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- Kladionice KORNER
- Mathematical Logic for Computer Science (Third edition)
- Lecture notes
- Essential Logic for Computer Science

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Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author. Full-text access to all papers is freely available.

## Kladionice KORNER

Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:. Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory formerly called recursion theory , modal logic and category theory.

The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing. One of the first applications to use the term artificial intelligence was the Logic Theorist system developed by Allen Newell , J.

Shaw, and Herbert Simon in One of the things that a logician does is to take a set of statements in logic and deduce the conclusions additional statements that must be true by the laws of logic.

For example, If given a logical system that states "All humans are mortal" and "Socrates is human" a valid conclusion is "Socrates is mortal". Of course this is a trivial example. In actual logical systems the statements can be numerous and complex. It was realized early on that this kind of analysis could be significantly aided by the use of computers.

The Logic Theorist validated the theoretical work of Bertrand Russell and Alfred North Whitehead in their influential work on mathematical logic called Principia Mathematica. In addition, subsequent systems have been utilized by logicians to validate and discover new logical theorems and proofs. There has always been a strong influence from mathematical logic on the field of artificial intelligence AI. From the beginning of the field it was realized that technology to automate logical inferences could have great potential to solve problems and draw conclusions from facts.

Ron Brachman has described first-order logic FOL as the metric by which all AI knowledge representation formalisms should be evaluated. There is no more general or powerful known method for describing and analyzing information than FOL. The reason FOL itself is simply not used as a computer language is that it is actually too expressive, in the sense that FOL can easily express statements that no computer, no matter how powerful, could ever solve.

For this reason every form of knowledge representation is in some sense a trade off between expressivity and computability. The more expressive the language is, the closer it is to FOL, the more likely it is to be slower and prone to an infinite loop.

Rather than arbitrary formulas with the full range of logical operators the starting point is simply what logicians refer to as modus ponens. As a result, rule-based systems can support high-performance computation, especially if they take advantage of optimization algorithms and compilation.

Another major area of research for logical theory was software engineering. Research projects such as the Knowledge Based Software Assistant and Programmer's Apprentice programs applied logical theory to validate the correctness of software specifications. They also used them to transform the specifications into efficient code on diverse platforms and to prove the equivalence between the implementation and the specification.

However, in specific domains with appropriate formalisms and reusable templates the approach has proven viable for commercial products. The appropriate domains are usually those such as weapons systems, security systems, and real time financial systems where failure of the system has excessively high human or financial cost.

An error in a chip is catastrophic. Unlike software, chips can't be patched or updated. As a result, there is commercial justification for using formal methods to prove that the implementation corresponds to the specification.

Another important application of logic to computer technology has been in the area of frame languages and automatic classifiers. This allows specialized theorem provers called classifiers to analyze the various declarations between sets, subsets, and relations in a given model. In this way the model can be validated and any inconsistent definitions flagged.

The classifier can also infer new information, for example define new sets based on existing information and change the definition of existing sets based on new data. The level of flexibility is ideal for handling the ever changing world of the Internet.

Classifier technology is built on top of languages such as the Web Ontology Language to allow a logical semantic level on to the existing Internet. This layer of is called the Semantic web. Temporal logic is used for reasoning in concurrent systems. From Wikipedia, the free encyclopedia. Academic discipline.

Elements of the Theory of Computation. Prentice Hall. In Rolf Herken ed. The Universal Turing Machine. Springer Verlag. Retrieved 26 December Interpreting Godel. Cambridge University Press. Retrieved 17 August Basic Books.

Hayes Machine Intelligence. Shaw; H. Simon In Ed Feigenbaum ed. Computers and Thought. McGraw Hill. In Ronald Brachman and Hector J. Levesque ed. Reading in Knowledge Representation. Morgan Kaufmann. The good news in reducing KR service to theorem proving is that we now have a very clear, very specific notion of what the KR system should do; the bad new is that it is also clear that the services can not be provided Artificial Intelligence.

Archived from the original PDF on Retrieved 25 December Waters November IEEE Expert. Formal Methods in Circuit Design. Press Syndicate of the University of Cambridge. Scientific American. Archived from the original on April 24, Abramsky; D. Gabbay; T. Maibaum eds. Handbook of Logic in Computer Science. Oxford University Press. Outline History. Argumentation Metalogic Metamathematics Set. Mathematical logic Boolean algebra Set theory. Logicians Rules of inference Paradoxes Fallacies Logic symbols.

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## Mathematical Logic for Computer Science (Third edition)

On-line Guide to Prolog Programming. Prolog is a declarative programming language with succesfull applications in several areas like artificial intelligence and scheduling. The guide provides a tutorial to programming in Prolog starting from the beginners level. There are a lot of examples of Prolog source code. On-line Guide to Constraint Programming. Constraint Programming is a framework for declarative problem solving using constraints; relations among problem variables.

By Rex Page and Ruben Gamboa. An introduction to applying predicate logic to testing and verification of software and digital circuits that focuses on applications rather than theory. Computer scientists use logic for testing and verification of software and digital circuits, but many computer science students study logic only in the context of traditional mathematics, encountering the subject in a few lectures and a handful of problem sets in a discrete math course. This book offers a more substantive and rigorous approach to logic that focuses on applications in computer science. Topics covered include predicate logic, equation-based software, automated testing and theorem proving, and large-scale computation. Formalism is emphasized, and the book employs three formal notations: traditional algebraic formulas of propositional and predicate logic; digital circuit diagrams; and the widely used partially automated theorem prover, ACL2, which provides an accessible introduction to mechanized formalism.

## Lecture notes

Most users should sign in with their email address. If you originally registered with a username please use that to sign in. To purchase short term access, please sign in to your Oxford Academic account above. Don't already have an Oxford Academic account? Oxford University Press is a department of the University of Oxford.

By reflecting the syntax of each system in the other and providing a flexible interface for extending translation, our connection allows for the exchange of arbitrary information between the two systems. I include several topics under this heading, although not alw, A comprehensive account of these proof systems based on, Two recent book accounts of methods used in SA. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. Philosophical Transactions. With kind permission of Dr.

Logic in computer science covers the overlap between the field of logic and that of computer science. The topic can essentially be divided into three main areas:. Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory formerly called recursion theory , modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing.

### Essential Logic for Computer Science

Mathematical Logic for Computer Science is a mathematics textbook with theorems and proofs, but the choice of topics has been guided by the needs of students of computer science. The method of semantic tableaux provides an elegant way to teach logic that is both theoretically sound and easy to understand. The uniform use of tableaux-based techniques facilitates learning advanced logical systems based on what the student has learned from elementary systems. The logical systems presented are: propositional logic, first-order logic, resolution and its application to logic programming, Hoare logic for the verification of sequential programs, and linear temporal logic for the verification of concurrent programs. The third edition has been entirely rewritten and includes new chapters on central topics of modern computer science: SAT solvers and model checking. I have used the second edition of this book for my class.

Были другие люди. Празднично одетые испанцы выходили из дверей и ворот на улицу, оживленно разговаривая и смеясь. Халохот, спустившись вниз по улочке, смачно выругался. Сначала от Беккера его отделяла лишь одна супружеская пара, и он надеялся, что они куда-нибудь свернут.

Окажись дома. Через пять гудков он услышал ее голос. - Здравствуйте, Это Сьюзан Флетчер. Извините, меня нет дома, но если вы оставите свое сообщение… Беккер выслушал все до конца. Где же .

PDF | On Jan 1, , Michael Huth and others published Logic in computer science - modelling and reasoning about systems. | Find, read and cite all the.

#### Table of contents

На экране высветилось: СЛЕДОПЫТ ОТПРАВЛЕН Теперь надо ждать. Сьюзан вздохнула. Она чувствовала себя виноватой из-за того, что так резко говорила с коммандером. Ведь если кто и может справиться с возникшей опасностью, да еще без посторонней помощи, так это Тревор Стратмор. Он обладал сверхъестественной способностью одерживать верх над всеми, кто бросал ему вызов. Шесть месяцев назад, когда Фонд электронных границ обнародовал информацию о том, что подводная лодка АНБ прослушивает подводные телефонные кабели, Стратмор организовал утечку информации о том, что эта подводная лодка на самом деле занимается незаконным сбросом токсичных отходов.

Проституция в Испании запрещена, а сеньор Ролдан был человеком осторожным. Он уже не один раз обжигался, когда полицейские чиновники выдавали себя за похотливых туристов. Я хотел бы с ней покувыркаться. Ролдан сразу решил, что это подстава.

Когда Сьюзан вернулась в Третий узел, Грег Хейл как ни в чем не бывало тихо сидел за своим терминалом. ГЛАВА 30 Альфонсо XIII оказался небольшим четырехзвездочным отелем, расположенным в некотором отдалении от Пуэрта-де-Хереса и окруженным кованой чугунной оградой и кустами сирени. Поднявшись по мраморным ступенькам, Дэвид подошел к двери, и она точно по волшебству открылась. Привратник проводил его в фойе.

*Для Сьюзан это не составляло проблемы: она была безмерно счастлива в своей скромной двухкомнатной квартире, водила вольво и довольствовалась весьма консервативным гардеробом. Но вот туфли - совсем другое .*

При всем моем уважении к вам, сэр, - сказала Мидж, - я бы порекомендовала послать в шифровалку бригаду службы безопасности - просто чтобы убедиться… - Ничего подобного мы делать не будем. На этом Мидж капитулировала: - Хорошо. Доброй ночи.

Минутку! - отрезал Стратмор, вопросительно глядя на Хейла. - Мне нужно закончить разговор. - Он повернулся и направился к своему кабинету. Сьюзан открыла рот, но слова застряли у нее в горле. Хейл - Северная Дакота.

Horn clause logic and resolution underlie the very widespread use of logic programming, while algorithms for automated theorem proving have long been of.

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PDF | On Jan 1, , Steve Reeves and others published Logic for computer science | Find, read and cite all the research you need on ResearchGate.

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