Premise Selection Research Articles

Graph sequence learning for premise selection

Premise selection is crucial for large theory reasoning with automated theorem provers as the sheer size of the problems quickly leads to resource exhaustion. This paper proposes a premise selection method inspired by the machine learning domain of image captioning, where language models automatically generate a suitable caption for a given image. Likewise, we attempt to generate the sequence of axioms required to construct the proof of a given conjecture. In our axiom captioning approach, a pre-trained graph neural network is combined with a language model via transfer learning to encapsulate both the inter-axiom and conjecture-axiom relationships. We evaluate different configurations of our method and experience a 14% improvement in the number of solved problems over a baseline.

Introduction to Mathematical Language Processing: Informal Proofs, Word Problems, and Supporting Tasks

Abstract Automating discovery in mathematics and science will require sophisticated methods of information extraction and abstract reasoning, including models that can convincingly process relationships between mathematical elements and natural language, to produce problem solutions of real-world value. We analyze mathematical language processing methods across five strategic sub-areas (identifier-definition extraction, formula retrieval, natural language premise selection, math word problem solving, and informal theorem proving) from recent years, highlighting prevailing methodologies, existing limitations, overarching trends, and promising avenues for future research.

THE OCURRENCES OF PITHANON IN GALEN’S PHP

This article presents a research on the occurrences of Pithanon in Galen’s On Doctrines of Hippocrates and Plato (PHP). Galen writes PHP to critique doctors, Peripatetics, and stoics about the powers that govern man. He considers his criticism to be justifiable because they have come to the wrong conclusions because of the wrong selection of premises. According to him, his opponents' conclusions are based on persuasive, mistaken, ambiguous or false assumptions. Pithanon is a key word he uses to identify one of the premises that is applied by the stoics in order to prove their thesis about the hegemonikon.

Contrastive Graph Representations for Logical Formulas Embedding

Currently, the non-transparent computing process of deep learning has become a significant reason hindering its further development. The Neural-Symbolic (NS) system formed by integrating logic rules into neural networks has attracted increasing attention owing to its direct interpretability. Embedding symbolic logical formulas into a low-dimensional continuous space provides an effective way for the NS system. However, current studies are all constrained by the modeling ability for its syntactic structure and fail to preserve the intrinsic semantics in embeddings, which causes poor performance on downstream reasoning tasks. To this end, this paper proposes a novel method of <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Con</b> trastive <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</b> raph <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b> epresentations (ConGR) for logical formulas embedding. First, to improve the modeling ability for the syntactic structure, ConGR introduces a densely connected graph convolutional network (GCN) with an attention mechanism to process syntax parsing graphs of formulas. In this way, discriminative local and global embeddings of formulas are obtained at the syntax level. Second, the contrastive instances (positive or negative) for each anchor formula are generated by the transformation under the guidance of logical properties. To preserve semantic information, two types of contrast, global-local and global-global, are carried out to refine formula embeddings. Extensive experiments demonstrate that ConGR obtains superior performance against state-of-the-art baselines on entailment checking and premise selection datasets.

Development of Decision-Making Framework for Food Premises Based on Wara’ Parameter towards Syubhah Assesment

The selection of food premises is an important practice that requires attention of Muslims. The emerging new trend of dietary culture has become one of the challenges for contemporary Muslims in ensuring halalan tayyiban aspect. Therefore, the selection criteria of food premises is crucial for Muslims, and this can be done through a concept known as wara’ (abstinence). This study is carried out to highlight the wara’ aspect within the selection criteria as well as in the decision-making process. This is because wara’ plays an important role when dealing with doubtful elements (syubhah). This research wholly utilized library research to obtain data and data was analysed qualitatively by using content analysis method. Based on findings, there are several forms of syubhah that can affect the halalan tayyiban status. Therefore, this study proposes a decision-making framework based on wara’ and syubhah.

Оценка санитарно-гигиенического состояния и организации учебно-тренировочного процесса в училище олимпийского резерва

To achieve high results in sports and preserve health, athletes need favorable conditions for a training process, accommodation and medical supply. The purpose of the study was to assess the sanitary and hygienic condition and organization of a training process at a school of Olympic reserve. Objectives of the study included assessment of architectural and planning concepts for the school-related buildings and premises; examination of sanitary and hygienic condition of training rooms, sports facilities, hall of residence, parameters of air thermal and light regimen; assessment of how the training process is organized and developing the activities to correct the found violations. A hygienic assessment of training and athletic premises, physical factors, medical and pedagogical observation (two types of sports) is done in the trial. It has been established during the examination that no requirements to light furniture labeling, temperature and light regimen, regimen of cleaning and storage of cleaning utensils and sanitary condition of the hall of residence are followed. Training sessions are structured and specific as far as physical activity dynamics goes. By a number of parameters (selection and arrangement of premises, class timetable and equipment), favorable conditions for education and training are created at the school. The established violations of sanitary and hygienic conditions in the school-related premises and buildings can promote fatigue, injuries and infectious diseases. A more proper medical control over the sanitary conditions of education and residence at the school is required.

LINGUISTIC ASPECT OF MODALITY IN MODERN MATH DISCOURSE IN ENGLISH

The article reveals linguistic aspect of modality in modern math discourse in English, critically outlines a number of actual problematic issues in the area, such as the distinction between epistemic modality and evidentiality marked by formal logics philosophical grounding. General reference to previous scholarly activity in math modality research proves that it is largely based on propositional aspects of meaning. The math text corpus analysis aims to extract a set of modalities that are indispensable for formulating modal deductive reasoning. However, from a linguistic perspective academic math discourse requires natural language premise selection in the processes of mathematical reasoning and argumentation. It is presumed that two different self-attention cognition layers are focused at the same time on the proper classical symbolic logic and mathematical elements (formal language), while the other attends to natural language. Defining the semantic meanings of math discourse modality markers involves the interpretation phase. Thus, objectivity is generally associated with evidential adverbs which are markers of the evidence verification concerning the speaker’s assessment of the truth value of the proposition. Modal auxiliaries of high, medium and low modality, semimodal verbs and conditionals involve ascribing a justification value in the set of possible logical inference making. The formal logical structure of mathematical reasoning explains the non-intuitive possibility of a deductive proof. It has been grounded that a linguistic category of modality in math discourse indispensably presupposes the universal truth of knowledge, high level of logical formalization in propositional verification status, formulaic nature of the argumentation, i.e. synthesis of hypothetical preconditions, theoretical knowledge and subjectivity of reasoning leading to a new hypothesis verification and visual exemplification of the empirical deductive processes in particular by linguistic means of modality expression.

Major problems of microclimate indicator measurements indoors of residential and public buildings and ways to solve them

Human health and efficiency are largely determined by the microclimate conditions and the air quality in residential, public and industrial buildings in which people spend a significant amount of time. The existing methods of measuring microclimate indicators largely do not correspond to the changed regulatory framework, do not fully reflect all the stages of measurements, have contradictions and inaccuracies, which leads to errors in the measurement and evaluation of the results obtained. The purpose of this study was to develop guidelines for measuring microclimate indicators in residential and public buildings, leveling the existing contradictions in the current documents and meeting modern requirements. The analysis of the current methodological documents regulating the requirements for measuring microclimate indicators was carried out, the main problems encountered by specialists during measurements and evaluation of laboratory and instrumental studies of the microclimate were identified and systematized. To date, the only methodological document in the field of microclimate for residential and public buildings is GOST 30494-2011 "Residential and public buildings. Indoor microclimate parameters". This standard sets the requirements for the organization of control and allows to measure and evaluate the microclimate in almost any residential and public building. However, the standard presents requirements for measurement conditions that are practically unrealizable for many regions of Russia, unreasonably high requirements for measuring instruments (MI), which do not allow to take measurements by MI included in the State Register and having the appropriate scope of application, insufficient requirements for the criteria for the selection of premises and their preparation for an objective assessment of the microclimate parameters, inaccuracies in the presented formulas for calculating the resulting room temperature and inconsistencies in individual paragraphs of the document. There are also no requirements for processing and presenting measurement results. In this situation, the development of a methodology for measuring microclimate indicators in residential and public buildings is extremely relevant. This paper presents the main provisions of the developed draft methodology for measuring microclimate indicators in residential and public buildings at different stages of operation of research objects. The developed procedural guidelines determine the order, conditions for carrying out and minimum scope of instrumental control required for microclimate parameters in residential and public buildings that meet the requirements of sanitary legislation. In the process of procedural guidelines development inconsistencies and discrepancies of current procedural documents were considered as much as possible.

A study of continuous vector representations for theorem proving

Abstract Applying machine learning to mathematical terms and formulas requires a suitable representation of formulas that is adequate for AI methods. In this paper, we develop an encoding that allows for logical properties to be preserved and is additionally reversible. This means that the tree shape of a formula including all symbols can be reconstructed from the dense vector representation. We do that by training two decoders: one that extracts the top symbol of the tree and one that extracts embedding vectors of subtrees. The syntactic and semantic logical properties that we aim to preserve include both structural formula properties, applicability of natural deduction steps and even more complex operations like unifiability. We propose datasets that can be used to train these syntactic and semantic properties. We evaluate the viability of the developed encoding across the proposed datasets as well as for the practical theorem proving problem of premise selection in the Mizar corpus.

Selective rationality? Argumentation of the Constitutional Court of the Russian Federation on the terms of office of the President in the mirror of cognitive science

The Decision (Zaklyuchenie) of the Constitutional Court of the Russian Federation on the constitutionality of the constitutional amendments played a significant role for the entry into force of the amendments to the Constitution of the Russian Federation adopted in 2020. For this reason, and in connection with the fact that many of the novels raise questions precisely from the point of view of their compliance with Chapters 1, 2 and 9 of the Russian Constitution, the positions formulated in the Decision attract serious attention. The article analyzes the arguments of the Court on one of the significant innovations – the possibility of being elected to the post of President of Russia by a person who held or holds this position at the time the amendment entered into force, without taking into account the previous terms. This reasoning is placed in the context of the demands of rationality in constitutional law. The article is aimed at implementing bona fide intentions related to confirming the subjectivity of the body of constitutional review and identifying ways to improve its argumentation. The activities of the constitutional court are presented in the article as part of reasonable foresight, which implies the creation of guarantees for the case of deviation from constitutional values. The rationality of its argumentation is understood as the sum of requirements connecting in a certain way 1) formal logic and 2) substantive reasonableness, determined by the value choice made in the constitution. It is demonstrated that the rationality of the argumentation formulated in the Decision of the Constitutional Court on the problem of the term of office of the head of state can be questioned from these points of view and, for this reason, cause associations with cognitive distortions (such as bias in the selection of initial premises for argumentation; incomplete study of scenarios reflecting the consequences of a reviewed amendment; framing; logical circle, etc.). At the same time, the article reveals the limitations of the “naive” cognitive approach, which is insufficient for working with the argumentation of the body of constitutional review and which actualizes additional consideration of the political and legal context of decision-making by this body.

Bayesian Optimisation for Premise Selection in Automated Theorem Proving (Student Abstract)

Modern theorem provers utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probabilistic framework for heuristic optimisation in theorem provers. We present results using a heuristic for premise selection and the Archive of Formal Proofs (AFP) as a case study.

ИССЛЕДОВАНИЕ УСИЛИЙ В ВЕРТИКАЛЬНЫХ ШПОНОЧНЫХ СТЫКАХ КРУПНОПАНЕЛЬНОГО ЗДАНИЯ В ПРОЦЕССЕ ВОЗВЕДЕНИЯ

Recently, the world has seen a tendency of reinforced concrete housing construction industrialization. Russia has gained extensive experience in large-panel housing construction, which helps to find optimal structural solutions, but new solutions lead to the need for additional study. Modern software systems allow you to build volumetric models of a building, taking into account physical non-linearity, which helps to take into account the actual distribution of efforts between the elements. At the same time, to build the correct model of a large-panel building, the flexibility of joints between them is required. The flexibility is calculated by online tests the results of which are used to build the future model of a building in the process of its designing. The calculation model of a building gives an approximate estimate of structural behavior and the degree of its accuracy depends on the correct selection of the initial premises. This article estimates the numerical model of a large-panel building by comparing it with the results of direct observations of shear movements in the vertical joints of the most loaded walls of a building under construction. The observations were carried out on a 26-story large-panel building with a cross structural system with self-supporting external longitudinal walls. Vertical joints are monolithic reinforced concrete with the use of dowels with cable loop transverse reinforcement. In addition, estimation of forces at the joints is also given. In general, we may conclude that the calculation model of a large-panel building is applied correctly using elastic-flexible connections with limiting ultimate forces for vertical joints modeling. The modeling part of the study is performed using a finite element model taking into account the magnitude of the joints flexibility and the actual stiffness of the building structural elements. The results of the study can be used in modeling, calculation and design of large-panel buildings, and they provide new scientific knowledge about the operation of buildings of this type.

Hammer for Coq: Automation for Dependent Type Theory

Hammers provide most powerful general purpose automation for proof assistants based on HOL and set theory today. Despite the gaining popularity of the more advanced versions of type theory, such as those based on the Calculus of Inductive Constructions, the construction of hammers for such foundations has been hindered so far by the lack of translation and reconstruction components. In this paper, we present an architecture of a full hammer for dependent type theory together with its implementation for the Coq proof assistant. A key component of the hammer is a proposed translation from the Calculus of Inductive Constructions, with certain extensions introduced by Coq, to untyped first-order logic. The translation is “sufficiently” sound and complete to be of practical use for automated theorem provers. We also introduce a proof reconstruction mechanism based on an eauto-type algorithm combined with limited rewriting, congruence closure and some forward reasoning. The algorithm is able to re-prove in the Coq logic most of the theorems established by the ATPs. Together with machine-learning based selection of relevant premises this constitutes a full hammer system. The performance of the whole procedure is evaluated in a bootstrapping scenario emulating the development of the Coq standard library. For each theorem in the library only the previous theorems and proofs can be used. We show that 40.8% of the theorems can be proved in a push-button mode in about 40 s of real time on a 8-CPU system.

Practical reasoning in corporate communication with multiple audiences

AbstractCorporate strategic communication has to be designed by considering multiple audiences of stakeholders. In this paper, we study the connection between the audience structure of corporate messages and the structure of the practical argumentation advanced to persuasively justify a business proposal. To this purpose, we combine a conceptual and analytical framework for the reconstruction of multiple audiences – theText Stakeholdersmodel (Palmieri &amp; Mazzali 2016), with a conceptual and analytical framework for the reconstruction of argument schemes – theArgumentum Model of Topics(Rigotti &amp; Greco Morasso 2010). A takeover proposal made by Ryanair for Aer Lingus is examined as an illustrative case in which this integrated framework is applied. We focus our analysis on Ryanair’s offer document to show how the particular structure of the audience is reflected in the selection of specific value and goal premises (endoxa) and in the activation of specific inferential relations (maxims) of practical reasoning.

Changing Requirements of Office Establishments in Dublin

The paper investigates the significance to companies of locational and building-related factors in the selection of office premises. Among businesses likely to relocate in the near future, it assesses the relative attraction of the traditional office core and that of suburban locations. The impact upon the decision-making process of financial incentives available in designated locations is also evaluated.

HOL(y)Hammer: Online ATP Service for HOL Light

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise and their solutions are discussed, and an initial account of using the system is given.

Learning-Assisted Automated Reasoning with Flyspeck

The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated in a bootstrapping scenario emulating the development of Flyspeck from axioms to the last theorem, each time using only the previous theorems and proofs. It is shown that 39 % of the 14185 theorems could be proved in a push-button mode (without any high-level advice and user interaction) in 30 seconds of real time on a fourteen-CPU workstation. The necessary work involves: (i) an implementation of sound translations of the HOL Light logic to ATP formalisms: untyped first-order, polymorphic typed first-order, and typed higher-order, (ii) export of the dependency information from HOL Light and ATP proofs for the machine learners, and (iii) choice of suitable representations and methods for learning from previous proofs, and their integration as advisors with HOL Light. This work is described and discussed here, and an initial analysis of the body of proofs that were found fully automatically is provided.

Premise Selection for Mathematics by Corpus Analysis and Kernel Methods

Smart premise selection is essential when using automated reasoning as a tool for large-theory formal proof development. A good method for premise selection in complex mathematical libraries is the application of machine learning to large corpora of proofs. This work develops learning-based premise selection in two ways. First, a newly available minimal dependency analysis of existing high-level formal mathematical proofs is used to build a large knowledge base of proof dependencies, providing precise data for ATP-based re-verification and for training premise selection algorithms. Second, a new machine learning algorithm for premise selection based on kernel methods is proposed and implemented. To evaluate the impact of both techniques, a benchmark consisting of 2078 large-theory mathematical problems is constructed,extending the older MPTP Challenge benchmark. The combined effect of the techniques results in a 50% improvement on the benchmark over the Vampire/SInE state-of-the-art system for automated reasoning in large theories.

Wessex shopping basket survey – a structured approach to local food sampling

The shopping basket approach to food sampling, in which ready-to-eat food items from a shopping list were sampled at premises chosen at random, was adopted by 15 Environmental Health Departments in the Wessex region. A total of 2,037 samples were analysed over a 30-month period. The microbiological quality varied considerably between food categories, with gravy and stock samples giving the highest proportion of satisfactory results. Sliced meats, cooked rice and sandwiches gave the poorest overall results. Whilst the majority of unsatisfactory results were due to elevated levels of indicator organisms (Aerobic Colony Count, Enterobacteriaceae and Escherichia coli), unsatisfactory or potentially hazardous levels of pathogens (Staphylococcus aureus, Bacillus cereus, Clostridium perfringens or Listeria monocytogenes) were detected in 1% of samples. Salmonella was not detected in any sample. The shopping basket survey was considered to be a useful way of structuring local sampling, and the random selection of premises was found to be a considerable advantage over previous sampling plans. In addition, the survey drew attention to a number of microbiological problems with specific food types, leading to more detailed investigations.

Relocation or dislocation? Key issues in the specialist management of group moves

Indicates the number of employees relocated in the UK each year and the amount of company money spent on making these moves as smooth as possible. Reports a five‐year research project which suggests that these moves remain very stressful for employees. Argues that this dislocation was caused by managers failing to understand the group move process. Explains the scope of the research, the types of UK company studied and the methods used. Underlines the finding that those organizations that approach group moves as holistic processes, requiring complex management responses, are likely to be more successful than those that approach it in a fragmented and poorly‐integrated way. Also stresses the need to see the group relocation as an opportunity for managed change. Analyses the perspectives of all those involved in managing and making the move (policymakers, those managing the personnel side and the move, those managing the physical side of the move (selection of new premises, etc.), line manager and the individual employees who are making the move) to show the issues that need to be considered.