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Logic & Formal Reasoning

Latest Advances in Inductive Logic Programming - Programmer Books


This book represents a selection of papers presented at the Inductive Logic Programming (ILP) workshop held at Cumberland Lodge, Great Windsor Park. The collection marks two decades since the first ILP workshop in 1991. During this period the area has developed into the main forum for work on logic-based machine learning. The chapters cover a wide variety of topics, ranging from theory and ILP implementations to state-of-the-art applications in real-world domains. The international contributors represent leaders in the field from prestigious institutions in Europe, North America and Asia.

Glossary of artificial intelligence - Wikipedia


This glossary of artificial intelligence is a list of definitions of terms and concepts relevant to the study of artificial intelligence, its sub-disciplines, and related fields. Related glossaries include Glossary of computer science, Glossary of robotics, and Glossary of machine vision. Also stochastic Hopfield network with hidden units. Also exhaustive search or generate and test. Also deep structured learning or hierarchical learning.

How Close Are Computers to Automating Mathematical Reasoning?


"They're this crazy contact between an imaginary, nonphysical world and biologically evolved creatures," said the cognitive scientist Simon DeDeo of Carnegie Mellon University, who studies mathematical certainty by analyzing the structure of proofs. "We did not evolve to do this." Computers are useful for big calculations, but proofs require something different. Conjectures arise from inductive reasoning -- a kind of intuition about an interesting problem -- and proofs generally follow deductive, step-by-step logic. They often require complicated creative thinking as well as the more laborious work of filling in the gaps, and machines can't achieve this combination. Computerized theorem provers can be broken down into two categories.

Google AI introduces TF-Coder, a program synthesis tool that helps you write TensorFlow code


Manipulating tensors is not an easy task as it requires a lot of prerequisites, such as keeping track of multiple dimensions, Dtype compatibility, mathematical correctness, and tensor shape. The real challenge is identifying the right TensorFlow operations from the hundreds of options available. TensorFlow Coder(TF-Coder) makes the tensor manipulation possible without coding and by using examples. TF-Coder helps you write the TensorFlow code. The process is providing input-output examples of the required transformation.

Keeping CALM

Communications of the ACM

Multiple unreliable machines are running in parallel, sending messages to each other across network links with arbitrary delays. How can we be confident these systems do what we want despite this chaos? This issue should concern us because nearly all of the software we use today is part of a distributed system. Apps on your phone participate with hosted services in the cloud; together they form a distributed system. Hosted services themselves are massively distributed systems, often running on machines spread across the globe. Big data systems and large-scale databases are distributed across many machines. Most scientific computing and machine learning systems work in parallel across multiple processors. Even legacy desktop operating systems and applications like spreadsheets and word processors are tightly integrated with distributed backend services. The challenge of building correct distributed systems is increasingly urgent, but it is not new. One traditional answer has been to reduce this complexity with memory consistency guarantees--assurances that accesses to memory (heap variables, database keys, and so on) occur in a controlled fashion. However, the mechanisms used to enforce these guarantees--coordination protocols--are often criticized as barriers to high performance, scale, and availability of distributed systems. Coordination protocols enable autonomous, loosely coupled machines to jointly decide how to control basic behaviors, including the order of access to shared memory. These protocols are among the most clever and widely cited ideas in distributed computing. Some well-known techniques include the Paxos33 and Two-Phase Commit (2PC)25,34 protocols, and global barriers underlying computational models like Bulk Synchronous Parallel computing.40

A brief pre-history of Classical AI


To talk about Reasoning, it's important to understand how we got here. This article covers what I call the pre-history of Classical AI -- those parts of the story that happened before the invention of modern computers (pre 1950s) but are crucial to understanding why we believe that AI is possible. This is part 2 in a series on Reasoning. Like most things, the very beginnings of classical AI is rooted in philosophy, and starts in the ancient world (the Greeks, Indians, and Chinese all had some early forms of logic). But, as I'm not a masochist we start in more contemporary times with two big ideas that lay the foundation for modern AI: The development of logic was humanity's first great attempt at mechanizing intelligence, and the basis for modern logic lies with George Boole, Charles Pierce, and Gottlob Frege.

A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2


In response to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), some politicians have been keen to exploit the idea of achieving herd immunity. Countering this possibility are estimates derived from work on historical vaccination studies, which suggest that herd immunity may only be achieved at an unacceptable cost of lives. Because human populations are far from homogeneous, Britton et al. show that by introducing age and activity heterogeneities into population models for SARS-CoV-2, herd immunity can be achieved at a population-wide infection rate of ∼40%, considerably lower than previous estimates. This shift is because transmission and immunity are concentrated among the most active members of a population, who are often younger and less vulnerable. If nonpharmaceutical interventions are very strict, no herd immunity is achieved, and infections will then resurge if they are eased too quickly. Science , this issue p. [846][1] Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if R = 2.5 in an age-structured community with mixing rates fitted to social activity, then the disease-induced herd immunity level can be ~43%, which is substantially less than the classical herd immunity level of 60% obtained through homogeneous immunization of the population. Our estimates should be interpreted as an illustration of how population heterogeneity affects herd immunity rather than as an exact value or even a best estimate. [1]: /lookup/doi/10.1126/science.abc6810

Formulog: ML + Datalog + SMT


If you read a description of a static analysis in a paper, what might you find? There'll be some cute model of a language. Maybe some inference rules describing the analysis itself, but those rules probably rely on a variety of helper functions. These days, the analysis likely involves some logical reasoning: about the terms in the language, the branches conditionals might take, and so on. What makes a language good for implementing such an analysis? You'd want a variety of features: Aaron Bembenek, Steve Chong, and I have developed a design that hits the sweet spot of those four points: given Datalog as a core, you add constructors, pure ML, and a type-safe interface to SMT.

Formal Methods for Web Services - Programmer Books


Formal Methods for Web Services PDF Download for free: Book Description: This book presents papers from the lectures of leading researchers given at the Ninth International School on Formal Methods for the Design of Computer, Communication and Software Systems, SFM 2009, which was devoted to formal methods for web services.

Mathematical models to guide pandemic response


The ongoing coronavirus disease 2019 (COVID-19) pandemic has put mathematical models in the spotlight. As the theoretical biologist Robert May wrote: “the virtue of a mathematical that it forces clarity and precision upon conjecture, thus enabling meaningful comparison between the consequences of basic assumptions and the empirical facts” ([ 1 ][1]). On page 413 of this issue, Walker et al. ([ 2 ][2]) use a mathematical model to study the impact and burden of COVID-19 across a wide range of socioeconomic and demographic settings, with a focus on low- and middle-income countries (LMICs). Their analyses show that limited health care capacity in LMICs could counterbalance the benefits of a generally younger population. Unless these countries control the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus causing COVID-19, high disease burdens are likely. This work adds to a growing corpus of disease modeling designed to inform and guide the pandemic response. Following the emergence of a previously unknown pathogen like SARS-CoV-2, mathematical models can be used to estimate parameters of pathogen spread, explore possible future scenarios, evaluate retrospectively the efficacy of specific interventions, and identify prospective strategies (see the figure). At every stage, communicating the scope of a model's aims and the uncertainty in its outputs is essential to ensure that models effectively inform public health policy. In early 2020, it was important to assess the global risk posed by SARS-CoV-2 ([ 3 ][3]). Models provided estimates of R (the average number of new infections caused by each infectious individual when no one in the population is immune) and the infection fatality ratio (IFR), clarifying ambiguities in the latter due to asymptomatic infections and delays between infection and death ([ 4 ][4]). Models also provided estimates of the incubation period (the time from infection to symptom onset), allowing public health agencies to decide on 14 days for quarantine of exposed individuals ([ 5 ][5]). However, this illustrates the need for careful communication: 14-day quarantine and isolation can effectively reduce disease spread on average, but some individuals may spread the disease beyond 14 days. Building on growing knowledge of mechanisms and parameter estimates allowed researchers to explore possible future scenarios, including worst-case outcomes, and determine the implications for precautionary action ([ 6 ][6], [ 7 ][7]). The results provided in Walker et al. fit within this class of analyses. Of note, the authors do not seek to provide a precise prediction of the epidemic trajectory, but rather to highlight key areas of concern for LMICs and evaluate mitigation measures. As initial pandemic responses are put in place and data accumulates, the focus shifts to retrospective estimates of the efficacy of particular strategies. Using statistical inference algorithms, researchers can fit core epidemiological models to case data and data on the timing and nature of control interventions. This allows them to account for unknown aspects of underlying transmission dynamics, to tease out the individual effects of interventions, and to quantify the degree of uncertainty in these estimates ([ 8 ][8]). The amount of mechanistic detail included in such a model depends on its aims. For example, accounting for age-dependent transmission and susceptibility is critical when building models for retrospective estimation of the impact of school closures ([ 9 ][9]), but that level of detail might be omitted when studying larger-scale interventions, such as contact tracing or bans on travel. A key challenge of retrospective statistical modeling is that interventions are often entangled with each other, and with other processes. For example, several interventions may be implemented at once, making the individual impact of each intervention on transmission difficult or impossible to estimate. One solution is to compare multiple countries, regions, or municipalities that responded differently or at different times, but this approach is complicated by inevitable differences in their social and economic characteristics. Such confounding factors can prevent mathematical models from providing “meaningful comparison between the consequences of basic assumptions and the empirical facts” ([ 1 ][1]). Robust estimates of the relative impact of different interventions could be obtained by introducing brief delays in tightening (or loosening) interventions in randomly chosen “treatment” locations. Randomization reduces the chance of systematic differences between “treatment” and “control” locations where no delay is implemented (such an approach may be ethical if the costs and benefits of interventions remain uncertain). After the delay, differences in new infections (or susceptibility) between the treatment and the control locations can be used as model inputs, and the effect of the intervention in question can be estimated ([ 10 ][10]). Such estimates could provide invaluable information: Knowing how well interventions work allows the determination of which costly restrictions can be loosened with least impact on transmission and case numbers. ![Figure][11] Modeling during an outbreak An imagined pandemic time course shows cases (blue), deaths (red), and availability of serological data (orange). Modeling can estimate associated parameters of infection and intervention efficacy. Models can also make projections about the outbreak and the effects of interventions. Quantities that rely on, or are substantially enhanced by, serology are shown in orange. GRAPHIC: N. CARY/ SCIENCE Retrospective evaluations of specific interventions and detailed modeling efforts naturally build toward the identification of more targeted prospective strategies: Different countries, states, cities, or even workplaces vary in their capacity to respond to the pandemic and therefore require separate strategies for tightening or loosening interventions. Models can also help identify shortcomings in existing strategies, and explore opportunities for improvement or innovation. Although presymptomatic and asymptomatic transmission of COVID-19 has made contact tracing more difficult, modeling studies suggest feasibility of controlling spread through digital contact tracing, which allows for instantaneous identification of contacts ([ 11 ][12]). Many countries have started to develop and implement digital contact tracing apps, with varying degrees of success. However, digital contact tracing has been hampered by technical and ethical challenges, including the ability to accurately determine the proximity between individuals and to store such information in a privacy-preserving way. Thus, although models are valuable tools for testing new ideas, they must be accompanied by thorough consideration of practicalities. Prospective modeling not only informs strategy but also guides data collection. Registers of confirmed COVID-19 cases may miss asymptomatic infections, which can bias estimates of disease severity and IFR. In principle, serological (antibody) measurements provide a more reliable indication of whether an individual has been infected. Estimates of the IFR and other key parameters can thus be improved by combining serological surveys with data on cumulative infection-associated mortality. But if serological surveys are deployed in low incidence populations, true positive tests will be a minority of all tests, and estimates of cumulative incidence will be too uncertain to produce an informative estimate of the IFR. Epidemiological models could help reduce this uncertainty. Although valuable, mathematical models must be one facet of a diverse scientific response to a pandemic. During the early phases, models helped establish the scale of global risk and motivated action ([ 3 ][3]). But arguably the most critical evidence of severity was empirical data from Wuhan, Iran, and Northern Italy. Recently, establishing how best to loosen distancing restrictions has become a central challenge. Modeling can capture the benefits of specific interventions in terms of reduced transmission, but say nothing about their relative economic and psychological costs. Measurement of these costs is important to identifying which interventions work best ([ 10 ][10]) and which are most costly; models that encompass both epidemiological and economic aspects ([ 12 ][13]) are needed. What is next in the deployment of models? Perhaps the greatest conceptual success of infectious disease modeling was revealing that because the spread of infection depletes susceptible individuals, feedbacks are inherent to disease dynamics and can produce unexpected outcomes, including multiannual cycles of outbreaks. Yet, despite the devastating burden that COVID-19 has imposed so far, most of the world is still susceptible to SARS-CoV-2 infection. Most countries have yet to see sufficient depletion of susceptibility to meaningfully reduce infection spread, but such effects are likely to shape the future. Models projecting into this future have evaluated policy scenarios ([ 13 ][14]) and assessed the potential impact of seasonal variation in transmission ([ 14 ][15]). Notably, the immunological details on which these models rely (duration of immunity, whether immunity blocks transmission or prevents disease after infection, etc.) remain unclear. Models are one tool among many for tackling the pandemic, but they are perhaps the best framework for grappling with these possible futures. 1. [↵][16]1. R. M. May , Science 303, 790 (2004). [OpenUrl][17][Abstract/FREE Full Text][18] 2. [↵][19]1. P. G. T. Walker et al ., Science 369, 413 (2020). [OpenUrl][20][Abstract/FREE Full Text][21] 3. [↵][22]1. S. Cobey , Science 368, 713 (2020). [OpenUrl][23][Abstract/FREE Full Text][24] 4. [↵][25]1. T. W. Russell et al ., Euro Surveill. 25, 2000256 (2020). [OpenUrl][26][CrossRef][27][PubMed][28] 5. [↵][29]1. J. A. Backer et al ., Euro Surveill. 25, 2000062 (2020). [OpenUrl][30][CrossRef][31] 6. [↵][32]1. N. M. Ferguson et al ., “Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand”; . 7. [↵][33]1. N. G. Davies et al ., Lancet Public Health 10.1016/S2468-2667(20)30133-X (2020). 8. [↵][34]1. S. Flaxman et al ., Nature 10.1038/s41586-020-24 (2020). 9. [↵][35]1. N. G. Davies et al ., Nat. Med. 10.1038/s41591-020-0962-9 (2020). 10. [↵][36]1. J. Haushofer, 2. C. J. E. Metcalf , Science 368, 1063 (2020). [OpenUrl][37][Abstract/FREE Full Text][38] 11. [↵][39]1. L. Ferretti et al ., Science 368, eabb6936 (2020). [OpenUrl][40][Abstract/FREE Full Text][41] 12. [↵][42]1. P. Klepac et al ., Proc. Natl. Acad. Sci. U.S.A. 108, 14366 (2011). [OpenUrl][43][Abstract/FREE Full Text][44] 13. [↵][45]1. S. M. Kissler et al ., Science 368, 860 (2020). [OpenUrl][46][Abstract/FREE Full Text][47] 14. [↵][48]1. R. E. Baker et al ., Science 369, 315 (2020). [OpenUrl][49][Abstract/FREE Full Text][50] Acknowledgments: Thanks to C. Buckee for the Robert May quote; and I. Werning, J. Haushofer, and B. Grenfell for helpful comments. All authors contributed equally. 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