Disjunctive Statements Research Articles

GOTzilla: Efficient Disjunctive Zero-Knowledge Proofs from MPC in the Head, with Application to Proofs of Assets in Cryptocurrencies

We present gOTzilla, a protocol for interactive zero-knowledge proofs for very large disjunctive statements of the following format: given publicly known circuit C, and set of values Y = {y1 , . . . , yn }, prove knowledge of a witness x such that C(x) = y1 ∨ C(x) = y2 ∨ · · · ∨ C(x) = yn . These type of statements are extremely important for the proof of assets (PoA) problem in cryptocurrencies where a prover wants to prove the knowledge of a secret key sk that associates with the hash of a public key H(pk) posted on the ledger. We note that the size of n in popular cryptocurrencies, such as Bitcoin, is estimated to 80 million. For the construction of gOTzilla, we start by observing that if we restructure the proof statement to an equivalent of proving knowledge of (x, y) such that (C(x) = y) ∧ (y = y1 ∨ · · · ∨ y = yn )), then we can reduce the disjunction of equalities to 1-out-of-N oblivious transfer (OT). Our overall protocol is based on the MPC in the head (MPCitH) paradigm. We additionally provide a concrete, efficient extension of our protocol for the case where C combines algebraic and non-algebraic statements (which is the case in the PoA application). We achieve an asymptotic communication cost of O(log n) plus the proof size of the underlying MPCitH protocol. While related work has similar asymptotic complexity, our approach results in concrete performance improvements. We implement our protocol and provide benchmarks. Concretely, for a set of size 1 million entries, the total run-time of our protocol is 14.89 seconds using 48 threads, with 6.18 MB total communication, which is about 4x faster compared to the state of the art when considering a disjunctive statement with algebraic and non-algebraic elements.

Exploring Natural Language Processing in Model-To-Model Transformations

In this paper, we explore the possibility to apply natural language processing in visual model-to-model (M2M) transformations. Therefore, we present our research results on information extraction from text labels in process models modeled using Business Process Modeling Notation (BPMN) and use case models depicted in Unified Modeling Language (UML) using the most recent developments in natural language processing (NLP). In this paper, we focus on three relevant tasks, namely, the extraction of verb/noun phrases that would be used to form relations, parsing of conjunctive/disjunctive statements, and the detection of abbreviations and acronyms. Relation extraction was attempted to solve by implementing techniques that combine state-of-the-art NLP language models with formal regular expressions grammar-based structure detection. In this paper, we perform thorough testing of the most recent state-of-the-art NLP tools (CoreNLP, Stanford Stanza, Flair, Spacy, AllenNLP, BERT, ELECTRA), as well as custom BERT-BiLSTM-CRF and ELMo-BiLSTM-CRF implementations, trained with certain data augmentations to improve performance on the most ambiguous cases; these tools are used as a foundation for building tools to extract noun and verb phrases from short text labels generally used in UML and BPMN models. Furthermore, we describe our attempts to improve these extractors by solving the abbreviation/acronym detection problem using machine learning-based detection, as well as process conjunctive and disjunctive statements, due to their relevance to performing advanced text normalization. The obtained results show that the best phrase extraction and conjunctive phrase processing performance was obtained using Stanza based implementation, yet, our trained BERT-BiLSTM-CRF outperformed it for the verb phrase detection task. Our acronym detection approach resulted in the precision of 0.78 and F1-Score of 0.73 which may also be considered quite positive. While this work was inspired by our ongoing research on partial model-to-model transformations, we believe it to be applicable in other areas requiring similar text processing capabilities as well.

Do Children Interpret ‘or’ Conjunctively?

AbstractPreschoolers often struggle to compute scalar implicatures involving disjunction (or), in which they are required to strengthen an utterance by negating stronger alternatives, e.g. to infer that, ‘The girl has an apple or an orange’ likely means she does not have both. However, recent reports surprisingly find that a substantial subset of children interpret disjunction as conjunction, concluding instead that the girl must have both fruits. According to these studies, children arrive at conjunctive readings not because they have a non-adult-like semantics, but because they lack access to the stronger scalar alternative and, and employ doubly exhaustified disjuncts when computing implicatures. Using stimuli modelled on previous studies, we test English-speaking preschoolers and replicate the finding that many children interpret or conjunctively. However, we speculate that conditions which replicate this finding may be pragmatically infelicitous, such that results do not offer a valid test of children’s semantic competence. We show that when disjunctive statements are uttered in contexts that render the speaker’s intended question more transparent, conjunctive readings disappear almost entirely.

Hurford\u2019s constraint, the semantics of disjunction, and the nature of alternatives

This paper contributes to two recent lines of work on disjunction: on the one hand, work on so-called Hurford disjunctions, i.e., disjunctions where one disjunct entails another, and on the other hand, work in alternative and inquisitive semantics where disjunction has been argued to generate multiple propositional alternatives. We point out that Hurford effects are found not only in disjunctive statements, but also in disjunctive questions. These cases are not covered by the standard accounts of Hurford phenomena, which assume a truth-conditional treatment of disjunction. We show that inquisitive semantics facilitates a unified explanation of Hurford phenomena in statements and questions. We also argue that Hurford effects provide an empirical handle on the subtle differences between inquisitive semantics and alternative semantics, providing insight into the notion of alternatives and the notion of meaning adopted in these two frameworks.

Children's knowledge of free choice inferences

This paper presents experimental results showing that four-year-old Mandarin- speaking children draw free choice inferences from disjunctive statements, though they are not able to compute inferences of exclusivity for disjunctive statements or other scalar implicatures. The findings connect to those of Chemla & Bott (under review) who report differences in how adults process free choice inferences versus scalar implicatures and, prima facie, the findings pose a challenge to treatments that attempt to unify inferences of both kinds. Instead, the findings appear to favour accounts that invoke different analyses for each kind of inference, such as Zimmerman 2000a, Geurts 2005, and Barker 2010. The results, however, also support the recent approach in the experimental literature which attributes children’s failures to compute scalar implicatures to a difficulty with alternatives: children may lack the lexical knowledge of alternatives, or these implicatures impose such a high processing cost that children are unable to handle the alternatives necessary to compute them (Gualmini, Crain, Meroni, Chierchia & Guasti 2001 Chierchia, Crain, Guasti & Thornton 2001 Reinhart 2006; Barner, Brooks & Bale 2011; Singh, Wexler, Astle, Kamawar & Fox 2012). If accessing alternatives is the source of children’s difficulty, then they would be expected to perform better if the requisite alternatives are made explicit, as sub-strings of the asserted sentences. This is exactly what we found. Children were able to compute free choice inferences based on alternatives that were made explicit in the assertion, but children were unable to compute ‘regular’ scalar implicatures arising from alternatives lacking this property. We discuss the implications of these findings for the debate about the relationship between free choice inferences and scalar implicatures and children’s knowledge of alternatives.

Children's Knowledge of Free Choice Inferences and Scalar Implicatures

This article presents experimental results showing that 4- and 5-year-old children are capable of drawing free choice inferences from disjunctive statements and from statements containing free choice indefinites, despite not being able to compute inferences of exclusivity for disjunctive statements, or other scalar implicatures. The findings appear to challenge accounts that attempt to unify the two kinds of inferences (Kratzer & Shimoyama 2002; Alonso Ovalle 2005; Fox 2007; Klinedinst 2007; Chemla 2010; van Rooij 2010; Franke 2011; Chierchia 2013). We discuss, however, the compatibility of the child data with a recent approach in the experimental literature, which attributes children's failures to compute scalar implicatures to a difficulty with alternatives (Chierchia et al. 2001; Gualmini et al. 2001; Reinhart 2006; Barner et al. 2011; Singh et al. 2013). Based on the results of two experiments, we propose an explanation for children's selective success on scalar inferences, according to which scalar inferences are generally unproblematic for children, unless they necessitate lexical retrieval of the required alternatives.

Uniform Interpolation and Forgetting for ALC Ontologies with ABoxes

Uniform interpolation and the dual task of forgetting restrict the ontology to a specified subset of concept and role names. This makes them useful tools for ontology analysis, ontology evolution and information hiding. Most previous research focused on uniform interpolation of TBoxes. However, especially for applications in privacy and information hiding, it is essential that uniform interpolation methods can deal with ABoxes as well. We present the first method that can compute uniform interpolants of any ALC ontology with ABoxes. ABoxes bring their own challenges when computing uniform interpolants, possibly requiring disjunctive statements or nominals in the resulting ABox. Our method can compute representations of uniform interpolants in ALCO. An evaluation on realistic ontologies shows that these uniform interpolants can be practically computed, and can often even be presented in pure ALC.

Children's knowledge of free choice inferences

This paper presents experimental results showing that four-year-old Mandarin- speaking children draw free choice inferences from disjunctive statements, though they are not able to compute inferences of exclusivity for disjunctive statements or other scalar implicatures. The findings connect to those of Chemla & Bott (under review) who report differences in how adults process free choice inferences versus scalar implicatures and, prima facie, the findings pose a challenge to treatments that attempt to unify inferences of both kinds. Instead, the findings appear to favour accounts that invoke different analyses for each kind of inference, such as Zimmerman 2000a, Geurts 2005, and Barker 2010. The results, however, also support the recent approach in the experimental literature which attributes children’s failures to compute scalar implicatures to a difficulty with alternatives: children may lack the lexical knowledge of alternatives, or these implicatures impose such a high processing cost that children are unable to handle the alternatives necessary to compute them (Gualmini, Crain, Meroni, Chierchia & Guasti 2001 Chierchia, Crain, Guasti & Thornton 2001 Reinhart 2006; Barner, Brooks & Bale 2011; Singh, Wexler, Astle, Kamawar & Fox 2012). If accessing alternatives is the source of children’s difficulty, then they would be expected to perform better if the requisite alternatives are made explicit, as sub-strings of the asserted sentences. This is exactly what we found. Children were able to compute free choice inferences based on alternatives that were made explicit in the assertion, but children were unable to compute ‘regular’ scalar implicatures arising from alternatives lacking this property. We discuss the implications of these findings for the debate about the relationship between free choice inferences and scalar implicatures and children’s knowledge of alternatives.

False Dilemma: A Systematic Exposition

False dilemma is a specific form of reasoning: despite the fact that it is based on a deductively valid argument form, it is rightly depicted as fallacy. A systematic exposition of false dilemma is missing in theoretical approaches to fallacies. This article formulates six criteria for a well-grounded exposition of a fallacy, suggesting also a systematic exposition of false dilemma. These criteria can be used to both explain, and categorise, the various false dilemma fallacies. The article introduces distinction between four types of false dilemma (and the respective subtypes): (1) False quandary, (2) Defeasible sound quandary, (3) False obstruction and (4) Defeasible sound obstruction. The types of criticism appropriate for each variant of false dilemma are suggested. Being able to discover false dilemma in situations when it is important to make good and free choices is a significant dimension of critical thinking. It may liberate us from accepting the consequences that necessarily follow from prearranged alternatives, when these are not the only alternatives possible. It may also liberate us from refraining from actions on the basis of obstructive disjunctive statements. In that respect, the faculty of critical thinking directed at uncovering reasoning based on false dilemma may also initiate the discovery of new alternatives, or discover the ways of unifying seemingly opposing alternatives. Thus, a well-developed ability to understand the tricky argumentative moves of false dilemma may be a good step towards initiating some features of creative thinking.

Improving Robustness via Disjunctive Statements in Imperative Programming

To deal with failures as simply as possible, we propose a new foundation for the core (untyped) C++, which is based on a new logic called task logic or imperative logic. We then introduce a sequential-disjunctive statement of the form S : R. This statement has the following semantics: execute S and R sequentially. It is considered a success if at least one of S, R is a success. This statement is useful for dealing with inessential errors without explicitly catching them.

A reappraisal of classical archetype theory and its implications for theory and practice

This paper begins with an overview of contemporary approaches to archetype theory and notes the radical nature of certain deductions. Some argue that there is no 'archetype-as-such' as a pre-existing entity at the core of a complex driving its formation whilst the findings of current neuroscience are calling into question one very thing on which the classical theory is built--innatism. Knox's argument for image schemas raises the question as to the extent to which archetypes can be conceived in any preformationist sense. The question is then posed--to what extent can Jung's classical theory of archetypes be read in light of these current models? The case examples Jung uses to evidence the existence of archetypes, his explications of synchronicity and his own Philemon experience are then reappraised. The conclusion is drawn that it is difficult to evidence the existence of autonomous archetypes unrelated to personal affective experience. Not only would this be expected by emergent/developmental models of archetype but it can explain many of Jung's disjunctive statements about archetype constellation; the difficulties in separating personal and collective psychic content and Jung's apparent Lamarckianism. The implications of these models for theory, clinical practice and analyst training are then offered for discussion.

The Image of Thought

The image of thought that Rembrandt proposes with his Philosopher in Meditation still wears the mask of the old philosophical pedagogy based on ascent and the heights, but it ushers in new percepts and affects corresponding to the philosopher's concept, fold, that Leibniz elevates to the status of the principle of Baroque variation. The fold unleashes a power that carries forms and statements over a variety of disjunctive statements.

Making disjunctions exclusive

This work examines how people interpret the sentential connective "or", which can be viewed either inclusively (A or B or both) or exclusively (A or B but not both). Following up on prior work concerning quantifiers (Bott & Noveck, 2004; Noveck, 2001; Noveck & Posada, 2003), which shows that the common pragmatic interpretation of "some", some but not all, is conveyed as part of an effortful step, we investigate how extra effort applied to disjunctive statements leads to a pragmatic interpretation of "or", or but not both. Experiment 1 compelled participants to wait for three seconds before answering, hence giving them the opportunity to process the utterance more deeply. Experiments 2 and 3 emphasized "or", either by visual means ("OR") or by prosodic means (contrastive stress) as another way to encourage participants to apply more effort. Following a relevance-theoretic line of argument, we hypothesized that conditions encouraging more processing effort would give rise to more pragmatic inferences and hence to more exclusive interpretations of the disjunction. This prediction was confirmed in the three experiments.

The Interpretation of Disjunction in Universal Grammar

Child and adult speakers of English have different ideas of what 'or' means in ordinary statements of the form 'A or B'. Even more far-reaching differences between children and adults are found in other languages. This tells us that young children do not learn what 'or' means by watching how adults use 'or'. An alternative is to suppose that children draw upon a priori knowledge of the meaning of 'or'. This conclusion is reinforced by the observation that all languages adopt the same meaning of 'or' in certain structures. For example, statements of the form 'not S[A or B]' have the same meanings in all languages, and disjunctive statements receive a uniform interpretation in sentences that contain certain focus expressions, such as English 'only'. These observations are relevant for the long-standing "nature versus nurture" controversy. A linguistic property that (a) emerges in child language without decisive evidence from experience, and (b) is common to all human languages, is a likely candidate for innate specification. Experience matters, of course. As child speakers grow up, they eventually learn to use 'or' in the same way as adults do. But, based on findings from child language and cross-linguistic research, it looks like certain aspects of language, including the interpretation of disjunction, are part of the human genome.

Reasoning with Realistic Disjunctives

The research reported here investigated how people interpret and reason with disjunctive statements. Experiment 1 demonstrated a general preference for exclusive over inclusive interpretations, although this varied as a function of the context in which the statement occurred, and there were some contexts in which other, quite different, interpretations were possible. Experiments 2 and 3 showed that the logical inferences subjects would draw from disjunctive statements also varied with context. It is concluded that or permits a number of different interpretations, which are determined by contextual cues. Previous research may have underestimated disjunctive reasoning performance by using contexts that lead to non-logical responses; certainly in the present experiments reasoning was generally accurate given the interpretation adopted.