Intuitionistic Layered Graph Logic: Semantics and Proof Theory

P ublic support for U.S. federal expenditures for basic research gained momentum with the science and technology breakthroughs that contributed to the Allies' victory in World War II. After World War II, the Korean and Cold Wars concentrated research appropriations in the Department of Defense (DOD). DOD research expenditures were massive from 1950 to 1990. They included not only direct investments in weapons and intelligence systems but support of the underlying science, centered in physical sciences and engineering. What is less well remembered today is that DOD's basic research investments were broadly based, ranging far beyond the physical sciences and engineering into the life and social sciences. Through its service research offices and the Advanced Research Projects agencies, DOD also fostered interdisciplinary research in promising new areas, such as computation, and developed new modes for the performance of research, as in university materials research laboratories. The large investment in the physical sciences also contributed indirectly to medical science and health care, giving rise to many technologies used today. The life sciences now account for more than 50 percent of U.S. federal investment in basic research. Biomedical research funding has followed a pattern of steady significant growth over four decades, and the National Institutes of Health (NIH) have slowly come to dominate that funding. Today's strong federal support for the life sciences is warranted, because biomedical research is on the cusp of a revolution in preventative medicine and treatment. Nevertheless, today's overall research budget is increasingly out of balance. Federal funding of many fields in the physical sciences and engineering is down substantially since 1993 (9 to 36% in real terms in fields such as chemistry, physics, and electrical and chemical engineering). This loss, if continued, will imperil advances in these disciplines and endanger the continued flow of valuable discoveries and technologies that have been important to biomedical research and health care. National science and technology (S&T) policy over the past four decades has largely been led by physical scientists who first gained national experience in World War II. They crafted policies for broad investment in basic research and infrastructure, including the life sciences. As we enter the 21st century, biological scientists must assume broader leadership responsibilities in S&T policy, and they must speak out about the importance of support for all disciplines, including the physical sciences and engineering. NIH's Harold Varmus and the National Science Foundation's Rita Colwell recognize the imbalance in the current federal research portfolio and have begun advocating increased investment in all areas of research. Their leadership is to be commended, but it is not enough. Government, organizations, institutions, and industry can and should do more to bolster all basic research. NIH must set the example by much more broadly supporting innovative interdisciplinary research embracing all science, just as DOD did when it was the prime funder of R&D. Some of this has already begun in NIH's cross-institute bioengineering initiative and in prospective increased NIH support of information technology for biocomputation. Similar initiatives should be launched in other areas of the physical sciences and in the social and behavioral sciences. Funding for these initiatives should become a much larger percentage of NIH's overall expenditures. The life science professional societies must speak broadly for basic research and not just argue their own disciplinary cases. Disease advocacy groups must also articulate the case for the physical sciences in their work with the public and before Congress. University leaders and corporate executives must make the case for investment in all research disciplines. Most of all, biologists in the laboratory—working scientists and their students—need to appreciate that their research rests on the legacy not only of the life sciences but also the physical and other sciences. Today's life scientists and the next generation they are training must be the national leaders of the future who will increasingly guide all of U.S. basic research policy in the 21st century.

Two algebraic structures, the contrapositionally complemented Heyting algebra (ccHa) and the contrapositionally $\vee $ complemented Heyting algebra (c$\vee $cHa), are studied. The salient feature of these algebras is that there are two negations, one intuitionistic and another minimal in nature, along with a condition connecting the two operators. Properties of these algebras are discussed, examples are given and comparisons are made with relevant algebras. Intuitionistic Logic with Minimal Negation (ILM) corresponding to ccHas and its extension ${\textrm {ILM}}$-${\vee }$ for c$\vee $cHas are then investigated. Besides its relations with intuitionistic and minimal logics, ILM is observed to be related to Peirce’s logic and Vakarelov’s logic MIN. With a focus on properties of the two negations, relational semantics for ILM and ${\textrm {ILM}}$-${\vee }$ are obtained with respect to four classes of frames, and inter-translations between the classes preserving truth and validity are provided. ILM and ${\textrm {ILM}}$-${\vee }$ are shown to have the finite model property with respect to these classes of frames and proved to be decidable. Extracting features of the two negations in the algebras, a further investigation is made, following logical studies of negations that define the operators independently of the binary operator of implication. Using Dunn’s logical framework for the purpose, two logics $K_{im}$ and $K_{im-{\vee }}$ are discussed, where the language does not include implication. The $K_{im}$-algebras are reducts of ccHas and are different from relevant algebraic structures having two negations. The negations in the $K_{im}$-algebras and $K_{im-{\vee }}$-algebras are shown to occupy distinct positions in an enhanced form of Dunn’s kite of negations. Relational semantics for $K_{im}$ and $K_{im-{\vee }}$ is provided by a class of frames that are based on Dunn’s compatibility frames. It is observed that this class coincides with one of the four classes giving the relational semantics for ILM and ${\textrm {ILM}}$-${\vee }$.

Models of complex systems can capture much useful information but can be difficult to apply to real-world decision-making because the type of information they contain is often inconsistent with that required for traditional decision analysis. New approaches, which use inductive reasoning over large ensembles of computational experiments, now make possible systematic comparison of alternative policy options using models of complex systems. This article describes Computer-Assisted Reasoning, an approach to decision-making under conditions of deep uncertainty that is ideally suited to applying complex systems to policy analysis. The article demonstrates the approach on the policy problem of global climate change, with a particular focus on the role of technology policies in a robust, adaptive strategy for greenhouse gas abatement.

Addressing the policy challenges and opportunities of “Big data”

According to the realist, the meaning of a declarative, non-indexical sentence is the condition under which it is true and the truth-condition of an undecidable sentence can obtain or fail to obtain independently of our capacity, even in principle, to recognize that it obtains or that fails to do so.1 In a series of papers, beginning with “Truth” in 1959, Michael Dummett challenged the position that the classical notion of truth-condition occupied as the central notion of a theory of meaning, and proposed that it should be replaced by the anti-realist (and intuitionistic) notion of assertability-condition. Taken together with normalization results obtained by Dag Prawitz, Dummett’s work truly opened up the anti-realist challenge at the level of proof-theoretical semantics.2 There has been since numerous rejoinders from partisans of classical logic, which were at times met with by attempts at watering down the anti-realist challenge, e.g., by arguing that anti-realism does not necessarily entail the adoption of intuitionistic logic. Only a few anti-realists, such as Crispin Wright and Neil Tennant, tried to look instead in the other direction, towards a more radical version of anti-realism which would entail deeper revisions of classical logic than those recommended by intuitionists.3 In this paper, which is largely programmatic, we shall also argue in favour of a radical anti-realism which would be a genuine alternative to the traditional anti-realism of Dummett and Prawitz. The debate about anti-realism has by now more or less run out of breath and we wish to provide it with a new lease on life, by taking into account the profound changes that took place in proof theory during the intervening years. We have in mind in particular the considerable development within Gentzen-style proof theory of non-classical, substructural logics other than intuitionistic logic, which seriously opens up the possibility that anti-realism, when properly understood, might end up justifying another logic, and the development of closer links between proof theory and computational complexity theory that has renewed interest in a radical form of anti-realism, namely strict finitism.KeywordsClassical LogicIntuitionistic LogicLinear LogicNatural DeductionProof TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Modern complex systems of responsible purposes are built as fault-tolerant systems, i.e. such systems have the ability to function while some of their separate elements have a fault. This feature is achieved by introduction of different kinds of redundancy (structural, algorithmic, time, etc.), which leads to complications of the algorithm of system internal behavior due to the introduction of the functions of monitoring, fault localization, switching and performance recovery system, resulting in the significant complication of the model of system reliability. The complexity of such fault-tolerant systems makes their reliability of greater dimension (of the order of tens till hundreds of thousand equations), which is almost impossible for their formation and analysis by hand. Therefore, the requires a high level of credibility and an appropriate level of formalization to built models are imposed on these models, which allows to implement the automation of their building and analysis of reliability using modern computer tools. The combination of analytical methods for the research of reliability and computing capability of modern computers is a promising direction for further development of methods of reliability theory. Experience shows that the manual building the state space of fault-tolerant systems even with a small number of elements (up to 10) without the use of software is a time-consuming process. This article describes the procedure of automated development of the reliability models of complex technical systems, implemented in software module ASNA, which developed at the chair Theoretical Radioengineering and Radiomeasurement of Lviv National Polytechnic University

Models of Society and Complex Systems introduces readers to a variety of different mathematical tools used for modelling human behaviour and interactions, and the complex social dynamics that drive institutions, conflict, and coordination. What laws govern human affairs? How can we make sense of the complexity of societies and how do individual actions, characteristics, and beliefs interact? Social systems follow regularities which allow us to answer these questions using different mathematical approaches. This book emphasises both theory and application. It systematically introduces mathematical approaches, such as evolutionary and spatial game theory, social network analysis, agent-based modelling, and chaos theory. It provides readers with the necessary theoretical background of each toolset as well as the underlying intuition, while each chapter includes exercises and applications to real-world phenomena. By looking behind the surface of various social occurrences, the reader uncovers the reasons why social systems exhibit both cultural universals and at the same time a diversity of practices and norms to a degree that even surpasses biological variety, or why some riots turn into revolutions while others do not even make it into the news. This book is written for any scholar in the social sciences interested in studying and understanding human behaviour, social dynamics, and the complex systems of society. It does not expect readers to have a particular background apart from some elementary knowledge and affinity for mathematics.

Several formal systems, such as resolution and minimal model semantics, provide a framework for logic programming. In this article, we will survey the use ofstructural proof theoryas an alternative foundation. Researchers have been using this foundation for the past 35 years to elevate logic programming from its roots in first-order classical logic into higher-order versions of intuitionistic and linear logic. These more expressive logic programming languages allow for capturing stateful computations and rich forms of abstractions, including higher-order programming, modularity, and abstract data types. Term-level bindings are another kind of abstraction, and these are given an elegant and direct treatment within both proof theory and these extended logic programming languages. Logic programming has also inspired new results in proof theory, such as those involving polarity and focused proofs. These recent results provide a high-level means for presenting the differences between forward-chaining and backward-chaining style inferences. Anchoring logic programming in proof theory has also helped identify its connections and differences with functional programming, deductive databases, and model checking.

A healthy lifestyle is fundamental for the prevention and treatment of cardiovascular disease and other noncommunicable diseases (NCDs). Investment in primary prevention, including modification of health risk behaviors, could result in a 4-fold improvement in health outcomes compared with secondary prevention based on pharmacological treatment. The American Heart Association (AHA) emphasized the importance of lifestyle in its 2020 goals for cardiovascular health promotion and disease reduction. In addition to defining “cardiovascular health” based on criteria for blood pressure and biochemical markers (lipids and glycemia), the AHA Strategic Planning Committee further identified lifestyle characteristics of central importance: nutrition, physical activity, smoking, and maintenance of a healthy body weight.1 The World Health Organization estimated that ≈80% of NCDs could be prevented if 4 key lifestyle practices were followed: a healthy diet, being physically active, avoidance of tobacco, and alcohol intake in moderation.2 To support healthy lifestyle initiatives, major changes are necessary at the societal level to improve population health. Numerous strategies might help to create a culture that promotes and facilitates healthy behaviors, including creating laws and regulations, mounting large-scale public awareness and education campaigns, implementing local community programs, and providing individual counseling.3 Physicians are uniquely positioned to encourage individuals to adopt healthy lifestyle behaviors: Approximately 80% of Americans visit their primary care physician at least once a year. Physicians directly communicate with their patients during clinical encounters across numerous settings, and research indicates that patients highly value recommendations provided by their physicians.4,5 However, data further indicate that lifestyle counseling does not routinely occur in physicians’ offices, thereby representing a lost opportunity. Physicians report that they perform lifestyle counseling during ≈34% of clinic visits.4 Patients, in turn, report an even lower frequency of physician lifestyle counseling. For example, obese patients reported receiving physical activity and …

This is a book about the modelling of complex systems and, unlike many books on this subject, concentrates on the discussion of specific systems and gives practical methods for modelling and simulating them. This is not to say that the author does not devote space to the general philosophy and definition of complex systems and agent-based modelling, but the emphasis is definitely on the development of concrete methods for analysing them. This is, in my view, to be welcomed and I thoroughly recommend the book, especially to those with a theoretical physics background who will be very much at home with the language and techniques which are used. The author has developed a formalism for understanding complex systems which is based on the Langevin approach to the study of Brownian motion. This is a mesoscopic description; details of the interactions between the Brownian particle and the molecules of the surrounding fluid are replaced by a randomly fluctuating force. Thus all microscopic detail is replaced by a coarse-grained description which encapsulates the essence of the interactions at the finer level of description. In a similar way, the influences on Brownian agents in a multi-agent system are replaced by stochastic influences which sum up the effects of these interactions on a finer scale. Unlike Brownian particles, Brownian agents are not structureless particles, but instead have some internal states so that, for instance, they may react to changes in the environment or to the presence of other agents. Most of the book is concerned with developing the idea of Brownian agents using the techniques of statistical physics. This development parallels that for Brownian particles in physics, but the author then goes on to apply the technique to problems in biology, economics and the social sciences. This is a clear and well-written book which is a useful addition to the literature on complex systems. It will be interesting to see if the use of Brownian agents becomes a standard tool in the study of complex systems in the future.

Algebra, Proof Theory and Applications for a Logic of Propositions, Actions and Adjoint Modal Operators

To summarize the scientific revolution in one phrase: it was the time when a new way of studying the natural, physical world became widely accepted by a small “community of scholars,” although not necessarily by nonscientists. But the specific status of that “new way” is hotly disputed and the precise historical steps involved in that development are extremely complex. Standard histories are those by Dampier (1966) and Cohen (2001). Cohen stresses the stages involved from initial creative insight to dissemination (orally or in letters, later on in print) and then widespread acceptance. For example, Descartes’ theory of inertia of 1633 was held back when the Inquisition condemned Galileo's theological interpretations and Descartes decided it was not a good time to publish. In the seventeenth century there was a significant qualitative transformation in the approach to the study of natural philosophy and that major change is now often called the “scientific revolution,” but it is clear that small‐scale “revolutions” took place before and have happened since. It was at that time that the transition from undifferentiated “astronomy/astrology” and “alchemy/chemistry” first really got under way. Moreover, great advances were made in mathematics. The story of the rise of modern science begins even earlier, however, with the Arab contacts with Greek science, and modern science eventually led to Enlightenment philosophy (Hellemans & Bunch 1988: 58–188). Different natural philosophies changed at different rates and in different ways. For example, empirical and theoretical progress in astronomy and physics was different from progress in other physical sciences like chemistry (Goodman & Russell 1991: 387–414). However, it was between circa 1500 and1800 that the distinction between true science and proto‐science or pseudo‐science (Shermer 2001: 22–65) became somewhat clearer. Many thinkers have seen the essence of the intellectual revolution as a leap beyond the tradition inherited from Aristotelianism and rationalism. But the notion that simple inductive empiricism, often identified with Francis Bacon's New “Organon” ( Novum organum ) of 1620, is the basis of the scientific method has been rejected. It should be remembered that the introduction of Aristotle's Organon concerning “categories” and “interpretation,” and his physics, astronomy, and biology transferred into Roman Catholic theology by Thomas Aquinas, was considered a radical step and indeed did open a window to the study of the actual order of nature and the universe (Funkenstein 1986). The idea of the importance of nuances of general theoretical assumptions concerning ontology and epistemology has been widely shared ever since the early 1960s, when Kuhn's (1970) history of paradigmatic changes in physical science became widely accepted. Indeed, the social sciences now also regularly use Kuhn's general theory of an oscillation between “normal science” and “paradigmatic revolutions.” The link between Kuhn's theories and earlier views concerning a dialectic of reason – views primarily associated with Hegel's critique of Cartesian dualism (Russon 1991) – should be noted. However, the seventeenth‐century paradigmatic revolution associated with Descartes, Galileo, Copernicus, Kepler, von Helmont, and many others was extremely important, since it laid the foundation for what was considered to be true science for the next four centuries. Newton's laws of gravitational attraction, motion, and force (i.e., inverse square law) in the Principia Mathematica (1687 manuscript) led to British Newtonianism, which was widely exported throughout Europe (e.g., the Low Countries), but Cartesianism in France was a rival for many years (Russell 1991). In the eighteenth century botany and zoology became more systematic with the use of binomial nomenclature, although Linnaeus's theories of nature and of society were deeply flawed (Koerner 1999). It was only at the beginning of the twentieth century that a series of new ideas constituting a general change in worldviews made a radical shift in scientific thinking possible. Einstein's theory of relativity did not reject Newtonian mechanics, but did make it clear that Newton's assumptions about space and time were too limited and that a true explanation of gravity required postulating “space‐time.” Similarly, discoveries in mathematics and statistics, particularly the invention of non‐Euclidean geometry, revolutionized science in the twentieth century in somewhat the same way they had in earlier times (Newman 1956). The same can be said for Boolean and Fregean mathematical and symbolic logic (Bartley in Dodgson 1986: 3–42). Comte (1957) wrote that scientific thinking moves only gradually, but inevitably, from the study of distant objects, such as stars, to that which is closest to human life – society itself. His positivism had a profound impact on logical positivism and the quest for “consilience,” a unified general science of all of the natural world (Wilson 1998). In English the distinction between science and social science is more rigid than in many other languages. In German the term Wissenschaft encompasses not only physical and natural sciences, but also social sciences and other disciplines such as history and jurisprudence.

A More Accurate View of the Scientific Method in the Physical Sciences and Implications for Learning and Research in the Social Sciences The Chapter Four focuses on more accurate view of the scientific method in the physical sciences and implications for learning and research in the social sciences. The Authors perspective of the scientific method and its applicability to the social sciences and how is more in line with the actual practice of scientific inquiry in the physical sciences. Rather than a mechanistic conception of the scientific method, we describe a richer view where creativity and rigor have equal voice. Based on our experiences and perspectives, as teacher-educator and physicist, we think our interpretation of the scientific method more accurately illuminates what research is really about in both the physical sciences and the social sciences. It is therefore the Authors intention to help ameliorate this conflict for the purpose of moving forward with a more creative, integrative, and rigorous template for scholarly inquiry in the social sciences.

Many large scale problems, particularly in the physical sciences, are solved using complex, high dimensional models whose outputs, for a given set of inputs, are expensive and time consuming to evaluate. The complexity of such problems forces us to focus attention on those limited aspects of uncertainty which are directly relevant to the tasks for which the model will be used. We discuss methods for constructing the relevant partial prior specifications for these uncertainties, based on the prior covariance structure. Our approach combines two sources of prior knowledge. First, we elicit both qualitative and quantitative prior information based on expert prior judgments, using computer-based elicitation tools for organizing the complex collection of assessments in a systematic way. Secondly, we test and refine these judgments using detailed experiments based on versions of the model which are cheaper to evaluate. Although the approach is quite general, we illustrate it in the context of matching hydrocarbon reservoir history

Precise dynamic mathematical models of complex systems are important in control and diagnostic systems design and allow testing a complex system in virtual environment at a low cost. They can be also utilized in rapid prototyping using a concept of hardware in the loop. Ever improving methods of experimental identification and using approaches in non-linear approximation can considerably increase the precision of dynamic models of complex systems. The article deals with non-linear approximation of transfer gains of a complex system and evaluates the influence of operational point selection on precision of the resulting model using methods of experimental data driven identification. The object of control is represented by two similar small turbojet engines at the Departments of the authors, the iSTC-21v and TKT-1, both based on the same power section having two degrees of freedom: fuel mass flow rate and variable convergent nozzle position.