Constraint detection in natural language problem descriptions

Modeling in constraint programming is a hard task that requires considerable expertise. Automated model reformulation aims at assisting a naive user in modeling constraint problems. In this context, formal specification languages have been devised to express constraint problems in a manner similar to natural yet rigorous specifications that use a mixture of natural language and discrete mathematics. Yet, a gap remains between such languages and the natural language in which humans informally describe problems. This work aims to alleviate this issue by proposing a method for detecting constraints in natural language problem descriptions using a structured-output classifier. To evaluate the method, we develop an original annotated corpus which gathers 110 problem descriptions from several resources. Our results show significant accuracy with respect to metrics used in cognate tasks

A hybrid framework for the specification of automated material handling systems

This paper presents a hybrid framework that specifies and characterizes the capabilities of generic components in an automated material handling system (AMHS). The framework also provides rules and mechanism for binding these capabilities together so as to facilitate the process of task planning for AMHSs. As a hybrid framework, the formal mathematics of Communicating Sequential Process (CSP) is tightly integrated to the Unified Modeling Language (UML) to provide three important entities, namely, the object structure diagram, object communication diagram and CSP-based statechart to extend the capability of a UML model in specifying the key properties of AMHSs including synchronization, parallelism and communication. The results will bring us a step closer to the generation of a fully automated task-planning executive for AMHSs.published_or_final_versio

Transformer-Based Models Are Not Yet Perfect At Learning to Emulate Structural Recursion

This paper investigates the ability of transformer-based models to learn structural recursion from examples. Recursion is a universal concept in both natural and formal languages. Structural recursion is central to the programming language and formal mathematics tasks where symbolic tools currently excel beyond neural models, such as inferring semantic relations between datatypes and emulating program behavior. We introduce a general framework that nicely connects the abstract concepts of structural recursion in the programming language domain to concrete sequence modeling problems and learned models' behavior. The framework includes a representation that captures the general \textit{syntax} of structural recursion, coupled with two different frameworks for understanding their \textit{semantics} -- one that is more natural from a programming languages perspective and one that helps bridge that perspective with a mechanistic understanding of the underlying transformer architecture. With our framework as a powerful conceptual tool, we identify different issues under various set-ups. The models trained to emulate recursive computations cannot fully capture the recursion yet instead fit short-cut algorithms and thus cannot solve certain edge cases that are under-represented in the training distribution. In addition, it is difficult for state-of-the-art large language models (LLMs) to mine recursive rules from in-context demonstrations. Meanwhile, these LLMs fail in interesting ways when emulating reduction (step-wise computation) of the recursive function.Comment: arXiv admin note: text overlap with arXiv:2305.1469

Эпистемическая модальная логика, универсальная философская эпистемо-логия и естественная теология: всеведение Бога как формально-аксиологический закон двузначной алгебры метафизики как формальной аксиологии (Обоснование этого закона "вычислением" соответствующих ценностных функций)

The method of constructing and investigating discrete mathematical models is applied to the problem of Omniscience-by-God, which is located at the intersection of epistemology, theol-ogy, and epistemic logic. For the first time in epistemology and philosophical theology, the tenet of God’s Omniscience is formulated by the artificial language of two-valued algebra of metaphysics as formal axiology, and demonstrated as a formal-axiological law of that alge-bra by “computing” relevant evaluation-functions. The present article continues the author’s attempts to apply the conceptual apparatus and meth-ods of discrete mathematics to analytical theology, namely, to represent and solve difficult problems of philosophical theology by means of constructing and investigating their models at the level of artificial language of two-valued algebraic system of metaphysics as formal axiology. The author has already published a paper on discrete mathematical modeling the tenet of God’s omnipotence in [Tomsk State University Journal of Philosophy, Sociology and Political Science. 2019. Vol. 47. P. 87–93]. In com-parison with the mentioned paper, the present article submits significantly new scientific results of constructing and investigating a discrete mathematical model of another famous attribute of God, namely, of His omniscience. In contrast to the tenet of God’s omnipotence affirming that He is al-mighty, the tenet of God’s omniscience affirms that He knows everything. However, the literature on philosophical theology contains indicating and discussing a set of nontrivial logical and epistemologi-cal problems concerning All-Knowing-God. Just these problems (and solving them at the level of their mathematical model) make up the subject-matter of the given article. The paper starts with explicating a formal-axiological meaning of the statement “God knows everything” by explicating formal-axiological meanings of the words “God”, “knows”, and “thing”. In particular, it is emphasized that the word “knowledge” is a homonym possessing at least three qualitatively different meanings, namely, “a-priori knowledge”, “empirical knowledge”, and knowledge-in-general”. It is demonstrated that God’s knowledge is not empirical but a-priori one. All the formal-axiological meanings under discus-sion are considered as evaluation-functions and defined precisely by tables. Significantly new scien-tific result of the present article: for the first time in the world literature on philosophical theology, the tenet of All-Knowing God is precisely formulated by means of the artificial language of two-valued algebra of metaphysics as formal axiology, and proved as a formal-axiological law in this algebra by computing relevant evaluation-tables. The hitherto never published affirming God’s omniscience as the law of two-valued algebra of metaphysics as formal axiology is quite nontrivial and psychological-ly unexpected one, although from the viewpoint of mathematics proper, its proof is simple

Developing algebraic and didactical knowledge in pre-service primary teacher education

This study analyzes the contribution of a teaching experiment for the development of prospective primary teachers regarding knowledge of algebra and of algebra teaching as well as their professional identity. The case study of a prospective teachersuggests that an exploratory approach combining content and pedagogy supports this development, especially in the need to propose challenging tasks, to provide opportunity for students’ autonomous work and collective discussions and to be attentive to children’s representations and strategies in order to promote algebraic thinking

First-grade Latino English language learners' performance on story problems in spanish versus english

To explore whether teaching English Language Learners (ELLs) with an emphasis on English story problem is appropriate, we compared the performance of a group of Latino first graders when working in Spanish and in English on two equivalent sets of story problems. The students’ performance was slightly higher in English than in Spanish, but lower than monolingual students from other studies. ELLs’ success in English indicated that the children’s knowledge of conversational English was sufficient to comprehend story problems, leading us to conclude that teaching through story problems is a viable approach with ELLs