immediately evident that the dichotomy between pre- and post-verbal subjects results inadequate to provide adequate characterisations for the Spanish cases, in contrast to the situation in English. This is so because post-verbal subjects may appear, a priori, to the right of each auxiliary in a chain. These new data, which have received little attention, constitute a challenge for standard hypotheses about the position of subjects in Spanish.
Studies in Hispanic and Lusophone Linguistics, 2022
In this work we analyse some aspects of the interaction between coordination and clitic climbing ... more In this work we analyse some aspects of the interaction between coordination and clitic climbing in Spanish sentences with auxiliary verbs. We aim at shedding light on three kinds of structures, or ‘scenarios’: (1) those in which we find coordinated auxiliaries taking a single lexical verb as complement (Puede y debe hacerlo); (2) those in which a single auxiliary takes coordinated lexical verbs as complement (estás molestándonos y mirándonos), and (3) those in which coordinated
auxiliaries take coordinated lexical verbs as complement (puede y debe
terminarlo y entregarlo). Our proposal will involve a combination of Gapping and Across-the-Board rule application for Scenarios (1) and (2) and Right Node Raising for Scenario (3). We will argue that well-known syntactic constraints on long distance dependencies, such as those proposed in Ross (1967), can account for the facts without the need for ad hoc machinery.
Plos One, 2020
In this paper we probe the interaction between sequential and hierarchical learning by investigat... more In this paper we probe the interaction between sequential and hierarchical learning by investigating implicit learning in a group of school-aged children. We administered a serial reaction time task, in the form of a modified Simon Task in which the stimuli were organised following the rules of two distinct artificial grammars, specifically Lindenmayer systems: the Fibonacci grammar (Fib) and the Skip grammar (a modification of the former). The choice of grammars is determined by the goal of this study, which is to investigate how sensitivity to structure emerges in the course of exposure to an input whose surface transitional properties (by hypothesis) bootstrap structure. The studies conducted to date have been mainly designed to investigate low-level superficial regularities, learnable in purely statistical terms, whereas hierarchical learning has not been effectively investigated yet. The possibility to directly pinpoint the interplay between sequential and hierarchical learning is instead at the core of our study: we presented children with two grammars, Fib and Skip, which share the same transitional regularities, thus providing identical opportunities for sequential learning, while crucially differing in their hierarchical structure. More particularly, there are specific points in the sequence (k-points), which, despite giving rise to the same transitional regularities in the two grammars, support hierarchical reconstruction in Fib but not in Skip. In our protocol, children were simply asked to perform a traditional Simon Task, and they were completely unaware of the real purposes of the task. Results indicate that sequential learning occurred in both grammars, as shown by the decrease in reaction times throughout the task, while differences were found in the sensitivity to k-points: these, we contend, play a role in hierarchical reconstruction in Fib, whereas they are devoid of structural significance in Skip. More particularly, we found that children were faster in correspondence to k-points in sequences produced by Fib, thus providing an entirely new kind of evidence for the hypothesis that implicit learning involves an early activation of strategies of hierarchical reconstruction, based on a straightforward interplay with the statistically-based computation of transitional regularities on the sequences of symbols.
Philosophies, 2021
Contemporary generative grammar assumes that syntactic structure is best described in terms of se... more Contemporary generative grammar assumes that syntactic structure is best described in terms of sets, and that locality conditions, as well as cross-linguistic variation, is determined at the level of designated functional heads. Syntactic operations (merge, MERGE, etc.) build a structure by deriving sets from lexical atoms and recursively (and monotonically) yielding sets of sets. Additional restrictions over the format of structural descriptions limit the number of elements involved in each operation to two at each derivational step, a head and a non-head. In this paper, we will explore an alternative direction for minimalist inquiry based on previous work, e.g., Frank (2002, 2006), albeit under novel assumptions. We propose a view of syntactic structure as a specification of relations in graphs, which correspond to the extended projection of lexical heads; these are elementary trees in Tree Adjoining Grammars. We present empirical motivation for a lexicalised approach to structure building, where the units of the grammar are elementary trees. Our proposal will be based on cross-linguistic evidence; we will consider the structure of elementary trees in Spanish, English and German. We will also explore the consequences of assuming that nodes in elementary trees are addresses for purposes of tree composition operations, substitution and adjunction.
Biolinguistics, 2023
This paper examines Minimal Search, an operation that is at the core of current Minimalist inquir... more This paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered set formation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore, some problematic configurations for Minimal Search (namely, {XP, YP} and {X, Y}) are argued to be an artefact of these set-theoretic commitments. However, if unordered sets are given up as the format of structural descriptions in favour of directed graphs such that Merge(X, Y) creates an arc from X to Y, Minimal Search can be straightforwardly characterised as a sequential deterministic search algorithm: the total order required to define MS as a sequential search algorithm is provided by structure building.
Linguistic Frontiers
In this paper, we will motivate the application of specific rules of inference from the propositi... more In this paper, we will motivate the application of specific rules of inference from the propositional calculus to natural language sentences. Specifically, we will analyse De Morgan’s laws, which pertain to the interaction of two central topics in syntactic research: negation and coordination. We will argue that the applicability of De Morgan’s laws to natural language structures can be derived from independently motivated operations of grammar and principles restricting the application of these operations. This has direct empirical consequences for the hypothesised relations between natural language and logic.
Canadian Journal of Linguistics/Revue canadienne de linguistique, 2017
Some years ago, one of the authors of this squib was working in a large organization with many la... more Some years ago, one of the authors of this squib was working in a large organization with many layers of management. It often happened that a manager who usually performed certain functions was unavailable to do so, and those functions were performed by a so-called backup, who was authorized to perform them in the manager's absence. It was common for a backup performing such a function to say a sentence like (1) to other employees, and those other employees might speak of the occasion using a sentence like (2).
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Papers by Diego Gabriel Krivochen
(principalmente restrictivas), y propondremos un análisis para las relativas españolas desde la perspectiva de una gramática de adjunción (TAG) lexicalizada. Presentaremos un panorama de las principales propuestas existentes y examinaremos las preguntas a las que todo análisis de las oraciones de relativo debe responder. La propuesta que desarrollamos aquí sintetiza las ventajas descriptivas y teóricas de los modelos existentes (el análisis de núcleo externo, el análisis de ascenso, y el análisis de correspondencia), y ofrece una solución a algunos de los principales problemas que
han sido observados anteriormente en la bibliografía. Nos ocuparemos de la configuración interna de las oraciones de relativo, de su posición estructural, y de la categoría de la expresión 'que' en español.
auxiliaries take coordinated lexical verbs as complement (puede y debe
terminarlo y entregarlo). Our proposal will involve a combination of Gapping and Across-the-Board rule application for Scenarios (1) and (2) and Right Node Raising for Scenario (3). We will argue that well-known syntactic constraints on long distance dependencies, such as those proposed in Ross (1967), can account for the facts without the need for ad hoc machinery.
(principalmente restrictivas), y propondremos un análisis para las relativas españolas desde la perspectiva de una gramática de adjunción (TAG) lexicalizada. Presentaremos un panorama de las principales propuestas existentes y examinaremos las preguntas a las que todo análisis de las oraciones de relativo debe responder. La propuesta que desarrollamos aquí sintetiza las ventajas descriptivas y teóricas de los modelos existentes (el análisis de núcleo externo, el análisis de ascenso, y el análisis de correspondencia), y ofrece una solución a algunos de los principales problemas que
han sido observados anteriormente en la bibliografía. Nos ocuparemos de la configuración interna de las oraciones de relativo, de su posición estructural, y de la categoría de la expresión 'que' en español.
auxiliaries take coordinated lexical verbs as complement (puede y debe
terminarlo y entregarlo). Our proposal will involve a combination of Gapping and Across-the-Board rule application for Scenarios (1) and (2) and Right Node Raising for Scenario (3). We will argue that well-known syntactic constraints on long distance dependencies, such as those proposed in Ross (1967), can account for the facts without the need for ad hoc machinery.
This work is a study of the nature of cognitive computation, with a focus on the relation between computation, linguistic theory, and grammar. We review traditional notions of computation and analyse their applicability to natural language, distinguishing the latter from formal languages as these are usually studied in computer science.
The main theoretical result of the thesis is that imposing a single computational template for the assignment of structural descriptions to natural language sentences, while long accepted, is both empirically inadequate and theoretically more costly than a strongly cyclic approach in which computational dependencies vary, oscillating up and down the Chomsky Hierarchy of formal grammars. Specifically, we defend the idea that such a system delivers the simplest possible structural description that captures semantic dependencies between syntactic objects in local substrings. This hypothesis will be referred to as the theory of mixed computation. The analysis of theories of computation starting with the seminal work of Alan Turing (1936) will reveal that the theory of computable functions must not be identified with the theory of effective computation; this then permits us to argue for the necessity of introducing aspects of interaction in the study of physically realized computational procedures which configure dynamical systems. We show that mixed computation lends itself naturally to modelling dynamical systems.
Empirically, we present evidence for mixed computation derived from an analysis of strong locality conditions in natural language syntax, that is, locality constraints whose violation cannot be repaired or ameliorated. Specifically, we set our focus on the Coordinate Structure Constraint (Ross, 1967), which pertains to the extraction of terms from coordinated structures and how it can be shown to arise from a mixed-computation analysis. Data from English, Spanish, and Latin support the identification of two kinds of coordinated structures: one is finite state in nature, and cannot be probed into. The other is phrase structural (context-free), and its internal complexity is visible to further syntactic operations, including extraction. We argue that data from locality conditions as well as cyclicity in natural-language syntax are accounted for naturally under a dynamical model of mixed computation.
Es importante notar que el libro no trata sobre los aspectos cognitivos o biológicos relacionados con la teoría generativa, ni tampoco sobre cuestiones de adquisición, o patología del lenguaje, aunque todos ellos sean aspectos que han recibido tratamiento dentro del programa generativo: el foco del presente libro es la historia del desarrollo de la teoría de la sintaxis y su relación con aspectos formales de computación, a la vez que con las teorías de la semántica y la morfofonología. No se trata de un manual de gramática, ni de una introducción a la lingüística general. Se verá en detalle cómo ha cambiado la concepción de la sintaxis en gramática generativa transformacional, lo que es y lo que hace, en el paso de reglas particulares a principios generales. El objetivo es que el lector adquiera las herramientas teóricas y metodológicas para acceder a los textos especializados en cualquiera de los modelos generativo-transformacionales. Se presentan, además, traducciones al español de citas tomadas de textos especializados que resultan cruciales para entender el desarrollo de la teoría, traducciones que en todos los casos nos pertenecen.
segunda edición de las Jornadas de Jóvenes Investigadores de la Antigüedad
Grecolatina (JIJIAG), llevadas a cabo en la Facultad de Filosofía y Letras de
la Universidad de Buenos Aires los días 1 y 2 de agosto de 2013. En
continuidad con la primera edición, las Jornadas tuvieron como objetivo
principal construir un espacio de discusión sobre temáticas relacionadas con la
Antigüedad Grecolatina desde el ámbito de la Filosofía, la Historia, las Letras,
la Antropología y la Arqueología. En ellas contamos con la participación de
una gran cantidad de expositores y asistentes de diversas áreas de los estudios
clásicos, que fortalecieron con sus colaboraciones el carácter de diálogo
interdisciplinario al que las Jornadas aspiran.
En un intento por continuar generando un ámbito de intercambio
académico entre los asistentes, en esta edición de las Jornadas se propusieron
dos paneles de discusión para los cuales fueron convocadas la Dra. Claudia
Mársico y la Dra. Elsa Rodríguez como investigadoras, y la profesora María
Eugenia Steinberg, la Dra. Liliana Pégolo y la Dra. María Elena Díaz para
integrar el panel de discusión sobre Didáctica de los estudios clásicos. En
ambos casos se abordaron de forma dinámica y en diálogo con los asistentes
temas de profundo interés para los estudiantes y graduados en estudios
clásicos. Las Jornadas contaron también con dos conferencias a cargo de la
Dra. María Angélica Fierro y al Dr. Carlos García Mac Gaw respectivamente,
y con el Taller a cargo del Dr. Emiliano Buis "Haz el humor, no la guerra.
Repercusiones y variaciones cómicas de la performance bélica en el teatro de
Aristófanes", que con amplia asistencia dio cierre a las Jornadas.
En relación con la organización del presente volumen, hemos distribuido
los trabajos que lo integran en los siguientes ejes temáticos: “Economía y
sociedad”, “Estrategias discursivas: retórica, verdad y persuasión”, “Kósmos,
phýsis y metaphysiká: aproximaciones a las percepciones de la realidad”,
“Poder, política y gobierno” y “Religión y culto”. De esta forma intentamos
respetar la distribución original y reflejar el carácter interdisciplinario y
polisémico del encuentro.
In this seminar we will examine the consequences of adopting a strictly graph-theoretic approach to the analysis of sentence structure in natural languages which departs from traditional (transformational and non-transformational) theories of syntax in a number of ways. We will define the expressions and relations that make up the grammar of a language in graph-theoretic terms and examine some of the empirical consequences of our approach.
Conditions that emerge from the dynamics of the computation as well as external conditions restrict the space of possible complex objects (explored by Piattelli-Palmarini in his talk, also Medeiros & Piattelli-Palmarini, 2018). We argue that these dynamics are common to several cognitive systems, including -but not limited to- language, and there is evidence to suggest that assuming a single mode of information encoding misses important features of these systems. We propose that systems can oscillate between modes of representing information, as driven by the complexity of the input and the availability of limited resources. Furthermore, we will explore the architectural conditions that give rise to such systems. A fundamental organisational principle that results in systems with the properties just described is one of the building blocks of chaotic regimes: the existence of a tension between mutually incompatible tendencies or conditions that hold simultaneously for a dynamical system, a dynamical frustration (Binder, 2008). We contend that information compression and frustration are manifestations of ‘Natural Law’ shaping cognitive systems.
The main theoretical result of the thesis is that imposing a single computational template for the assignment of structural descriptions to natural language sentences is not only empirically inadequate, but also theoretically more costly than assuming a strongly cyclic approach in which computational dependencies vary, oscillating up and down the Chomsky Hierarchy of formal grammars. The idea that the grammar assigns substrings the simplest possible structural description that captures semantic dependencies between syntactic objects will be referred to as mixed computation. The analysis of theories of computation will reveal that the theory of computable functions must not be identified with the theory of effective computation, and we will argue for the necessity to introduce aspects of interaction in the study of physically realized computational procedures, which configure dynamical systems of a very specific kind: those defined by the irreconcilable tension between opposing requirements.
12/08/2015: Slightly revised version.
v. 1.0.2: Numeration fixed. Also, minor corrections.
In this paper we attempt a logic-mathematical formalization of the program for (linguistic) investigation that we have called Radical Minimalism, in order to make the model fully explicit and reveal its potential to be applied not only sub-personally and to the language domain exclusively, but to any physical system one considers. For those purposes, we have devised a logical model of syntax (understood as a general-purpose free and unbounded generative algorithm), with which we capture the properties of mental workspaces and the cognitive organization of the phenomenological reality. We will combine our Strong Radically Minimalist Thesis with Tegmark’s (2007) Mathematical Universe Hypothesis, and analyze how both strengthen in interaction gaining in empirical coverage and theoretical weight. The aim is to formalize a possibility for the study of language as a physical system from an interdisciplinary perspective: a joint work between Formal Linguistics, Logic, Physics and Mathematics.
Corrected version: 'Verbos de Ascenso como Expresiones Modales'
Parts of this paper are included in "The Syntax and Semantics of the Nominal Construction" (2012, Peter Lang Publishing Company)
Appendix A: Some considerations about 'distance' in Minimalism
Appendix B: Restricting the probing space