Deductive Steps Research Articles

Racism in German healthcare: uncovering the construction and silencing of the "other".

While the impact of racism on healthcare interactions has been researched extensively in many parts of the world, substantive studies on healthcare-related racism in Europe, and particularly in Germany, remain scarce. This paper builds on a study that applies Community-Based Participatory Research (CBPR) and aims to explore healthcare users' experiences of racism within German healthcare. Community members were trained as peer researchers and given support as they conducted a total of six focus group discussions that involved a total of 14 study participants: these participants were organized into two subsamples of seven participants each (subsample one: Black, African, Afro-diasporic healthcare users; subsample two: healthcare users perceived or self-describing as Muslim), and each subsample had three focus group discussions. A democratic approach to qualitative data analysis was applied in the form of the DEPICT model. The data analysis developed iteratively, with inductive and deductive steps complementing one another. The study results illustrate how the collaboratively developed concepts of being treated as "other" and being made inaudible can advance our understanding of the forms, dynamics, and effects of racism in healthcare encounters. Because this paper focuses on the process of racialization, it helps illumine the mechanisms of subtle racism, which, as study results suggest, can damage healthcare users, cause a loss of trust in the system, and lead to invisibilization of racism in healthcare. By doing so, it draws attention to areas for change and transformation, to larger power structures that must be challenged in order to ensure responsive and equal healthcare for all healthcare users. The application of CBPR and, particularly, the engagement of racialized healthcare users in the research process offered pathways for analyzing the subtle, otherwise hard-to-detect mechanisms of racism, and for learning from the wisdom of situated knowledges.

From data acquisition to digital reconstruction: virtual restoration of the Great Wall’s Nine Eyes Watchtower

This article presents the virtual restoration of the Nine Eyes Watchtower, a significant cultural heritage site along the Great Wall. By applying the Seville Charter and digital technology, a detailed virtual restoration workflow is developed. The methodology involves acquiring data from multiple sources, including physical evidence, historical data, and comparative data. Advanced survey technologies, architectural knowledge, historical research, and computer modelling techniques are integrated to accurately capture the architectural and historical significance of the Nine Eyes Watchtower. The virtual restoration process follows a systematic approach, combining evidence interpretation and explicit deduction steps. The main outcome is a comprehensive virtual restoration model that accurately represents the architectural features and historical context of the Nine Eyes Watchtower. The virtual scene includes environmental elements, with potential for immersive exploration. By bridging the gap between interpretation and deduction, this study advances the scientific understanding and presentation of virtual restorations. The project contributes to ongoing research, education, and appreciation of the Great Wall's cultural legacy, ensuring its continued relevance for future generations.

Illuminating health aspects for immigrant Thai women in Swedish transnational marriages

BackgroundWomen who are migrants experience discrimination and face major risks, including sexual exploitation, trafficking, and violence, which affect their health and well-being.This study explored critical health incidents experienced by immigrant Thai women in marriage migration.MethodsA qualitative explorative approach with in-depth interviews was used. Forty immigrant Thai women who currently or previously had a Swedish spouse were recruited for the study. An inductive critical incident technique was used to collect and analyze the data as the first step. In a second deductive step, the Newman system model was used to categorize health dilemmas.ResultsThe women reported 438 critical health incidents in five main areas. Psychological health dilemmas included emotional abuse, feeling overwhelmed due to family responsibilities and the stress of leaving family behind. Sociocultural health dilemmas included transnational family duties or not performing family duties. Physiological health dilemmas included experiencing physical violence and environmental, domestic or work accidents. Developmental health dilemmas included failing health, difficulties upholding the duties expected of a spouse in the target culture and caring for an elderly husband. Spiritual health dilemmas included critical incidents in which the women perceived themselves to have failed in their hopes and duties as a wife, which intensified their dependence on faith, particularly the Buddhist concept of karma.ConclusionProfessionals in health and welfare practices in Thailand together with professionals in Western countries who work with women in marriage migration situations need to recognize the psychological, sociocultural, physiological, developmental, and spiritual health dilemmas experienced by these women. Furthermore, civil organizations that meet Thai women in foreign countries, such as Buddhist cultural associations, would benefit from the multicultural knowledge revealed by the present study. This knowledge can facilitate healthcare and welfare support for women in marriage migration situations.

Rationality in Mathematical Proofs

ABSTRACT Mathematical proofs are not sequences of arbitrary deductive steps—each deductive step is, to some extent, rational. This paper aims to identify and characterize the particular form of rationality at play in mathematical proofs. The approach adopted consists in viewing mathematical proofs as reports of proof activities—that is, sequences of deductive inferences—and in characterizing the rationality of the former in terms of that of the latter. It is argued that proof activities are governed by specific norms of rational planning agency, and that a deductive step in a mathematical proof qualifies as rational whenever the corresponding deductive inference in the associated proof activity figures in a plan that has been constructed rationally. It is then shown that mathematical proofs whose associated proof activities violate these norms are likely to be judged as defective by mathematical agents, thereby providing evidence that these norms are indeed present in mathematical practice. We conclude that, if mathematical proofs are not mere sequences of deductive steps, if they possess a rational structure, it is because they are the product of rational planning agents.

Interprofessional weaning boards for invasively ventilated patients in intensive care units: Qualitative interview study with healthcare professionals in Germany.

Numbers of mechanically ventilated patients are increasing worldwide. Weaning Boards could support weaning from the ventilator by facilitating interprofessional consultations between Weaning Centers and nonpneumological intensive care units. This study, which is linked to the project Prevention of invasive Ventilation, aimed to explore the design and implementation of future Weaning Boards. Semistructured interviews were conducted with physicians, nurses, respiratory therapists, and physiotherapists of intensive care units and Weaning Centers in Baden-Wuerttemberg, Germany. Participants were asked to share their views on (a) required characteristics of Weaning Boards and (b) the current care of weaning patients in their wards. Qualitative data analysis included inductive and deductive steps referring to the Template for Intervention Description and Replication checklist and the Consolidated Framework for Implementation Research. The 14 interviewed healthcare professionals addressed characteristics of future Weaning Boards including (a) preconditions, (b) procedure, (c) interprofessional participants, (d) type of performance, and (d) time frame. Identified determinants for successful implementation were related to (a) individual characteristics of healthcare professionals, (b) ward characteristics, and (c) healthcare system characteristics. Weaning Boards could be a useful tool to advance knowledge sharing between professionals, improve education about weaning protocols, and support patient-oriented care. The implementation of Weaning Boards can be influenced by individual characteristics of participating professionals, difficulties in the interaction between professional groups, the present workplace culture, and the current coronavirus disease 2019 (COVID-19) pandemic.

Clinicians' psychological empowerment to engage inmanagement as part oftheirdaily work.

The purpose of the article is to analyze how physicians and nurses, as the two major health care professions, experience psychological empowerment for managerial work. The study was designed as a qualitative interview study at four primary care centers (PCCs) in Sweden. In total, 47 interviews were conducted, mainly with physicians and nurses. The first inductive analysis led us to the concept of psychological empowerment, which was used in the next deductive step of the analysis. The study showed that both professions experienced self-determination for managerial work, but that nurses were more dependent on structural empowerment. Nurses experienced that they had competence for managerial work, whereas physicians were more ignorant of such competence. Nurses used managerial work to create impact on the conditions for their clinical work, whereas physicians experienced impact independently. Both nurses and physicians experienced managerial work as meaningful, but less meaningful than nurses and physicians' clinical work. For an effective health care system, structural changes in terms of positions, roles, and responsibilities can be an important route for especially nurses' psychological empowerment. The qualitative method provided a complementary understanding of psychological empowerment on how psychological empowerment interacted with other factors. One such aspect was nurses' higher dependence on structural empowerment, but the most important aspect was that both physicians and nurses experienced that managerial work was less meaningful than clinical work. This implies that psychological empowerment for managerial work may only make a difference if psychological empowerment does not compete with physicians' and nurses' clinical work.

On structures of regular standard contradictions in propositional logic

The contradiction separation (CS) based automated deduction is an extension of the binary resolution principle for deductive inference rules, whose CSE prover and combined versions have unique performance among others in CADE ATP system competitions since their first appearances in 2018. The contradictions constructing method is one of the most important factors to determine the efficiency of the CS based deduction, which is more complex compared to the complementary pair finding in the binary resolution. To get structures and concrete forms of contradictions, this paper examines two types of standard contradictions, i.e., the regular standard contradictions and the standard contradictions for non-unit clauses sets. The concepts of the regular standard contradiction and its extended form are presented. Some properties of them are discussed. In order to get simpler contradiction separation clauses in every deductive step, four types of structures for standard contradictions obtained by adding related literals in the regular standard contradiction and its extended form are gotten. Two structures for the standard contradictions for non-unit clauses set are obtained. Two unified algorithms for constructing standard contradictions are also contrived.

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.

Implementing logical inference based on DNA assembly

Algorithms and information processing, fundamental to biological system, are an essential aspect of many elementary physical phenomena, such as molecular self-assembly. Self-assembly system has been proved to be capable of performing many logic operations by the early work. A significant challenge related to the design of molecular information processing systems is to develop a programmable architecture that controls the states of individual molecular events. Here, a novel systematic implementation of logical inference is presented based on DNA tile assembly system. Exploiting the intrinsic programmable capability of molecular interactions, firstly a seed tile configuration is constructed to encode the input information of a logical inference problem, including all facts, all inference rules and their equivalent rules. Then, three tile assembly subsystems are discussed to fulfil the main logical deduction steps. We describe mechanisms for finding the successful solutions among the many parallel assemblies. A whole tile assembly system is established on the base of a seed configuration and three subsystems. This prototype is the first programming language to implement deduction operations based on two-dimensional DNA assembly. It is demonstrated that algorithmic DNA tile assembly system can be treated as an important way to implement logic inference, which will shed light on aspects of applications in the field of artificial intelligence in the future.

School-based obesity prevention for busy low-income families-Organisational and personal barriers and facilitators to implementation.

Little research has targeted multiple-level barriers and facilitators in school-based parental support programmes. This qualitative study aims to describe barriers and facilitators, at organisational and personal levels, that teachers and parents in disadvantaged settings in Sweden perceived as influencing the implementation of the Healthy School Start II (HSS II) intervention. Data collection, analysis and interpretation were guided by the Consolidated Framework for Implementation Research (CFIR). Focus groups and interviews were conducted with 14 parents and ten teachers within the HSS II trial. Data were analysed using qualitative content analysis in a deductive step using the three CFIR domains-inner and outer setting, and personal characteristics-followed by an inductive analysis. The theme 'being on the same page-getting burdened teachers and parents to work on common ground' was found. Among teachers, barriers and facilitators were related to the structure of the schoolwork and curriculum, involvement from other staff and school management, the practical school workday, perception of high family needs but low parental interest, insufficient resources in the families, and teacher's personal knowledge, interests, and opinions about health and food. For parents, barriers and facilitators were related to the perceived family needs and resources, parents' health knowledge, consensus about healthy behaviours and ability to cooperate, and school involvement in health issues and the intervention. Interventions should facilitate parents' and teachers' work on common ground, with activities suitable for a stressful and burdensome workday and everyday life. This could be achieved by integrating evidence-based practices within school routines, and including activities that are practicable despite parents' stressful lives, and that increase parental consensus about promoting health. Strategies to increase involvement of parents in families with high needs are necessary. Also, this study suggests an expansion of the CFIR to capture the interface between different micro-level organisations, and account for several delivering/receiving organisations.

Diagnosis by ruling out other diseases or conditions

Pig production is nowadays highly specialised, and is dominated by large, intensive, indoor-rearing production systems around the world. As farming systems have evolved, so also has our understanding of the...

Aristotle’s Prototype Rule-Based Underlying Logic

This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, and a deductive logic by which the steps of the deduction proceed. Every demonstration produces (or confirms) knowledge of (the truth of) its conclusion for every person who comprehends the demonstration. Aristotle presented a general truth-and-consequence theory of demonstration meant to apply to all demonstrations: a demonstration is an extended argumentation that begins with premises known to be truths and that involves a chain of reasoning showing by deductively evident steps that its conclusion is a consequence of its premises. In short, a demonstration is a deduction whose premises are known to be true. Aristotle’s general theory of demonstration required a prior general theory of deduction presented in the Prior Analytics. His general immediate-deduction-chaining theory of deduction was meant to apply to all deductions: any deduction that is not immediately evident is an extended argumentation that involves a chaining of immediately evident steps that shows its final conclusion to follow logically from its premises. His deductions, both direct and indirect, were rule-based and not tautology-based. The idea of tautology-based deduction, which dominated modern logic in the early years of the 1900s, is nowhere to be found in Analytics. Rule-based (or “natural”) deduction was rediscovered by modern logicians. To illustrate his general theory of deduction, Aristotle presented a prototype: an ingeniously simple and mathematically precise special case traditionally known as the categorical syllogistic. With reference only to propositions of the four so-called categorical forms, he painstakingly worked out exactly what those immediately evident deductive steps are and how they are chained to complete deductions. In his specialized prototype theory, Aristotle explained how to deduce from a given categorical premise set, no matter how large, any categorical conclusion implied by the given set. He did not extend this treatment to non-categorical deductions, thus setting a program for future logicians. The prototype, categorical syllogistic, was seen by Boole as a “first approximation” to a comprehensive logic. Today, however it appears more as the first of the dozens of logics already created and as the first exemplification of a family that continues to expand.

MATHEMATICAL INFERENCE AND LOGICAL INFERENCE

AbstractThe deviation ofmathematical proof—proof in mathematical practice—from the ideal offormal proof—proof in formal logic—has led many philosophers of mathematics to reconsider the commonly accepted view according to which the notion of formal proof provides an accurate descriptive account of mathematical proof. This, in turn, has motivated a search for alternative accounts of mathematical proof purporting to be more faithful to the reality of mathematical practice. Yet, in order to develop and evaluate such alternative accounts, it appears as a necessary prerequisite to first possess a clear picture of what the deviation of mathematical proof from formal proof consists in. The present work aims to contribute building such a picture by investigating the relation between the elementary steps of deduction constituting the two types of proofs—mathematical inferenceandlogical inference. Many claims have been made in the literature regarding the relation between mathematical inference and logical inference, most of them stating that the former is lacking properties that are constitutive of the latter. Suchdifferentiating claimsare, however, usually put forward without a clear conception of the properties occurring in them, and are generally considered to be immediately justified by our direct acquaintance, or phenomenological experience, with the two types of inferences. The present study purports to advance our understanding of the relation between mathematical inference and logical inference by developing a detailed philosophical analysis of the differentiating claims, that is, an analysis of themeaningof the differentiating claims—through the properties that occur in them—as well as thereasonsthat support them. To this end, we provide at the outset a representative list of the different properties of logical inference that have occurred in the differentiating claims, and we notice that they all boil down to the three properties offormality,generality, andmechanicality. For each one of these properties, our analysis proceeds in two steps: we first provide precise conceptual characterizations of the different ways logical inference has been said to be formal, general, and mechanical, in the philosophical and logical literature on formal proof; we then examine why mathematical inference does not appear to be formal, general, and mechanical, for the different variations of these notions identified. Our study results in a precise conceptual apparatus for expressing and discussing the properties differentiating mathematical inference from logical inference, and provides a first inventory of the various reasons supporting the observations of those differences. The differentiating claims constitute thus a set of data that any philosophical account of mathematical inference and proof purporting to be more faithful to mathematical practice ought to be able to accommodate and explain.

Closure Failure and Scientific Inquiry

Deduction is important to scientific inquiry because it can extend knowledge efficiently, bypassing the need to investigate everything directly. The existence of closure failure—where one knows the premises and that the premises imply the conclusion but nevertheless does not know the conclusion—is a problem because it threatens this usage. It means that we cannot trust deduction for gaining new knowledge unless we can identify such cases ahead of time so as to avoid them. For philosophically engineered examples we have “inner alarm bells” to detect closure failure, but in scientific investigation we would want to use deduction for extension of our knowledge to matters we don’t already know that we couldn’t know. Through a quantitative treatment of how fast probabilistic sensitivity is lost over steps of deduction, I identify a condition that guarantees that the growth of potential error will be gradual; thus, dramatic closure failure is avoided. Whether the condition is fulfilled is often obvious, but sometimes it requires substantive investigation. I illustrate that not only safe deduction but the discovery of dramatic closure failures can lead to scientific advances.

Finding Proofs in Tarskian Geometry

We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski’s axioms of Hilbert’s 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some OTTER proofs in Tarskian geometry (solving challenges issued in Wos’s 1998 book). There are 212 theorems in this collection. We were able to find OTTER proofs of all these theorems. We developed a methodology for the automated preparation and checking of the input files for those theorems, to ensure that no human error has corrupted the formal development of an entire theory as embodied in two hundred input files and proofs. We distinguish between proofs that were found completely mechanically (without reference to the steps of a book proof) and proofs that were constructed by some technique that involved a human knowing the steps of a book proof. Proofs of length 40–100, roughly speaking, are difficult exercises for a human, and proofs of 100–250 steps belong in a Ph.D. thesis or publication. 29 of the proofs in our collection are longer than 40 steps, and ten are longer than 90 steps. We were able to derive completely mechanically all but 26 of the 183 theorems that have “short” proofs (40 or fewer deduction steps). We found proofs of the rest, as well as the 29 “hard” theorems, using a method that requires consulting the book proof at the outset. Our “subformula strategy” enabled us to prove four of the 29 hard theorems completely mechanically. These are Ph.D. level proofs, of length up to 108.

The Inductive and Deductive Methods in Customary International Law Analysis: Traditional and Modern Approaches

This paper will criticize the current characterization of customary international law analysis as falling into two competing analytical methods, specifically, the “traditional” and “modern” methods. Following Koskennieni, Roberts, Wouters, Ryngaert, and others, contemporary customary international legal analysis is said to have divided into two schools: the traditional and modern. These schools are supposed to reflect the use of the inductive and deductive methods, respectively, and, in turn, to either apologize for the freedom of state action or establish a utopia where the freedom of the state is limited. This image of struggle between competing methods, however, does not fully capture the ways in which the inductive and deductive methods are actually intertwined in customary international law analysis. The methods are not two opposing monolithic techniques. Instead, in practice, the methods are intermixed, combining a variety of choices. Deductive steps are taken regarding the use of induction, inductive steps are taken in reaching patterns from practice, deductive steps are taken in identifying sample pools, and so on. This paper concludes that induction and deduction are both used in parallel in most analyses of customary international law in a delicate, yet valuable, balance of corrective tension. Furthermore, this situation is neither traditional, nor modern – in a chronological sense – but is consistent throughout the history of customary international law analysis. Following an introductory section reviewing the background to the debate over approaches, the paper will consider deduction and induction in more detail, attempting to understand these two methods of logical reasoning. Then the author will examine the way customary international law is analyzed by international tribunals by deconstructing the analytical process into smaller logical steps. For each step, an analysis will be undertaken of whether the conclusion is reached through induction or deduction, and whether this approach is consistent across tribunals and historical eras. Through this approach, the paper will take a first step to suggest the complex ways inductive and deductive analyses are layered in the assessment of customary international law.

NEXCEL, A Deductive Spreadsheet

Usability and usefulness have made the spreadsheet one of the most successful computing applications of all times: millions rely on it every day for anything from typing grocery lists to developing multimillion dollar budgets. One thing spreadsheets are not very good at is manipulating symbolic data and helping users make decisions based on them. By tapping into recent research in logic programming, databases and cognitive psychology, we propose a deductive extension to the spreadsheet paradigm which addresses precisely this issue. The accompanying tool, which we call NEXCEL, is intended as an automated assistant for the daily reasoning and decision-making needs of computer users, in the same way as a spreadsheet application such as Microsoft Excel assists them every day with calculations simple and complex. Users without formal training in logic or computer science can interactively define logical rules in the same simple way as they define formulas in Excel. NEXCEL immediately evaluates these rules thereby returning lists of values that satisfy them, again just like with numerical formulas. The deductive component is seamlessly integrated into the traditional spreadsheet so that a user not only still has access to the usual functionalities, but is able to use them as part of the logical inference and, additionally, to embed deductive steps in a numerical calculation. Under the hood, NEXCEL uses a small logic programming language inspired by Datalog to define derived relations: the target region of the spreadsheet contains a set of logical clauses in the same way that calculated cells contain a numerical formula in a traditional spreadsheet. Therefore, logical reasoning reduces to computing tables of data by evaluating Datalog-like definitions, a process that parallels the calculation of numerical formulas. Each row in the calculated relation is a tuple of values satisfying the definition for this relation, so that the evaluated table lists all such solutions, without repetitions. This linguistic extension significantly enriches the expressive power of the spreadsheet paradigm. Yet, it is provided to the user through a natural extension of the mostly excellent interfaces of modern spreadsheet applications.

The Academic Journal Ranking Problem: A Fuzzy-Clustering Approach

The Academic Journal Ranking Problem consists in formulating a formal assessment of scientific journals. An outcome variable must be constructed that allows valid journal comparison, either as a set of tiers (ordered classes) or as a numerical index. But part of the problem is also to devise a procedure to get this outcome, that is, how to get and use relevant data coming from expert opinions or from citations database. We propose a novel approach to the problem that applies fuzzy cluster analysis to peer reviews and opinion surveys. The procedure is composed of two steps: the first is to collect the most relevant qualitative assessments from international organizations (for example, the ones available in the Harzing database) and, as inductive analysis, to apply fuzzy clustering to determine homogeneous journal classes; the second deductive step is to determine the hidden logical rules that underlies the classification, using a classification tree to reproduce the same patterns of the first step. Our approach is applied to the classification of 138 academic journals that were selected by members of AMASES, an Italian mathematics association, as the most prominent journals of our field. The clusters that are determined by our method show that rankings are affected by two hidden dimensions: one is the academic prestige of a publication, but the other is the disciplinary diffusion of a mathematics subfield. In particular, mathematics journals that are close to finance or economics are usually ranked better than journals dealing with linear algebra or systems dynamics.

Getting mathematical concepts and learning proofs by computer aided linear algebra

Two of the most important aims of learning mathematics are to get the exact mathematical concepts and to learn how to make proofs. To achieve these aims, first year students need many examples and exercises as well as visualisations. Especially, visualisations were the targets which should be realised by the computer learning environment for linear algebra. This article will show many visualisations for concepts within the linear algebra. In the computer learning environment, there are besides mere visualisations experimental pages provided, where the students may try out many cases (e.g. of mappings in two or three dimensions, for finding fixed points or eigenvectors). Helping students to learn many proofs are shown in their clear layout and all explanations to the essential reasons of the steps of deduction are shown by display upon mouse over.

NEXCEL, a deductive spreadsheet

AbstractUsability and usefulness have made the spreadsheet one of the most successful computing applications of all times: millions rely on it every day for anything from typing grocery lists to developing multimillion-dollar budgets. One thing spreadsheets are not very good at is manipulating the symbolic data and helping users make decisions based on them. By tapping into recent research in Logic Programming, Databases and Cognitive Psychology, we propose a deductive extension to the spreadsheet paradigm that precisely addresses this issue. The accompanying tool, which we call NEXCEL, is intended as an automated assistant for the daily reasoning and decision-making needs of computer users, in the same way as a spreadsheet application such as Microsoft Excel assists them every day with simple and complex calculations. Users without formal training in Logic or even Computer Science can interactively define logical rules in the same simple way as they define formulas in Excel. NEXCEL immediately evaluates these rules, thereby returning lists of values that satisfy them, again just like with numerical formulas. The deductive component is seamlessly integrated into the traditional spreadsheet so that a user not only still has access to the usual functionalities but is also able to use them as part of the logical inference and, dually, to embed deductive steps in a numerical calculation.