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David Makinson
David Clement Makinson (born 27 August 1941), is an Australian mathematical logician living in London, England. Career Makinson began his studies at Sydney University in 1958 and was an associate of the Libertarian Society and Sydney Push. He is a Visiting Professor in the London School of Economics, University of London, and an associate member of the Centre de Recherche en Epistémologie Appliquée (CREA), École Polytechnique, Paris. He has held professorial rank positions in King's College London, University of London and in the American University of Beirut, Lebanon. From 1980 till 2001 he worked for UNESCO, Paris. Contributions David Makinson is highly regarded for his work on belief revision, uncertain reasoning, and modal logic. While studying in Oxford University (Worcester College) for his D.Phil under the supervision of Michael Dummett, he identified the preface paradox. In belief revision he created the AGM account of theory change with Carlos Alchourrón ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Australians
Australians, colloquially known as Aussies, are the citizens Citizenship is a "relationship between an individual and a state to which the individual owes allegiance and in turn is entitled to its protection". Each state determines the conditions under which it will recognize persons as its citizens, and ..., nationality, nationals and individuals associated with the country of Australia. This connection may be residential, legal, historical or ethno-cultural. For most Australians, several (or all) of these connections exist and are collectively the source of their being Australian. Australian law does not provide for a racial or ethnic component of nationality, instead relying on Australian nationality law, citizenship as a legal status. Since the postwar period, Australia has pursued an official policy of multiculturalism and has the List of sovereign states and dependent territories by immigrant population, world's eighth-largest immigrant population, Immigration to Aust ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inference
Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word '' infer'' means to "carry forward". Inference is theoretically traditionally divided into deduction and induction, a distinction that in Europe dates at least to Aristotle (300s BCE). Deduction is inference deriving logical conclusions from premises known or assumed to be true, with the laws of valid inference being studied in logic. Induction is inference from particular evidence to a universal conclusion. A third type of inference is sometimes distinguished, notably by Charles Sanders Peirce, contradistinguishing abduction from induction. Various fields study how inference is done in practice. Human inference (i.e. how humans draw conclusions) is traditionally studied within the fields of logic, argumentation studies, and cognitive psychology; artificial intelligence researchers develop automated inference systems to emulate human inference. Statistical infer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Logic
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional logic is included in first-order logic and higher-order logics. In this sense, propositional logic is the foundation of first-order logic and higher-order logic. Explanation Logical connectives are found in natural languages. In English for example, some examples are "and" ( conjunction), "or" (disjunction), "not" (negation) and "if ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximal Consistent Set
In mathematical logic, a theory is complete if it is consistent and for every closed formula in the theory's language, either that formula or its negation is provable. That is, for every sentence \varphi, the theory T contains the sentence or its negation but not both (that is, either T \vdash \varphi or T \vdash \neg \varphi). Recursively axiomatizable first-order theories that are consistent and rich enough to allow general mathematical reasoning to be formulated cannot be complete, as demonstrated by Gödel's first incompleteness theorem. This sense of ''complete'' is distinct from the notion of a complete ''logic'', which asserts that for every theory that can be formulated in the logic, all semantically valid statements are provable theorems (for an appropriate sense of "semantically valid"). Gödel's completeness theorem is about this latter kind of completeness. Complete theories are closed under a number of conditions internally modelling the T-schema: * For a set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete. The term "complete" is also used without qualification, with differing meanings depending on the context, mostly referring to the property of semantical validity. Intuitively, a system is called complete in this particular sense, if it can derive every formula that is true. Other properties related to completeness The property converse to completeness is called soundness: a system is sound with respect to a property (mostly semantical validity) if each of its theorems has that property. Forms of completeness Expressive completeness A formal language is expressively complete if it can express the subject matter for which it is intended. Functional completeness A set of logical connectives associated with a formal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-classical Logic
Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic. There are several ways in which this is done, including by way of extensions, deviations, and variations. The aim of these departures is to make it possible to construct different models of logical consequence and logical truth. Philosophical logic is understood to encompass and focus on non-classical logics, although the term has other meanings as well. In addition, some parts of theoretical computer science can be thought of as using non-classical reasoning, although this varies according to the subject area. For example, the basic boolean functions (e.g. AND, OR, NOT, etc) in computer science are very much classical in nature, as is clearly the case given that they can be fully described by classical truth tables. However, in contrast, some computerized proof methods may not use classical logic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Gärdenfors
Björn ''Peter'' Gärdenfors (born 21 September 1949) is professor of cognitive science at the University of Lund, Sweden. Gärdenfors is a recipient of the Gad Rausing Prize ( Swedish: ''Rausingpriset''). He received his doctorate from Lund University in 1974. Internationally, he is one of Sweden's most notable philosophers. In 1996, he was elected a member of the Royal Swedish Academy of Letters, History and Antiquities and in 2009 he became a member of Royal Swedish Academy of Sciences. He is member of Deutsche Akademie für Naturforscher and of Academia Europaea. In 2014 Gärdenfors was awarded a Senior Fellowship of the Zukunftskolleg at the University of Konstanz.https://www.zukunftskolleg.uni-konstanz.de/people/senior-fellows/ He was a member of the Prize Committee for the Prize in Economic Sciences in Memory of Alfred Nobel 2011-2017. Peter Gärdenfors' research covers several areas: Belief revision, decision theory, philosophy of science, concept formation, conceptual ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carlos Alchourrón
Carlos may refer to: Places ;Canada * Carlos, Alberta, a locality ;United States * Carlos, Indiana, an unincorporated community * Carlos, Maryland, a place in Allegany County * Carlos, Minnesota, a small city * Carlos, West Virginia ;Elsewhere * Carlos (crater), Montes Apenninus, LQ12, Moon; a lunar crater near Mons Hadley People * Carlos (given name), including a list of name holders * Carlos (surname), including a list of name holders Sportspeople * Carlos (Timorese footballer) (born 1986) * Carlos (footballer, born 1995), Brazilian footballer * Carlos (footballer, born 1985), Brazilian footballer Others * Carlos (Calusa) (died 1567), king or paramount chief of the Calusa people of Southwest Florida * Carlos (DJ) (born 1966), British DJ * Carlos (singer) (1943—2008), French entertainer * Carlos the Jackal, a Venezuelan terrorist *Carlos (DJ) (born 2010) Guyanese DJ Arts and entertainment * ''Carlos'' (miniseries), 2010 biopic about the terrorist Carlos the Jackal * ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Belief Revision
Belief revision is the process of changing beliefs to take into account a new piece of information. The logical formalization of belief revision is researched in philosophy, in databases, and in artificial intelligence for the design of rational agents. What makes belief revision non-trivial is that several different ways for performing this operation may be possible. For example, if the current knowledge includes the three facts "A is true", "B is true" and "if A and B are true then C is true", the introduction of the new information "C is false" can be done preserving consistency only by removing at least one of the three facts. In this case, there are at least three different ways for performing revision. In general, there may be several different ways for changing knowledge. Revision and update Two kinds of changes are usually distinguished: ; update : the new information is about the situation at present, while the old beliefs refer to the past; update is the operation of cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Preface Paradox
The preface paradox, or the paradox of the preface, was introduced by David Makinson in 1965. Similar to the lottery paradox, it presents an argument according to which it can be rational to accept mutually incompatible beliefs. While the preface paradox ''nullifies'' a claim contrary to one's belief, it is opposite to Moore's paradox which ''asserts'' a claim contrary to one's belief. Overview The argument runs along these lines: It is customary for authors of academic books to include in the preface of their books statements such as "any errors that remain are my sole responsibility." Occasionally they go further and actually claim there are errors in the books, with statements such as "the errors that are found herein are mine alone." (1) Such an author has written a book that contains many assertions, and has factually checked each one carefully, submitted it to reviewers for comment, etc. Thus, he has reason to believe that each assertion he has made is true. (2) Howev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michael Dummett
Sir Michael Anthony Eardley Dummett (27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics. He was known for his work on truth and meaning and their implications to debates between realism and anti-realism, a term he helped to popularize. He devised the Quota Borda system of proportional voting, based on the Borda count. In mathematical logic, he developed an intermediate logic, already studied by Kurt Gödel: the Gödel–Dummett logic. Education and army service Born 27 June 1925, Dummett was the son of George Herbert Dummett (1880–1970), a silk merch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title '' Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
