Formula Language Research Articles

Analyzing and supporting mental representations and strategies in solving Bayesian problems.

Solving Bayesian problems poses many challenges, such as identifying relevant numerical information, classifying, and translating it into mathematical formula language, and forming a mental representation. This triggers research on how to support the solving of Bayesian problems. The facilitating effect of using numerical data in frequency format instead of probabilities is well documented, as is the facilitating effect of given visualizations of statistical data. The present study not only compares the visualizations of the 2 × 2 table and the unit square, but also focuses on the results obtained from the self-creation of these visualizations by the participants. Since it has not yet been investigated whether the better correspondence between external and internal visualization also has an effect on cognitive load when solving Bayesian tasks, passive and active cognitive load are additionally measured. Due to the analog character and the proportional representation of the numerical information by the unit square, it is assumed that the passive cognitive load is lower when using the unit square as visualization than when using the 2 × 2 table. The opposite is true for active cognitive load.

FlashFill++: Scaling Programming by Example by Cutting to the Chase

Programming-by-Examples (PBE) involves synthesizing an "intended program" from a small set of user-provided input-output examples. A key PBE strategy has been to restrict the search to a carefully designed small domain-specific language (DSL) with "effectively-invertible" (EI) operators at the top and "effectively-enumerable" (EE) operators at the bottom. This facilitates an effective combination of top-down synthesis strategy (which backpropagates outputs over various paths in the DSL using inverse functions) with a bottom-up synthesis strategy (which propagates inputs over various paths in the DSL). We address the problem of scaling synthesis to large DSLs with several non-EI/EE operators. This is motivated by the need to support a richer class of transformations and the need for readable code generation. We propose a novel solution strategy that relies on propagating fewer values and over fewer paths. Our first key idea is that of "cut functions" that prune the set of values being propagated by using knowledge of the sub-DSL on the other side. Cuts can be designed to preserve completeness of synthesis; however, DSL designers may use incomplete cuts to have finer control over the kind of programs synthesized. In either case, cuts make search feasible for non-EI/EE operators and efficient for deep DSLs. Our second key idea is that of "guarded DSLs" that allow a precedence on DSL operators, which dynamically controls exploration of various paths in the DSL. This makes search efficient over grammars with large fanouts without losing recall. It also makes ranking simpler yet more effective in learning an intended program from very few examples. Both cuts and precedence provide a mechanism to the DSL designer to restrict search to a reasonable, and possibly incomplete, space of programs. Using cuts and gDSLs, we have built FlashFill++, an industrial-strength PBE engine for performing rich string transformations, including datetime and number manipulations. The FlashFill++ gDSL is designed to enable readable code generation in different target languages including Excel's formula language, PowerFx, and Python. We show FlashFill++ is more expressive, more performant, and generates better quality code than comparable existing PBE systems. FlashFill++ is being deployed in several mass-market products ranging from spreadsheet software to notebooks and business intelligence applications, each with millions of users.

Religious motives and reminiscences in the poetry of kazakh akyn-zhyraus

The poetry of akyn-zhyraus is the most important stage in the formation of aesthetic principles, canons, and traditional formula language of all Kazakh poetry. The authority of poetry of five centuries (XIV-XIX centuries) was unshakable until XX century and created the basis of both epic and lyrical Kazakh poetry, the transformation of which began only in XX century. One of the most important principles of Zhyrau's poetry was spirituality, a deep connection with the religious and mythological principle, rooted in ancient beliefs andarchaic worldview systems. As the analysis shows, spiritual syncretism was peculiar for Zhyraus of the ХIV–ХVI centuries when tengrian, animistic relicts and Islamic motives and concepts were consistently united in the worldview. This syncretism is especially vividly appeared in the poetry of Asan-kaigy, Dospambet and Shalkiyiz zhyrau. In the era of the Kazakh-Jungar wars, in the XVI - XVIII centuries, which contributed to the spiritual consolidation of the Kazakh people, Islamic motives strengthened in the poetry of Zhyrau, which was manifested in the active penetration of Muslim vocabulary into the poetry of Zhyrau, reminiscence functionality, quotations, and appeals in God’s names. This tendency is most characteristic to the poetry of Bukhar Zhyrau, who was not only a poet- preacher but to some extent, was also the spiritual leader of the people. The article starts with an introduction to the concepts in the poetry of the akyn-zhyraus which is not studied sufficiently in Kazakhstani context. Then, moves to methodology section that is based on the principles of comparative, systematic and historical-literary methods. Later, the authors continue discussing the findings which are followed by the conclusion section at the end. Key words: Kazakhstan, akyn-zhyraus, comparative, motives, myth-poetics.

ARQMath Lab: An Incubator for Semantic Formula Search in zbMATH Open?

The zbMATH database contains more than 4 million bibliographic entries. We aim to provide easy access to these entries. Therefore, we maintain different index structures, including a formula index. To optimize the findability of the entries in our database, we continuously investigate new approaches to satisfy the information needs of our users. We believe that the findings from the ARQMath evaluation will generate new insights into which index structures are most suitable to satisfy mathematical information needs. Search engines, recommender systems, plagiarism checking software, and many other added-value services acting on databases such as the arXiv and zbMATH need to combine natural and formula language. One initial approach to address this challenge is to enrich the mostly unstructured document data via Entity Linking. The ARQMath Task at CLEF 2020 aims to tackle the problem of linking newly posted questions from Math Stack Exchange (MSE) to existing ones that were already answered by the community. To deeply understand MSE information needs, answer-, and formula types, we performed manual runs for tasks 1 and 2. Furthermore, we explored several formula retrieval methods: For task 2, such as fuzzy string search, k-nearest neighbors, and our recently introduced approach to retrieve Mathematical Objects of Interest (MOI) with textual search queries. The task results show that neither our automated methods nor our manual runs archived good scores in the competition. However, the perceived quality of the hits returned by the MOI search particularly motivates us to conduct further research about MOI.

Training OC: A New Course Concept for Training the Application of Basic Concepts in Organic Chemistry

The course design “Training OC” for training the application of basic concepts consists of four topics: formula language, structure–property relations, reaction mechanisms, and complex tasks that the students should solve with the conceptual knowledge they acquired in the first three topics. A main goal of the course was to enable the students to solve reaction mechanisms. To achieve the goals of the course, several games were specially designed and used. The course was conducted at a German university with ca. 30 students who participated voluntarily. The course was evaluated by several tools: students’ products were collected in the course, there were two pre/post-tests, and additionally, interviews on the strategy of designing reaction mechanisms were conducted. The performance of the teacher and the self-assessment of the students were also part of the evaluation. The results of the written exam were compared with the results of the bachelor chemistry major students. The course “Training OC” was rated very well by the students. They were of the opinion that they learned the application of basic concepts taught in this course. This is supported by the results of the evaluation and the written exams. The course concept of Training OC will therefore become a permanent part of the course “Organic Chemistry I” which will be redesigned for the next round in 2020–21.

Parsing Excel formulas: A grammar and its application on 4 large datasets

AbstractSpreadsheets are popular end user programming tools, especially in the industrial world. This makes them interesting research targets. However, there does not exist a reliable grammar that is concise enough to facilitate formula parsing and analysis and to support research on spreadsheet codebases. This paper presents a grammar for spreadsheet formulas that can successfully parse 99.99% of more than 8 million unique formulas extracted from 4 spreadsheet datasets. Our grammar is compatible with the spreadsheet formula language, recognizes the spreadsheet formula elements that are required for supporting spreadsheets research, and produces parse trees aimed at further manipulation and analysis. Additionally, we use the grammar to analyze the characteristics of the formulas of the 4 datasets in 3 different dimensions: complexity, functionality, and data utilization. Our results show that (1) most Excel formulas are simple, however formulas with more than 50 functions or operations exist, (2) almost all formulas use data from other cells, which is often not local, and (3) a surprising number of referring mechanisms are used by less than 1% of the formulas.

Initial Implementation of Natural Language Turn-Based Dialog System

Our prototype implements a natural language dialog system for Excel spreadsheets. The work is motivated by a pilot study which shows that novice users have difficulties with the formula language of Excel and need interactive assistance. JustLingo1 allows spreadsheet calculations in ordinary, written English. Furthermore, users can extend the system functionality by explaining of the calculations to the prototype. The keyword-based system analyzes the input using natural language processing techniques and translates it into Excel formulas. It asks for missing information such as operands and target cells and provides alternatives if there are ambiguities. It also handles references to previous inputs, allowing step-by-step construction of calculations. An evaluation shows that it properly resolves 82% of references and correctly interprets 79,5% of overall user input. Although far from perfect, the prototype demonstrates that computers may soon begin to take on simple, limited-domain programming tasks based on natural-language input.1http://ps.ipd.kit.edu/english/JustLingo.php

Fitting Linear Mixed-Effects Models Usinglme4

Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.

Structured Additive Regression Models: AnRInterface toBayesX

Structured additive regression (STAR) models provide a flexible framework for modeling possible nonlinear effects of covariates: They contain the well established frameworks of generalized linear models and generalized additive models as special cases but also allow a wider class of effects, e.g., for geographical or spatio-temporal data, allowing for specification of complex and realistic models. BayesX is standalone software package providing software for fitting general class of STAR models. Based on a comprehensive open-source regression toolbox written in C++, BayesX uses Bayesian inference for estimating STAR models based on Markov chain Monte Carlo simulation techniques, a mixed model representation of STAR models, or stepwise regression techniques combining penalized least squares estimation with model selection. BayesX not only covers models for responses from univariate exponential families, but also models from less-standard regression situations such as models for multi-categorical responses with either ordered or unordered categories, continuous time survival data, or continuous time multi-state models. This paper presents a new fully interactive R interface to BayesX: the R package R2BayesX. With the new package, STAR models can be conveniently specified using R’s formula language (with some extended terms), fitted using the BayesX binary, represented in R with objects of suitable classes, and finally printed/summarized/plotted. This makes BayesX much more accessible to users familiar with R and adds extensive graphics capabilities for visualizing fitted STAR models. Furthermore, R2BayesX complements the already impressive capabilities for semiparametric regression in R by a comprehensive toolbox comprising in particular more complex response types and alternative inferential procedures such as simulation-based Bayesian inference.

Undecidability of Propositional Separation Logic and Its Neighbours

In this article, we investigate the logical structure of memory models of theoretical and practical interest. Our main interest is in “the logic behind a fixed memory model”, rather than in “a model of any kind behind a given logical system”. As an effective language for reasoning about such memory models, we use the formalism of separation logic. Our main result is that for any concrete choice of heap-like memory model, validity in that model is undecidable even for purely propositional formulas in this language. The main novelty of our approach to the problem is that we focus on validity in specific, concrete memory models, as opposed to validity in general classes of models. Besides its intrinsic technical interest, this result also provides new insights into the nature of their decidable fragments. In particular, we show that, in order to obtain such decidable fragments, either the formula language must be severely restricted or the valuations of propositional variables must be constrained. In addition, we show that a number of propositional systems that approximate separation logic are undecidable as well. In particular, this resolves the open problems of decidability for Boolean BI and Classical BI. Moreover, we provide one of the simplest undecidable propositional systems currently known in the literature, called “Minimal Boolean BI”, by combining the purely positive implication-conjunction fragment of Boolean logic with the laws of multiplicative *-conjunction, its unit and its adjoint implication, originally provided by intuitionistic multiplicative linear logic. Each of these two components is individually decidable: the implication-conjunction fragment of Boolean logic is co-NP-complete, and intuitionistic multiplicative linear logic is NP-complete. All of our undecidability results are obtained by means of a direct encoding of Minsky machines.

Teaching & Learning Guide for: Logic and Divine Simplicity

Teaching & Learning Guide for: Logic and Divine Simplicity

Potential Risks of “Risk” Language in Breastfeeding Advocacy

In this article the authors analyze the use of “risks of formula language” versus “benefits of breastfeeding language” in breastfeeding advocacy texts. Feeding intentionality and 434 adult respondents' assessments of advocacy texts were examined at a mid-western university in the fall of 2009. No significant difference was observed between those who read text phrased in terms of “risks of formula feeding” and those who read text describing “benefits of breastfeeding” in feeding intentionality. Results supported the expectation that respondents would less favorably assess texts using risk language—respondents rated risk texts as less trustworthy, accurate, and helpful compared to benefit text. Texts were also varied in “medical” and “breastfeeding advocacy group” affiliations. Analyses revealed that texts including the medical logo were rated significantly more favorably compared to breastfeeding advocacy logo and no logo conditions. Findings suggest that use of risk language may not be an advantageous health promotion strategy, but may be counter-productive to the goals of breastfeeding advocates.

A Spreadsheet Approach to Facilitate Visualization of Uncertainty in Information

Information uncertainty is inherent in many problems and is often subtle and complicated to understand. Although visualization is a powerful means for exploring and understanding information, information uncertainty visualization is ad hoc and not widespread. This paper identifies two main barriers to the uptake of information uncertainty visualization: firstly, the difficulty of modeling and propagating the uncertainty information; and secondly, the difficulty of mapping uncertainty to visual elements. To overcome these barriers, we extend the spreadsheet paradigm to encapsulate uncertainty details within cells. This creates an inherent awareness of the uncertainty associated with each variable. The spreadsheet can hide the uncertainty details, enabling the user to think simply in terms of variables. Furthermore, the system can aid with automated propagation of uncertainty information, since it is intrinsically aware of the uncertainty. The system also enables mapping the encapsulated uncertainty to visual elements via the formula language and a visualization sheet. Support for such low-level visual mapping provides flexibility to explore new techniques for information uncertainty visualization.

An introduction to logical spreadsheets

AbstractA logical spreadsheet is a spreadsheet in which the formula language is composed of logical expressions. Logical spreadsheets were invented shortly after traditional electronic spreadsheets were introduced, but since then logical spreadsheet research has been somewhat sparse. Recently, however, there has been a resurgence in the interest of logical spreadsheets in the research community. In this article, we summarize logical spreadsheet research up to this point.

Propositional Logic for Ground Semigroups of Context

A propositional framework of formal reasoning is proposed, which emphasises the pattern of entering and exiting context. Contexts are modelled by an algebraic structure which reflects the order and manner in which context is entered into and exited from. The equations of the algebra partitions context terms into equivalence classes. A formal semantics is defined, containing models that map equivalence classes of certain context terms to sets of interpretations of the formula language. The corresponding Hilbert system incorporates the algebraic equations as axioms asserted in context. In semigroups of contexts, where combination of contexts is associative, finite ground algebraic equations correspond to contingent equivalence between certain logical formulas. Systems for sets and multisets of contexts are obtained by presenting their respective algebras as associativity plus finite ground equations. Soundness and completeness results are proved. Some contextual reasoning systems in the literature are inherently associative, and we present those as special cases.

A micromodularity mechanism

A simple mechanism for structuring specifications is described. By modelling structures as atoms, it remains entirely first-order and thus amenable to automatic analysis. And by interpreting fields of structures as relations, it allows the same relational operators used in the formula language to be used for dereferencing. An extension feature allows structures to be developed incrementally, but requires no textual inclusion nor any notion of subtyping. The paper demonstrates the flexibility of the mechanism by application in a variety of common idioms.

Motion Simulation With Working Model 2D and MSC.visualNastran 4D

Motion Simulation With Working Model 2D and MSC.visualNastran 4D

Managing engineering data for complex products

In this article we propose a design framework that integrates many application programs and manages the enormous quantity and variety of data generated while designing a complex product. Our discipline-independent framework provides data management services, such as version control and configuration management, needed by many engineering disciplines. This discipline-independent framework may be extended to satisfy the particular needs of specific engineering disciplines. The framework supports a message passing system and a flexible formula language, which facilitate the integration of design data from multiple disciplines. Our framework also includes powerful features for designing products with customer selectable options. First, we provide constructs, called option variables and option restrictions, for indicating what options are to be offered. Then, our option language allows designers to specify the product parametrically as a function of the option variables. Finally, we provide features for verifying that the design satisfies specified constraints for all combinations of options to be offered.

On the use of advanced logic programming languages in computational linguistics

Computational Linguistics and Logic Programming have strong connections, but the former uses concepts that are absent from the most familiar implementations of the latter. We advocate that a Logic Programming language need not feature the Computational Linguistics concepts exactly, it must only provide a logical way of dealing with them. We focus on the manipulation of higher-order terms and the logical handling of context, and we show that the advanced features of Prolog II and λProlog are useful for dealing with these concepts. Higher-order terms are native in λProlog, and Prolog II's infinite trees provide a handy data-structure for manipulating them. The formula language of λProlog can be transposed in the Logic Grammar realm to allow for a logical handling of context.

Recent Publications in Logic

'... we doubt that anything has been gained by the formula language' (Hoppe); '... makes a strange and chilling impression with its long and short, vertical and horizontal strokes ... whether ... logic would gain considerably if it were to improve its tools and expand in this direction may justly be doubted' (MichaElis); '. . . indulges in the Japanese habit of writing vertically . .. monstrous waste of space' (Schr6der); '. . . cumbrous and inconvenient' (Venn). Frege's Begriffsschrift, now recognized as a crucially important pioneering work in the development of modern logic, was accorded a distinctly unfavourable reception by his contemporariesa fact which may usefully remind reviewers of their fallibility. Bynum's new edition' contains, besides an English translation of the Begriffsschrift, translations also of two papers in which Frege explains the motivation for his work and defends it against critics, and of the half-dozen reviews the Begriffsschrift received. Bynum has contributed a biographical sketch, an Introduction, and a comprehensive bibliography. Frege explains that his work in pursuit of his logicist programme, which was to provide arithmetic with firm foundations in the form of rigorous proofs of arithmetical theorems from purely logical axioms, was hindered by the deficiencies of ordinary language, which encouraged ambiguities and the smuggling in of implicit premisses. In the Begriffsschrift, therefore, he proposed a new, formal language, free of ambiguities, and with as few as possible rules of inference. The new language was a great advance on previous formalizations of logic: the propositional connectives (including material implication) were introduced, and the interdefinability relations between these connectives were recognized; quantifiers were invented-a crucial innovation, for the Aristotelian subject-predicate logic was, as Frege saw, too weak to express arithmetical concepts; an axiomatization (subsequently shown to be complete) of propositional and predicate logic was provided; and logical definitions were given of 'hereditary property' and 'ancestor'-a vital preliminary to the definition of arithmetical concepts in logical terms. Part of the explanation for the poor reception of this pioneering work lies, no doubt, in Frege's somewhat forbidding two-dimensional symbolism. He expressly intended to exploit the two-dimensionality of the writing