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1. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
theory Abstract and axiomatic computability and recursion 03D75 theory Abstract and axiomatic homotopy 55U35 theory Abstract bifurcation 47J15
textbooks, tutorial papers, etc.) # instructional exposition (
textbooks, tutorial papers, etc.) # instructional exposition (
textbooks, tutorial papers, etc.) # instructional exposition (
textbooks. textbook use in the classroom # analysis of textbooks, development and evaluation of
th and 16th centuries, renaissance # 15
th centuries, renaissance # 15th and 16
th century # 17
th century # 18
th century # 19
th century # 20 th problem and ramifications) # theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16 theorem # Hilbertian fields; Hilbert's irreducibility theorem proving (deduction, resolution, etc.) theorem, asphericity # Dehn's lemma, sphere theorem, loop theorem, loop theorem, asphericity # Dehn's lemma, sphere theorem. polynomials. finite sums) # elementary algebra (variables, manipulation of expressions. binomial theorems # $L^p$-limit theorems # abstract inverse mapping and implicit function theorems # algebraic dependence theorems # analytic algebras and generalizations, preparation

2. List KWIC DDC And MSC Lexical Connection
Abstract (Maeda) geometries 51D05 Abstract algebra 512.02 Abstract and axiomatic computability and recursion theory 03D75 Abstract and axiomatic homotopy
Abel, Borel and power series methods
Abel, Picard, Toeplitz and Wiener - Hopf type) # integral equations of the convolution type (
Abelian and metabelian extensions # other
Abelian categories
Abelian functions # transcendence theory of elliptic and
Abelian groups
Abelian groups # analysis on specific locally compact
Abelian groups # finite
Abelian groups # Fourier and Fourier - Stieltjes transforms on locally compact
Abelian groups (LCA groups) # locally compact
Abelian groups, Riesz groups, ordered linear spaces # ordered Abelian integrals and differentials # analytic theory; Abelian varieties # complex multiplication and moduli of Abelian varieties # results involving Abelian varieties and schemes absolute and convective instability and stability absolute and strong summability absolute convergence of Fourier and trigonometric series # convergence and absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties) absolute neighborhood retracts absolute planes absolute spaces absolute summability of Fourier and trigonometric series # summability and absolutely continuous functions absolutely continuous functions, functions of bounded variation

3. 03Dxx
03D65 Highertype and set recursion theory; 03D70 Inductive definability; 03D75 Abstract and axiomatic computability and recursion theory
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Computability and recursion theory
  • 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also 03D10 Turing machines and related notions [See also 03D15 Complexity of computation [See also 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. [See also 03D45 Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section

4. DC MetaData For:A Structure Of Finite Signature With Identity Relation And With
68Q05 Models of computation 68Q10 Modes of computation 68Q15 Complexity classes 03D75 Abstract and axiomatic computability and recursion theory 03C10
A Structure of Finite Signature with Identity Relation and with P = NP - A Formal Proof
Preprint series: Preprintreihe Mathematik 2005, 1 MSC 2000
68Q05 Models of computation 68Q10 Modes of computation 68Q15 Complexity classes 03D75 Abstract and axiomatic computability and recursion theory 03C10 Quantifier elimination, model completeness and related topics
Here, we construct a simple structure of finite signature with identity relation and with P = NP respecting the uniform models of computation. So, a solution is also given for a problem that was put by Bruno Poizat in his work "Les petits cailloux". For the considered structure, we define an NP-hard problem and a problem which is decidable by a relation of this structure in constant time, and we give a polynomial time reduction of the first problem to the second problem.
The ideas for the development of the used method resulted from investigations of computation paths and small guesses by Felipe Cucker, Pascal Koiran, M. Matamala, and Klaus Meer. The connections will be demonstrated shortly. This document is well-formed XML.

5. MathNet-Mathematical Subject Classification
03D70, Inductive definability. 03D75, Abstract and axiomatic computability and recursion theory. 03D80, Applications of computability and recursion theory

6. HeiDOK
03D75 Abstract and axiomatic computability and recursion theory ( 0 Dok. ) 03D80 Applications of computability and recursion theory ( 0 Dok.

7. MSC 2000 : CC = Act
03B22 Abstract deductive systems; 03C95 Abstract model theory; 03D75 Abstract and axiomatic computability and recursion theory

8. [math/0409142] Axiomatic Theory Of Algorithms: Computability And Decidability In
Mathematics, Abstract math.LO/0409142 axiomatic Theory of Algorithms computability and Decidability in Algorithmic Classes. Authors Mark Burgin math
Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages
Full-text links: Download:
Citations p revious n ... ext
Mathematics > Logic
Title: Axiomatic Theory of Algorithms: Computability and Decidability in Algorithmic Classes
Authors: Mark Burgin (Submitted on 8 Sep 2004) Abstract: Subjects: Logic (math.LO) MSC classes: Cite as: arXiv:math/0409142v1 [math.LO]
Submission history
From: Mark Burgin [ view email
Wed, 8 Sep 2004 22:30:11 GMT (246kb)
Which authors of this paper are endorsers?
Link back to: arXiv form interface contact

9. 03Dxx
03D75, Abstract and axiomatic computability and recursion theory. 03D80, Applications of computability and recursion theory. 03D99, None of the above,
Computability and recursion theory Thue and Post systems, etc. Automata and formal grammars in connection with logical questions [See also Turing machines and related notions [See also Complexity of computation [See also Recursive functions and relations, subrecursive hierarchies Recursively (computably) enumerable sets and degrees Other Turing degree structures Other degrees and reducibilities Undecidability and degrees of sets of sentences Word problems, etc. [See also Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see Recursive equivalence types of sets and structures, isols Hierarchies Computability and recursion theory on ordinals, admissible sets, etc. Higher-type and set recursion theory Inductive definability Abstract and axiomatic computability and recursion theory Applications of computability and recursion theory None of the above, but in this section

10. Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical Logic A
39 03D75 Abstract and axiomatic computability and recursion theory; 40 03D80 Applications of computability and recursion theory; 41 03Dxx computability and
var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia";
Wikipedia:WikiProject Mathematics/PlanetMath Exchange/03-XX Mathematical logic and foundations
From Wikipedia, the free encyclopedia
Wikipedia:WikiProject Mathematics PlanetMath Exchange Jump to: navigation search This page provides a list of all articles available at PlanetMath in the following topic:
03-XX Mathematical logic and foundations
This list will be periodically updated. Each entry in the list has three fields:
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  • Status means PM article N not needed A adequately covered C copied M merged NC needs copying NM needs merging
    • Please update the WP and Status fields as appropriate. if the WP field is correct please remove the qualifier "guess". If the corresponding Wikipedia article exists, but the link to it is wrong, please fix the link. If you copy or merge an article from PlanetMath, please update the WP and Status fields for that entry. If you have any comments, for example, thoughts on how the PlanetMath article compares to the corresponding Wikipedia article(s), please place such comments on a new indented line following the entry. Comments of this kind are very valuable.
    Don't forget to include the relevant template if you copy over text or feel like an external link is warranted See the main page for examples and usage criteria.

    11. Award#0555381 - Computability Theory
    Abstract computability theory is the area of mathematical logic studying more and more from an algorithmic to a more Abstract axiomatic point of view.

    12. BRICS Workshop: Proof Theory And Complexity
    Then we will extend our results to axiomatic theories of algebraically closed D. Scott (Pittsburgh) Title Types and computability Abstract Over the
    Titles and Abstracts
    N. Arai (Hiroshima)
    Title: Cut-free LK Quasi-Polynomially Simulates Resolution
    J. Avigad (Pittsburgh)
    Title: Interpreting classical theories in constructive ones
    Abstract: In this talk I will discuss a surprisingly uniform method of interpreting a number of classical theories in constructive theories having the same proof-theoretic strength. The classical theories considered range in strength from bounded fragments of arithmetic to Kripke-Platek admissible set theory.
    Title: Dynamic ordinal analysis - a tool for separating fragments of bounded arithmetic
    Abstract: We define the dynamic ordinal
    S. Bellantoni (Toronto)
    Title: Ramification Today
    Abstract: This presentation will survey recent results in ramification and complexity theory, in both the functional and logical settings. Recent work has shown that ramification is an important tool in controlling the computational complexity of subrecursive and arithmetic systems. Another important tool in restricting computational complexity is linearity, which is particularly useful at higher type levels. The two can be integrated using mechanisms from modal logic. The use of modality allows one to generalize the concept of "ramification level" from ground type to all higher types. Thus, for a type (sigma -> tau) one defines a corresponding "complete" type !(sigma -> tau) at one higher ramification level. Analogous to the modal axiom of distribution, in the functional setting one has a term of type !(sigma -> tau) -> !sigma -> !tau.

    13. General General Mathematics Mathematics For Nonmathematicians
    Highertype and set recursion theory Inductive definability Abstract and axiomatic computability and recursion theory Applications of computability and
    General mathematics Mathematics for nonmathematicians (engineering, social sciences, etc.) Problem books Recreational mathematics [See also 97A20] Bibliographies External book reviews Dictionaries and other general reference works Formularies Philosophy of mathematics [See also 03A05] Methodology of mathematics, didactics [See also 97Cxx, 97Dxx] Theory of mathematical modeling General methods of simulation Dimensional analysis Physics (use more specific entries from Sections 70 through 86 when possible) Miscellaneous topics Collections of abstracts of lectures Collections of articles of general interest Collections of articles of miscellaneous specific content Proceedings of conferences of general interest Proceedings of conferences of miscellaneous specific interest Festschriften Volumes of selected translations Miscellaneous volumes of translations Collections of reprinted articles [See also 01A75] General histories, source books Ethnomathematics, general Paleolithic, Neolithic Indigenous cultures of the Americas Other indigenous cultures (non-European) Indigenous European cultures (pre-Greek, etc.)

    14. Gödel's Theorem
    axiomatic systems are equivalent to Abstract computers, to Turing machines, George S. Boolos and Richard C. Jeffrey, computability and Logic Textbook,
    20 Aug 2007 21:31 A much-abused result in mathematical logic , supposed by many authors who don't understand it to support their own favored brand of rubbish, and even subjected to surprisingly rough handling by some who really should know better. consistent if, given the axioms and the derivation rules, we can never derive two contradictory propositions; obviously, we want our axiomatic systems to be consistent. (The trick is to replace each symbol in the proposition, including numerals, either the system is inconsistent (horrors!), or there are true propositions which can't be reached from the axioms by applying the derivation rules. The system is thus incomplete, and the truth of those propositions is undecidable (within that system). Such undecidable propositions are known as or Update, June 2005 : Actually, that's wrong. Wolfgang Beirl has pointed out to me that Goodstein's Theorem is a result about natural numbers which is undecidable within Peano arithmetic, but provable within stronger set-theoretic systems. And it's actually a neat theorem, with no self-referential weirdness!] So far we've just been talking about Peano arithemtic, but now comes the kicker. Results about an axiomatic system apply to any bunch of things which satisfy the axioms. There are an immense number of other axiomatic systems which either include Peanese numbers among their basic entities, or where such things can be put together; they either have numbers, or can construct them. (These systems are said to provide

    15. Alex Simpson: Research Papers
    Replaces the Abstract Properties of Fixed Points in axiomatic Domain Theory, In Proceedings of International Conference on computability and Complexity
    Alex Simpson: Research Papers
    The papers are listed in chronological order, together with relevant bibliographic information. If you have problems downloading papers from this page then please contact me: Kripke Semantics for a Logical Framework.
    Unpublished paper, presented at Workshop on Types for Proofs and Programs, Baastad, Sweden, June 1992.
    Last revision July 1993. Recursive types in Kleisli categories.
    Unpublished paper, August 1992.
    Last revision August 1992. A characterisation of the least-fixed-point operator by dinaturality.
    Revised version of paper in Theoretical Computer Science
    Last revision September 1995. The Proof Theory and Semantics of Intuitionistic Modal Logic.
    PhD Thesis, December 1993, revised September 1994.
    Last revision September 1994. Reflection using the derivability conditions.
    Presented at International Conference in memory of Roberto Magari, Siena, Italy, April 1994.
    In Logic and Algebra , A. Ursini and P. Agliano (editors), pp. 603-616, Marcel Dekker Inc, 1996. Last revision August 1994.

    16. Axiomatic Theory Of Algorithms: Computability And Decidability In Algorithmic Cl
    Abstract. axiomatic approach has demonstrated its power in mathematics. science and technology as computability, decidability, and acceptability.
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    17. DoCIS Search Result
    axiomatic Synthesis of Computer Programs and computability Theorems Recent Results on . Proving Group Isomorphism Theorems (Extended Abstract)

    18. Front: [math.LO/0409142] Axiomatic Theory Of Algorithms: Computability And Decid
    Title axiomatic Theory of Algorithms computability and Decidability in Abstract axiomatic approach has demonstrated its power in mathematics.
    Front for the arXiv Mon, 24 Dec 2007
    math LO math.LO/0409142 search register submit
    ... iFAQ math.LO/0409142 Title: Axiomatic Theory of Algorithms: Computability and Decidability in Algorithmic Classes
    Authors: Mark Burgin
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    Abstract Representations of Biological Systems in Supercategories. Bull. Math. An axiomatic Explanation of Complete SelfReproduction. Bull.Math.
    @import url(; @import url(; @import url(; Cogprints
    • Home About Browse by Year ... Create Account
      Baianu, Professor I.C. and Lin, Ms. H.C. COMPUTER SIMULATION AND COMPUTABILITY OF BIOLOGICAL SYSTEMS. [Book Chapter] Full text available as: Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader
      Item Type: Book Chapter Additional Information: This updated paper addresses recent developments in quantum computation models of cognitive processes in the brain as well as in genetic networks, based on QMV- Logic and Lukasiewicz Logic Algebras (LLA)on the basis of the original published section that raised the question of biomimetics, or simulation of biosystems beyond recursive computation-based modeling, by means of n-valued logic, Quantum Computation, Quantum Automata and algebraic-topological symbolic models of both neural and genetic networks with very large numbers of components and complex, hierarchically organized brain structures. Keywords: Cognitive Neural Networks simulation by quantum computers; algebraic-topological, symbolic computation; Genetic Networks/Genome; Interactome simulations by computers; Recursive and digital computability limitations for biological and chaotic dynamics simulations;Kauffman, random networks and Boolean algebra; Lukasiewics Logic Algebra isomporphic to MV-logic algebra as model of biological system networks; Quantum MV-Logic algebras for microphysical modelling in Quantum Genetics and Enzyme Kinetics; Categories, functors, natural transformations and Topos as adequate tools for modelling hierarchical organization in biological systems and especially super-structures involved in cognitive processes supported by multi-layered neural networks.

    20. Citebase - Axiomatic Theory Of Algorithms: Computability And Decidability In Alg
    axiomatic Theory of Algorithms computability and Decidability in Algorithmic Classes. Authors Burgin, Mark. axiomatic approach has demonstrated its power

    21. PlanetMath: Ackermann Function
    AMS MSC, 03D75 (Mathematical logic and foundations computability and recursion theory Abstract and axiomatic computability and recursion theory)
    (more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia



    meta Requests



    talkback Polls
    Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Ackermann function (Definition) Ackermann's function is defined by the recurrence relations Ackermann's function is an example of a recursive function that is not primitive recursive , but is instead -recursive (that is, Turing-computable Ackermann's function grows extremely fast. In fact, we find that ... and at this point conventional notation breaks down, and we need to employ something like Conway notation or Knuth notation for large numbers. Ackermann's function wasn't actually written in this form by its namesake, Wilhelm Ackermann. Instead, Ackermann found that the -fold exponentiation of with was an example of a recursive function which was not primitive recursive. Later this was simplified by Rosza Peter to a function of two variables similar to the one given above.

    22. JSTOR Algorithmic Procedures, Generalized Turing Algorithms, And
    An introduction to the use of computability on Abstract structures in this area of The last paper is by Byerly and considers two subjectsaxiomatic<876:APGTAA>2.0.CO;2-Q

    23. Number Theory And Logic, Languages, Information And Computability
    Abstract A formal model of the structure of information is presented in five axioms which define identity, containment, and joins of infons.
    logic, languages, information and computability
    Set theorist and mathematical philosopher Gregory Chaitin, inspired by the recent appearance of three popular books on the Riemann hypothesis, discusses the possibility that it might in some sense be appropriate to consider it as an axiom "The traditional view held by most mathematicians is that... the RH cannot be taken as [an] axiom, and cannot require new axioms, we simply must work much harder to prove them. According to the received view, we're not clever enough, we haven't come up with the right approach yet. This is very much the current concensus. However this majority view completely ignores there is no proof?
    "One is faced with an infinite series of axioms which can be extended further and further, without any end being visible...It is true that in the mathematics of today the higher levels of this hierarchy are practically never is not altogether unlikely that this character of present-day mathematics may have something to do with its inability to prove certain fundamental theorems, such as, for example, Riemann's Hypothesis." from M. du Sautoy

    Abstract, This proposal studies mathematical models of computation. and axioms , which seeks axiomatic accounts of the common properties amongst such

    25. Mathematics And Computation » Talks
    Abstract computability theory, which investigates computable functions and and develop basic computability theory, starting from a few simple axioms.
    @import url( );
    Mathematics and Computation
    September 18, 2007
    The Role of the Interval Domain in Modern Exact Real Arithmetic
    Filed under: RZ Talks Computation Constructive math With Iztok Kavkler Abstract: I will review the data structures and algorithms that are used in modern implementations of exact real arithmetic. They provide important insights, but some questions remain about what theoretical models support them, and how we can show them to be correct. It turns out that the correctness is not always clear, and that the good old interval domain still has a few tricks to offer. Download slides: domains8-slides.pdf Comments (0)
    May 24, 2007
    Synthetic Computability (MFPS XXIII Tutorial)
    Filed under: Synthetic computability Talks Tutorial Constructive math A tutorial presented at the Mathematical Foundations of Programming Semantics XXIII Tutorial Day.
    Comments (1)
    May 22, 2007
    Metric Spaces in Synthetic Topology
    Filed under: Talks Constructive math With Davorin Lešnik. Abstract:
    We investigate the relationship between constructive theory of metric spaces and synthetic topology. Connections between these are established by requiring a relationship to exist between the intrinsic and the metric topology of a space. We propose a non-classical axiom which has several desirable consequences, e.g., that all maps between separable metric spaces are continuous in the sense of metrics, and that, up to topological equivalence, a set can be equipped with at most one metric which makes it complete and separable.

    26. Computability Of Simple Games: A Complete Investigation Of The Sixty-four Possib
    2007 Abstract Classify simple games into sixteen. Keywords Voting games; axiomatic method; complete independence; Turing computability;
    This file is part of IDEAS , which uses RePEc data
    Papers Articles Software Books ... Help!
    Computability of simple games: A complete investigation of the sixty-four possibilities
    Author info Abstract Publisher info Download info ... Statistics Author Info Kumabe, Masahiro
    Mihara, H. Reiju

    Additional information is available for the following registered author(s): Abstract
    Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and algorithmic computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable infinite games and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms. Download Info To download: If you experience problems downloading a file, check if you have the proper

    In the 20th century algebra became the study of Abstract, axiomatic systems such as computability or recursion theory addresses the question of what is,
    FALL/WINTER COURSE OUTLINES NOTE: Faculty of Graduate Studies regulations regarding integrated courses (6000/5000 level course with a 4000 level course): Masters students who are enrolled in a thesis option must complete at least one full course (or equivalent) which is not integrated with an undergraduate course. Master’s students who are enrolled in a course work or research-review option must complete at least one and a half (or equivalent) courses, which are not integrated with an undergraduate course. Doctoral candidates shall not receive credit towards the Ph.D. degree for more than one full integrated course. Math 5200 6.0 PROBLEM SOLVING
    (FW 2002-2003, R 6-9, 003MC) This course aims to develop the student's problem
    solving ability by examining a variety of challenging problems from famous collections. Emphasis will be placed on problem?solving techniques of wide applicability, such as recursion and iteration methods, generating functions and power series, transformation methods, vector methods (both geometric and algebraic), and congruences. As well as specific mathematical techniques, we will discuss general approaches, typically a list such as: "Guess and Check", "Look for a Pattern", "Make A Systematic List", "Make A Drawing Or Model", "Simplify the Problem". There will be an emphasis throughout the course on teaching problem solving and items in the school curriculum will be looked at from a problem?solving point of view. We will use the MAPLE computer algebra to generate special solutions to help in discovering solutions in more general situations.

    28. [FOM] Simple Turing Machines, Universality, Encodings, Etc.
    If recursion theory is the axiomatic answer to what is computability? have since the mid1960s advocated more Abstract axioms, e.g. by taking certain
    [FOM] Simple Turing machines, Universality, Encodings, etc.
    Vaughan Pratt pratt at
    Fri Nov 2 00:59:24 EDT 2007 The overall point I'm making is that universality is a hard concept to pin down, and I suspect that there may never be a definition that fits everyone's intuition as to whether a system should be considered universal or not. Likewise with defining what information should be included as part of a system, or group of systems, and what is part of its initial condition. More information about the FOM mailing list

    29. Computable And Continuous Partial Homomorphisms On Metric Partial
    Abstract. We analyse the connection between the computability and continuity Finally, the PourEl and Richards axioms for computable sequence structures
    Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options

    30. Computability Of Simple Games: A Complete Investigation Of The Sixty-four Possib
    Abstract. Classify simple games into sixteen types in terms of the four conventional axioms monotonicity, properness, strongness, and nonweakness.
    @import url(; @import url(; Munich Personal RePEc Archive
    • Home Browse Search About ... Create Account
      Computability of simple games: A complete investigation of the sixty-four possibilities
      Kumabe, Masahiro and Mihara, H. Reiju Computability of simple games: A complete investigation of the sixty-four possibilities. Unpublished. There is a more recent version of this eprint available. Click here to view it. Full text available as: Preview PDF - Requires a PDF viewer such as GSview Xpdf or Adobe Acrobat Reader
      Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and computability. For each such class, we either show that it is empty or give an example of a game belonging to it. We observe that if a type contains an infinite game, then it contains both computable infinitegames and noncomputable ones. This strongly suggests that computability is logically, as well as conceptually, unrelated to the conventional axioms. Item Type: MPRA Paper Language: English Keywords: Voting games; infinitely many players; axiomatic method; complete independence; algorithms; Turing computability; recursion theory

    31. Preface
    It introduces the themes of the text models of computation, syntax, semantics, with Abstract types and axiomatic semantics with imperative programming.

    32. Axioms And Theorems For Integers, Lists And Finite Sets In Logic For Computable
    Abstract LCF (Logic for Computable Functions) is being promoted as a formal language environment for future LCF experiments and its axiomatic basis.

    33. Logic Colloquium 2006
    In the talk I will show that the normalisation proof can also be carried out in an Abstract axiomatic setting where the computability predicates are indexed
    main invited contributed registration how to get there
    Invited talks
    This page contains the schedule and abstracts of the tutorials, the plenary talks and the special sessions at the Logic Colloquium 2006
    The following facilities will be available in each room:
    • Beamer Laptop (for people who did not bring their own laptop: possible file formats .pdf .ps .ppt) Overhead projector Black board or white board
    At your convenience you can send a .pdf file with your slides to Jasper Stein ( ) who will have it pre-installed on the presentation computer.
    Room 1
    Room 1
    Room 1
    Room 1 (Chair: Ralf Schindler) Room 2 (Chair: Michael Rathjen)
    • Klaus Aehlig

    34. North Texas Logic Conference
    Abstract Working at the interface of computability theory and model theory, we classify the computabilitytheoretic complexity of two index sets of classes
    North Texas Logic Conference
    October 8 th th
    UNT Logic Schedule Abstracts Future Directions ... Transportation
    All talks will be held in GAB 105. The official program can be found here Friday, October 8 Saturday, October 9 Sunday, October 10 Morning Session: Morning Session: Morning Session: Andreas Blass Julia Knight
    Steffen Lempp

    Ilijas Farah
    Benedikt Loewe
    Break For Lunch Break For Lunch Break For Lunch Afternoon Session: Afternoon Session: Afternoon Session: Dan Mauldin
    Reed Solomon

    Millican Lecture
    Ted Slaman

    Denis Hirschfeldt

    Peter Cholak
    Peter Komjath ...
    Future Directions
    Contributed Talks
    Thomas Kent
    Alexander Raichev Bart Kastermans Ross Bryant ... Charles Boykin Dinner Trail Dust
    Becker Title: Cocycles Abstract: This talk is a contribution to the descriptive set theory of Polish group actions. Like much of the recent research in this field, it is concerned with a known theorem about locally compact groups and with the question of whether or to what extent the result generalizes to arbitrary Polish groups. The theorem in question is Mackey's Cocycle Theorem: Every almost cocycle is equivalent to a strict cocycle. This question is relevant to the foundations of quantum mechanics. Blass Title: Abstract State Machines and Choiceless Polynomial Time Abstract: Choiceless polynomial time is a complexity class of decision problems whose instances are finite structures. The polynomial-time computations here are not permitted to use an ordering of the input structure (or, what amounts to the same thing, arbitrary choices), but parallelism and rich data structures are allowed. The underlying computational framework is given by Gurevich's abstract state machines, to which I'll provide a brief introduction. Then I'll discuss what can (and what cannot) be computed in choiceless polynomial time, particularly when it is augmented by an oracle for cardinality. My work in this area is joint with Yuri Gurevich and Saharon Shelah.

    35. Logic In Informatics : Mykola (Nikolaj) Stepanovich Nikitchenko
    Special notions of Abstract computability over various data structures – natural A special axiomatic system is constructed which can represent all
    Go to Logic in Informatics Home Page
    Mykola (Nikolaj) Stepanovich Nikitchenko
    Prof. Dr. Mykola (Nikolaj) Stepanovich Nikitchenko
    Chairman of the Department of Theory of Programming
    of the Faculty of Cybernetics
    at the National Taras Shevchenko University of Kyiv.
    See below:
    Short C.V.

    Membership, Positions, Participation in Projects

    Scientific Interests

    Main Publications

    SHORT CURRICULUM VITAE Born: 1951, Berdichev, Ukraine Student: Kiev Taras Shevchenko State University, Faculty of Mechanics and Mathematics (1968 – 1969), Faculty of Cybernetics (1969 - 1973) Candidate of physics and mathematics (Ph.D) and Doctor of physics and mathematics by speciality “Mathematical and program software of computers and systems” Employment: Kiev State University, Faculty of Cybernetics, Department of Programming Theory: since 1973 on positions of Assistant Professor, Lecturer, Associate Professor. Now Professor, Chairman of the department. Miscellaneous: Improvement in skill:
    • Institute of Cybernetics (Kiev, 1976),
    • Novosibirsk State University (Novosibirsk, 1982)

    36. Computability, Universality And Unsolvability Anima Ex Machina
    So talking about the universal Abstract device E_n for example because of the arithmetical level tag systems, axioms or any other equivalent system.

    37. (C. Calude, G. Stefanescu) Automata, Logic, And Computability: J.UCS Special Iss
    Automata, Logic, and computability J.UCS Special issue dedicated to Professor from the first one, Axioms of Lattices and Boolean Algebras published in"UJSeries_Window"; Search Subscription Submission Procedure Login User: anonymous Special Issues Volume 13 (2007) Volume 12 (2006) Volume 11 (2005) ... Collection of other papers top.location.href = "/jucs_6_1/automata_logic_and_computability/managing.html";

    38. Search Seminars
    away from an algorithmic approach toward a more Abstract, axiomatic approach. The use of computers in understanding algebraic

    39. Center For Philosophy Of Science ::: Als 2003-04
    Beyond Church s Canons Axioms for computability Wilfried Sieg, Carnegie Mellon University Friday, 6 February 2004, 330 p.m. 2P56 Posvar Hall. Abstract


    ::: about

    ::: news

    ::: links
    ... annual lecture series 44th annual lecture series, 2003-04 What Was Natural Philosophy in the Late Middle Ages?
    Edward Grant, Indiana University
    Friday, 10 October 2003, 3:30 p.m.
    Frick Fine Arts Auditorium Abstract It's Not That They Couldn't: Mathematic
    Reviel Netz, Stanford University
    Friday, 14 November 2003, 3:30 p.m.
    2P56 Posvar Hall s, Ancient and Modern Abstract: Why is science not everywhere the same? A popular strategy for answering this question works from what may be called "the argument from conceptual impossibility": that certain authors could not do X because they did not have concept Y (typically, "they" did not have a concept which "we" have). I doubt this strategy. To articulate my doubt, I consider the case of the divide between Greek and later mathematics. In what sense was Greek mathematics non-arithmetical in character, and why? Are Infants Little Scientists?

    40. Solomon Feferman Publications
    Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic, .. Computation on Abstract data types. The extensional approach, with an
    Solomon Feferman Publications
  • Formal Consistency Proofs and Interpretability of Theories . PhD thesis, University of California, Berkeley, July 1957. Degrees of unsolvability associated with classes of formalized theories, J. Symbolic Logic , vol. 22, pp. 161-175, 1957. (with R. L. Vaught), The first order properties of products of algebraic systems, Fund. Math. , vol. 47, pp. 57-103, 1959. (with A. Ehrenfeucht), Representability of recursively enumerable sets in formal theories, Arch. Math. Logik Grundlagenforsch. , vol. 5, pp. 37-41, 1959. Arithmetization of metamathematics in a general setting, Fund. Math. , vol. 49, pp. 35-92, 1960. (with G. Kreisel and S. Orey), 1-consistency and faithful interpretations, Arch. Math. Logik Grundlagenforsch. , vol. 5, pp. 52-63, 1960. Classifications of recursive functions by means of hierarchies, Trans. Amer. Math. Soc. , vol. 104, pp. 101-122, 1962. Transfinite recursive progressions of axiomatic theories, J. Symbolic Logic , vol. 27, pp. 259-316, 1962. (with C. Spector), Incompleteness along paths in progressions of theories
  • 41. Southern California Security And Cryptography Workshop ABSTRACTS
    Abstract. We present two new approaches to improving the integrity of network broadcasts and multicasts with low storage and computation overhead.
    Southern California Security and Cryptography Workshop ABSTRACTS
  • Eyal Kushilevitz, Technion, "Cryptography in Constant Parallel Time" Abstract:
    We study the parallel time-complexity of basic cryptographic primitives such as one-way functions (OWFs) and pseudorandom generators (PRGs). Specifically, we consider the possibility of computing instances of these primitives by NC0 circuits, in which each output bit depends on a constant number of input bits. Despite previous efforts in this direction, there has been no convincing theoretical evidence supporting this possibility, which was posed as an open question in several previous works. We essentially settle this question by providing strong evidence for the possibility of cryptography in NC0. Our main result is that every "moderately easy" OWF (resp., PRG), say computable in NC1, can be compiled into a corresponding OWF (resp., low-stretch PRG) in which each output bit depends on only four input bits. The existence of OWF and PRG in NC1 is a relatively mild assumption, implied by most number-theoretic or algebraic intractability assumptions commonly used in cryptography. A similar compiler can also be obtained for other cryptographic primitives such as one-way permutations, encryption, signature, commitment, and collision-resistant hashing. Our results make use of the machinery of randomizing polynomials, which was originally motivated by questions in the domain of information-theoretic secure multiparty computation. By extending this tool to the computational setting we obtain additional results regarding NC0 cryptography. In particular, we show that even some relatively complex cryptographic primitives, including (stateless) symmetric encryption and digital signatures, are NC0-reducible to a PRG. No parallel reductions of this type were previously known, even in NC. Our reductions make a non-black-box use of the underlying PRG.
  • 42. DBLP: J. V. Tucker
    25, J. V. Tucker, Jeffery I. Zucker Toward a General Theory of Computation and Specification over Abstract Data Types. ICCI 1990 129133
    J. V. Tucker
    John V. Tucker List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Jan A. Bergstra , J. V. Tucker: The rational numbers as an abstract data type. J. ACM 54 EE John V. Tucker, Jeffery I. Zucker : Computability of analog networks. Theor. Comput. Sci. 371 EE Edwin J. Beggs , John V. Tucker: Can Newtonian systems, bounded in space, time, mass and energy compute all functions? Theor. Comput. Sci. 371 Arnold Beckmann Ulrich Berger , John V. Tucker: Logical Approaches to Computational Barriers, Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006, Proceedings Springer 2006 EE Jan A. Bergstra , John V. Tucker: Elementary Algebraic Specifications of the Rational Complex Numbers. Essays Dedicated to Joseph A. Goguen 2006 EE Edwin J. Beggs , J. V. Tucker: Embedding infinitely parallel computation in Newtonian kinematics. Applied Mathematics and Computation 178 EE J. V. Tucker, Jeffery I. Zucker : A Network Model of Analogue Computation over Metric Algebras. CiE 2005 EE J. V. Tucker

    43. Collegium Logicum 2007: Proofs And Structures
    17001800, K. Terui How and when axioms can be transformed into good structural rules (Abstract). 1800-1830, A. Ciabattoni Uniform Standard
    Collegium Logicum 2007: Proofs and Structures
    24/25 October 2007, Vienna, Austria
    LIX PPS ) and Vienna ( Theory and Logic Group ). Supported and organized by the Participation at the workshop is free.
    Institute for Computer Languages
    Theory and Logic Group
    Vienna University of Technology
    October 24: Seminar room SEM 185/2
    October 25: Laboratory (next to the seminar room)
    See this city map on how to find the building. The seminar room is located on the 3rd floor in the yellow area. It is most easily reached via staircase I (see map of the building
    Program and Organizing Committee
    Matthias Baaz
    Agata Ciabattoni
    Stefan Hetzl
    Norbert Preining
    Matthias Baaz (Institute of Discrete Mathematics and Geometry, Vienna)
    Arnold Beckmann
    (Departement of Computer Science, Swansea University) ... (Computer Science Departement, Munich Technical University)
    Daniel Weller (Theory and Logic Group, Vienna)
    Wednesday, October 24 - Seminar Room 185/2 A. Beckmann: On the complexity of definable total search problems (abstract) Coffee Break Interpreting interval based fuzzy logics (abstract) S. Terwijn:

    44. AAAI Spring Symposium On Metacognition In Computation
    Metacognition in computation A selected history. Slides. Abstract. We describe our progress toward developing 30 integrated axiomatic theories of
    AAAI Spring Symposium on Metacognition in Computation
    Paper List
    Proceedings (AAAI Tech Report)
    Invited Talks
    Stuart Russell. Rationality and metareasoning.

    John Dunlosky. Human Metacognition.

    Michael T. Cox. Metacognition in computation: A selected history.

    Abstract. This paper takes a cursory examination of some of the research roots concerning the topic of metacognition in computation. Various disciplines have examined the many phenomena of metacognition and have produced numerous results, both positive and negative. I discuss some of these aspects of cognition about cognition and the results concerning them from the point of view of the psychologist and the computer scientist, and I attempt to place them in the context of computational theories. We examine metacognition with respect to both problem solving and to comprehension processes of cognition. The history is limited to the 20th century.
    Research papers
    Eric Aaron. Hybrid dynamical systems, dynamical intelligence, and meta-intelligence in embodied agents. Abstract.

    45. Jiskha Homework Help - Mathematics
    Since errors can be made in a computation, is such a proof sufficiently rigorous? . as geometry starts from axioms and postulates about Abstract entities
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    December 24, 2007
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    46. Program Files\Netscape\Communicator\Program\nshsalg\ursmain
    Uniformly reflexive structures (URS) are an axiomatic approach to computability. They were introduced in my 1963 doctoral dissertation at Columbia

    47. Juris Reinfelds
    Starting with the axioms of equivalence and with the inference rules of equational logic we can . Hein J.L. Discrete Structures, Logic and computability.
    Logic in CS-1 and CS-2
    Juris Reinfelds
    Klipsch School of Electrical and Computer Engineering
    New Mexico State University
    P.O. Box 30001, Dept. 3-O,
    Las Cruces NM 88003 U.S.A.
    (505) 646-1231 fax: (505) 646-1002
    1.0 Introduction
    If we believe that logic is the backbone formalism of computer science, then it seems logical that logic should shape the backbone of the foundation course for CS majors. Unfortunately most humans are not logical. As shown by the Reid survey [Reid 1994], far too many universities still teach a first course built around the syntax, semantics and sequential problem solving methodology of Wirth's elegant, but somewhat outdated, teaching language Pascal, while too many others are engaged in an irrelevant debate whether to replace Pascal with Ada or C++. Only a handful of universities have extended their first course to two paradigms (usually functional followed by imperative) [Joosten et al. 1993] [Lambert et al. 1993] and they have discovered that in this way more material can be taught because of the natural separation of the concern for "how an algorithm works" (functional view) from the concern for "how to implement it with pointers or arrays" (imperative view).
    2.0 Our Course

    48. ILLC Publications, All Series, 1998
    Abstract, 2.Full text. ML1998-07 Victor N. Krivtsov A Negationless Interpretation of Intuitionistic axiomatic Theories Higher-Order Arithmetic.

    49. Mathematics Enclyclopedia - Engineers Edge
    Although arithmetic computation is crucial to accountants, as geometry starts from axioms and postulates about Abstract entities called points and
    Mathematics Enclyclopedia Encyclopedia Menu
    Engineering Basic Menu
    Mathematics is often defined as the study of topics such as quantity, structure, space, and change. Another view, held by many mathematicians, is that mathematics is the body of knowledge justified by deductive reasoning, starting from axioms and definitions. Practical mathematics, in nearly every society, is used for such purposes as accounting, measuring land, or predicting astronomical events. Mathematical discovery or research often involves discovering and cataloging patterns, without regard for application. The remarkable fact that the "purest" mathematics often turns out to have practical applications is what Eugene Wigner has called "the unreasonable effectiveness of mathematics." Today, the natural sciences, engineering, economics, and medicine depend heavily on new mathematical discoveries.The word "mathematics" comes from the Greek ( ) meaning "science, knowledge, or learning" and ( ) meaning "fond of learning". It is often abbreviated maths in Commonwealth English and math in North American History The evolution of mathematics might be seen to be an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction was probably that of numbers. The realization that two apples and two oranges do have something in common, namely that they fill the hands of exactly one person, was a breakthrough in human thought. In addition to recognizing how to count

    50. Yuri Gurevich: Simplified Publication List
    Abstract state machines behavioral computation theory . 150 On Polynomial Time Computation Over Unordered Structures; 149 Strong Extension Axioms and
    Articles Grouped by Research Areas
    under construction and incomplete
    An entry gives only the title and a URL to a fuller description in Annotated Articles. Admittedly, the categorization is somewhat arbitrary. The intersection between two categories is not necessarily empty.
  • Algebra and model theory
  • AI, automated reasoning and related
  • Average-case computational complexity
  • Classical decision problem and related ...
  • Odds and ends
    Abstract State Machines and Behavioral Computation Theory
  • General Interactive Small Step Algorithms
  • Interactive Algorithms 2005
  • Ordinary Interactive Small-Step Algorithms, III
  • Ordinary Interactive Small-Step Algorithms, II
  • Semantic Essence of AsmL: Extended Abstract
  • Semantic Essence of AsmL
  • Observations on the Decidability of Transitions
  • Intra-Step Interaction
  • Ordinary Interactive Small-Step Algorithms, I
  • Abstract State Machines: An Overview of the Project
  • Algorithms: A Quest for Absolute Definitions
  • Partial Updates
  • Abstract Communication Model for Distributed Systems
  • Algorithms vs. Machines
  • 51. Speaker Samson Abramsky Title Axiomatics Of No-Cloning And No
    Speaker Lou Kauffman Title Anyonic Topological Computation and Quantum Algorithms for Knot Polynomnials Abstract This talk will review the qdeformed

    52. Abstracts
    Church without dogma axioms for computability Church s and Turing s theses dogmatically assert that an informal notion of computability is captured by a
    The Origins and Nature of Computation
    The Rise of India as a Global Player in Information Technology: The Roles of Technical Education, Economic Advantage, Policy, and Global Markets
    The talk will discuss the various factors that contributed to the development of India as an important global provider of software services. The focus will be on the mid-1970s until recently. Topics will include tax and tariff policy, the role of foreign companies, infrastructure, the educational and training systems, the role of quality metrics, the Diaspora and its recent reverse, industry structure, and cultural and environmental issues. The talk will draw heavily from a recent ACM study on globalization and the offshoring of software.
    William Aspray
    Indiana University
    A Brief History of Museums Online: Widening Worldwide Access
    This presentation will trace the story of the growth of museum websites, particularly in the context of the Virtual Library museums pages, supported by the International Council of Museums. Web capabilities have allowed museums to broaden their access both internationally and to a wide variety of people, including the disabled such as the blind. Their educational potential has been greatly enhanced, although much more is still possible.

    53. A Natural Axiomatization Of Church's Thesis | Lambda The Ultimate
    The Abstract State Machine Thesis asserts that every classical algorithm is .. Finally, we can also ask whether an axiomatic theory of computation is
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    Lambda the Ultimate
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    A Natural Axiomatization of Church's Thesis
    . Nachum Dershowitz and Yuri Gurevich. July 2007.
    The Abstract State Machine Thesis asserts that every classical algorithm is behaviorally equivalent to an abstract state machine. This thesis has been shown to follow from three natural postulates about algorithmic computation. Here, we prove that augmenting those postulates with an additional requirement regarding basic operations implies Church's Thesis, namely, that the only numeric functions that can be calculated by effective means are the recursive ones (which are the same, extensionally, as the Turing-computable numeric functions). In particular, this gives a natural axiomatization of Church's Thesis, as G¶del and others suggested may be possible. While not directly dealing with programming languages , I still think this paper might be of interest, since our field (and our discussions) are often concerned with computability (or effective computation, if you prefer).

    54. Computational Complexity: Favorite Theorems: Abstract Complexity
    Blum defined a resource measure as any partially computable function M (think time) of a machine M that fulfilled some simple axioms.
    @import url(""); @import url(""); var BL_backlinkURL = "";var BL_blogId = "3722233";
    Computational Complexity
    About Computational complexity and other fun stuff in math and computer science as viewed by Bill Gasarch. Blog created and written until March 2007 by Lance Fortnow. My Links Bill's Home Page Lance's Home Page Weblog Home Weblog Archives and Search ... Favorite Theorems Recent Posts The New Research Labs Screenplays of Science Moons and Planets Two New Blogs ... What Kind of Science is Computer Science? Complexity Links IEEE Conference on Computational Complexity Electronic Colloquium on Computational Complexity BEATCS Computational Complexity Column Complexity Zoo ... Favorite Complexity Books Weblogs Andy Drucker Ars Mathematica Computing Research Policy D. Sivakumar ... Terence Tao Other Links DMANET FYI Nielsen's Principles of Research Parberry's TCS Guides ... Theorynet Discussion Groups Computer Science Theory Theory Edge
    This work is licensed under a Creative Commons License
    Monday, August 08, 2005

    55. CS200 Condensed
    We can express all computation that use mutation without using mutation, . An incomplete axiomatic system fails to produce some true theorems.
    CS 200
    Computer Science

    from Ada and Euclid to Quantum Computing and the World Wide Web
    Schedule Problem Sets Exams ... Links
    CS200 Condensed
    This document summarizes the most important things I hope you have learned in CS200.
    How to Describe Procedures
    Language: 1: Introduction [ Slides, Notes ]; 2: Formal Systems and Languages [ S N ]; 3: Rules of Evaluation S, N ] 5: Fibonacci [ S N Computer Science is the study of imperative ("how to") knowledge. Computer Science studies how to describe procedures and how to reason about the processes procedures produce. Ada, Countess of Lovelace, was the first Computer Scientist, because she was (probably) the first person to consider how to precisely describe proccedures. Computer Science is not a science, since it is not about understanding nature. It is not engineering, since computer scientists do not face the kinds of constraints engineers face. Computer science is best considered a liberal art. It encompasses all seven of the traditional liberal arts: the language trivium - grammar, rhetoric, logic; and the numbers quadrivium - arithmetic, geometry, music and astronomy. A formal system is a set of symbols and a set of rules for manipulating symbols. A

    56. 2006 August « Reperiendi
    and because the programs already satisfy the axioms of the computable theory, asserting the equivalence of two proofs is redundant they’re already
    Figure it out
    Archive for August, 2006
    Quantum lambda calculus, symmetric monoidal closed categories, and TQFTs
    2006 August 22 and The typical CCC in which models of a lambda theory are interpreted is Set . The typical SMCC in which models of a quantum lambda theory will be interpreted is Hilb , the category of Hilbert spaces and linear transformations between them. Models of lambda theories correspond to functors from the CCC arising from the theory into Set . Similarly, models of a quantum lambda theory should be functors from a SMCC to Hilb Two-dimensional topological quantum field theories (TQFTs) are close to being a model of a quantum lambda theory, but not quite. Set TQFTs are functors from , the theory of a commutative Frobenius algebra, to Hilb . We can look at as defining a data type and a TQFT as a quantum implementation of the type. When we take the free SMCC over , we ought to get a full-fledged quantum programming language with a commutative Frobenius algebra data type. A TQFT would be part of the implementation of the language. Posted in Category theory Math Programming Quantum ...
    CCCs and lambda calculus
    2006 August 22 I finally got it through my thick skull what the connection is between lambda theories and cartesian closed categories.

    57. Specializing In Logic
    A mathematician often works with axioms, from which he proves theorems. This process is analyzed (in an Abstract way) in Logic. One starts by introducing a
    Specializing in Logic in the Master Mathematical Sciences
    Contents of this page:
  • Prerequisites for a Logic specialization
  • What is Logic?
  • Am I interested in Logic?
  • Which are the important topics in Logic? ...
  • Further perspectives
    Prerequisites for a Logic specialization
    If you want to study Logic as part of a Master's program in Mathematics, you need to be admitted to this program; see here for details. Usually, you will have completed a Bachelor in Mathematics. We assume that you have followed at least one introductory course in Logic, such as the course Foundations of Mathematics offered at this Department. You can get an idea of the contents of this course here
    In addition it is helpful if you have done some abstract algebra and topology during your Bachelor. The courses are, however, open to students from other curricula too, and could be interesting to people from AI, Computer Science, Philosophy, and Physics. Consult your own master program advisor about incorporating our courses into your program.
    What is Logic?
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