61. Journals In WWW With Papers In Logic Manysorted logic. + Syntax and semantics up to the completeness theorem. - Modeltheory see Cn, particularly C07. Gödel's completeness theorem see C07. http://www-logic.uni-kl.de/class.html

Forschungsstelle Mathematische Logik A research enterprise of the Heidelberger Akademie der Wissenschaften Logic Subject Classification (annotated part 03 of MSC 2000 XX MATHEMATICAL LOGIC AND FOUNDATIONS General reference works, handbooks, dictionaries, bibliographies, etc. Instructional exposition textbooks, tutorial papers, etc. Research exposition monographs, survey articles Historical and biographical Proceedings, conferences, collections, etc. A PHILOSOPHICAL AND CRITICAL Philosophical and critical B GENERAL LOGIC Classical propositional logic + Axiomatizations of classical propositional logic - Boolean functions: see G05 - Fragments of propositional logic: see B20 - Switching circuits Classical first-order logic + Many-sorted logic + Syntax and semantics up to the Completeness Theorem - Model theory: see Cn, particularly C07 - Proof theory: see Fn Higher-order logic and type theory + Higher-order algebraic and other theories - Higher-order model theory: see C85 - Set theory with classes: see E30 and E70 - Intuitionistic theory of types: see F35 Subsystems of classical logic including intuitionistic logic + Fragments of propositional and of first-order logic + Fragments used in model theory, set theory, etc.

62. SUGGESTED SYLLABUS - TVIATH 280 A-B-C Formal deduction. Henkin Models. Compactness Theorem. Goedel's completeness theorem.Quarter 2. Basic Model Theory Diagrams and models constructed from constants. http://www.math.uci.edu/syllabus/math280ABC.html

SUGGESTED SYLLABUS - MATH 280 A-B-C Mathematical Logic Possible Sources: Enderton. H.: A mathematical introduction to Logic (Models, compactness and completeness and Incompleteness and Goedel's Theorems) Jech, T: Set Theory (Basic set theory, Constructible sets) Devlin, K: Constructibility (Constructible sets) Chang, C and Keisler, J.: Model Theory (Models, compactness and completeness; Basic model theory) Soare, R: Recursively enumerable sets and degrees (Basic recursion theory) Quarter I Basic Set Theory: Language of set theory Zermelo-Fraenkel axioms Natural numbers and Ordinal numbers Well-founded relations Transfinite induction and schema of definition by transfinite recursion. Ordinal arithmetic Mostowski collapsing theorem Cardinal numbers and basic cardinal carithmetic. Models, Compictness and Completeness: Languages and structures Satisfaction Formal deduction Henkin Models Compactness Theorem Goedel's Completeness Theorem Quarter 2 Basic Model Theory: Diagrams and models constructed from constants Loewenheim-Skolem Theorems Elementary Chains. Air application: Robinson Joint consistency Theorem)

63. Untitled 115 Go To Index. TITLE An Algebraic proof of the completeness theorem of MathematicalLogic. AREA Logic. KEYS completeness theorem. LEVEL Final Year. http://www.maths.abdn.ac.uk/maths/department/services/lms/f9.html

Go To Index TITLE An Algebraic proof of the Completeness theorem of Mathematical Logic SOURCE Alan West Department of Pure Mathematics School of Mathematics University of Leeds Leeds LS2 9JT e-mail: pmt6aw@gps.leeds.ac.uk AREA Logic KEYS Completeness theorem LEVEL Final Year LENGTH Expected workload: 3/4 of a 22 lecture course Length of report: 40 pp. PREREQ None HISTORY The project has actually been used in this form DESCRIPTION Introduces Propositional Calculus and the completeness theorem. Introduces Boolean Algebras, filters, ultra filters and the Lindenbaum algebra. Formulates the Predicate calculus. Go To Index TITLE Lattice Theory SOURCE Alan West Department of Pure Mathematics School of Mathematics University of Leeds Leeds LS2 9JT e-mail: pmt6aw@gps.leeds.ac.uk AREA Algebra KEYS Lattice Theory LEVEL Final Year LENGTH Expected workload: 3/4 of a 22 lecture course Length of report: 40 pp. PREREQ None HISTORY The project has actually been used in this form DESCRIPTION Looks at ordered sets then at lattices. Introduces complete, modular and distributive lattices. Shows the Schroeden-Bernstein theorem and the Jordan-Holder theorem. Application to abstract algebra and the mathematical model for mental operations. Go To Index TITLE Stability Theory for Ordinary Differential Equations SOURCE Alan West Department of Pure Mathematics School of Mathematics University of Leeds Leeds LS2 9JT e-mail: pmt6aw@gps.leeds.ac.uk

64. Models Of Arithmetic th floor). Contents The existence of nonstandard models of arithmeticis a corollary of the completeness theorem. In fact, there http://www.math.helsinki.fi/logic/opetus/arith.html

Models of Arithmetic An intensive course (tiiviskurssi) in the Mathematics Department September 1 - 14, 1999 Lecturer: Ph.D. Juliette Kennedy Lecture times: September 1-14, monday to friday 14-16 (except monday 9.9.1999) in lecture room SIII (6 th floor). Contents: Organizer: This intensive course is arranged by the Graduate School Analysis and logic . For more information, contact Juliette Kennedy or Logiikan opetus Matematiikan laitos

65. CSE 291 Lecture Notes, October 9, 2002 How do you do step (2)? Use the completeness theorem for an exponentialfamily. FACTORIZATION THEOREM. EXPONENTIAL FAMILY completeness theorem. http://www.cs.ucsd.edu/users/elkan/291/oct9.html

CSE 291 LECTURE NOTES October 9, 2002 ANNOUNCEMENTS I would like people to use the discussion boards to ask questions about the lectures and the first assignment. Remember, the assignment is due one week from now. You are welcome to work in study groups, but each student should write up his/her answers independently. See the October 7 lecture notes for books recommended as background reading. ALGORITHM TO OBTAIN MVUEs I'll describe this algorithm as a theorem. So E[ g hat(t) - g bar(t) ] = for every theta. By completeness g hat(t) - g bar(t) = for all t, so g hat and g bar are the same. So the Rao-Blackwell process always gives the same improved estimator, regardless of which crude estimator we begin with. Algorithm: (1) Find a sufficient statistic t. (2) Show that the family of distributions of t is complete. (3) Find a crude unbiased estimator g tilde(x). Instead of steps 3 and 4, sometines you can directly guess some g bar(t) and prove that it is unbiased. Steps 1 and 2 only have to be done once for a given family of distributions P_theta. They can then be reused for different estimation targets g(theta). How do you do step (1)? Use the factorization theorem.

66. Detailed Index Of Books By Nino Cocchiarella 141. § 3. A completeness theorem for Tense Logic, 217. 7. A CompletenessTheorem for Modal Natural Realism, 124. § 8. Modal Logical Realism, 134. http://www.formalontology.it/Cocchiarella_books.htm

Home Index of the books by Nino Cocchiarella Tense Logic: A Study of Temporal Reference (VI, 251 pages) Ph.D. Dissertation, University of California - Los Angeles, January 7, 1966). Committee in charge: Richard Montague, Charmain, Alfred Horn, Donald Kalish, Abraham Robinson, Robert Stockwell. Can be ordered to UMI Dissertation Express (reference number: 6609326) ABSTRACT: This work is concerned with the logical analysis of topological or non-metrical temporal reference. The specific problem with which it successfully deals is a precise formalization of (first-order) quantificational tense logic wherein both an appropriate formal semantics is developed and a meta-mathematically consistent and complete axiomatization for that semantics given. The formalization of quantificational tense logic herein presented adheres to all the canons o£ logical rigor by being carried out entirely as a definitional extension of (Zermelo-Fraenkel) set theory. Model-theoretical techniques are utilized in the semantics given and the notion of a history is formally developed as the tense-logical analogue of the notion of a model for standard first-order logic with identity. Corresponding to the key semantical concept of satisfaction (and consequently of truth) in a model, by means of which the central standard notion of

67. Modal Operators For Coequations We then discuss the dual to Birkhoff's completeness theorem, showing how closureunder deductive rules dualizes to yield two modal operators acting on http://www.cs.cmu.edu/Groups/LTC/papers/invariant.html

Modal Operators for Coequations S. Awodey and J. Hughes Abstract We present the dual to Birkhoff's variety theorem in terms of predicates over the carrier of a cofree coalgebra (i.e. in terms of ``coequations''). We then discuss the dual to Birkhoff's completeness theorem, showing how closure under deductive rules dualizes to yield two modal operators acting on coequations. We discuss the properties of these operators and show that they commute, and we prove as main result the invariance theorem, which is the formal dual of Birkhoff's completeness theorem.

68. Structured Operational Semantics the original system. As a simple corollary of the conservative extensiontheorem we prove a completeness theorem. As a first application http://adam.wins.uva.nl/~x/sos.html

Structured Operational Semantics On this page I will list some papers on general SOS theory. Now what is general SOS theory? Roughly, such theory tries to give answers on questions that normally take some time to prove them, but can now be dealt with more easily. For instance if you want to know whether or not a particular operational semantics is compositional, it would be interesting to have a theorem at hand giving you sufficient conditions to decide that this is indeed the case. On this page I will list some contributions that aid in this goal. Comments and or questions are most welcome! A congruence theorem for SOS with predicates This paper is written by J.C.M. Baeten and C. Verhoef. Please find below an abstract. Click here to view the paper as a PS file. I didnt include a dvi file since somehow you need to generate many fonts with METAFONT to view it.. obviously not what you want. Click here for a text only version produced by dvitty. Note: the paper appeared in the CONCUR 93 proceedings. Abstract Keywords and Phrases: structured operational semantics, term deduction system, transition system specification, structured state system, labelled transition system, strong bisimulation, congruence theorem, predicate.

69. Abstracts example of sentences involving witness comparison is the Rosser sentence.) In thisarticle the proof of the Kripke model completeness theorem employs tail http://turing.wins.uva.nl/~fransv/Abstracts.html

Abstracts publications Frans Voorbraak Independence assumptions underlying Dempster's rule of combination. NAIC-88. Proceedings First Dutch Conference on Artificial Intelligence, M. van Someren and G. Schreiber (eds.). University of Amsterdam (1988) pp. 162-172. Abstract : Dempster's rule of combination is the most important tool of Dempster-Shafer theory, which is considered to be a promising theory for the handling of uncertain information in expert systems. In this paper, we investigate the independence assumptions underlying the combination of evidence by Dempster's rule and give a description of these independence assumptions in terms of the canonical examples on which judgments expressed in terms of Dempster-Shafer theory are supposed to be based. Finally, some remarks on the applicability of Dempster's rule are included. The logic of actual obligation. An alternative approach to deontic logic. Philosophical Studies 55 (1989) 173-194. Abstract In [E] Job van Eck analyzes the relation between actual- and prima facie obligations in terms of tense. We don't agree with the details of his analysis, but we do believe that the role of time is important in deontic logic in general and in obtaining actual obligations from prima facie ones in particular. In section 1 we give a sketch of van Eck's system of temporally relative deontic logic (QDTL), to get some idea of the role of time in deontic logic. In section 2 QDTL is criticized, especially the fact that obligations are interpreted in terms of perfect alternatives.

70. CS792: Computational Logic of language formalism to expressive power, and includes discussion of logic as adatabase query language, as well as proof of the completeness theorem that can http://cs-people.bu.edu/mairson/Courses/cs792/factsheet.html

Computer Science 792 Computational Logic Spring Term, 2000 Course instructor: Harry Mairson ( mairson@cs.bu.edu ), MCS 283, phone 353-8926. Office hours 11am-12pm Tuesday and Friday, and by arrangement. I especially encourage you to communicate with me via electronic mail, for fastest and most reliable responses to your questions. I try to read e-mail every 5 minutes, 24 hours a day. Time and place: Tuesday and Thursday, 9.30-11am, MCS B46. What is this course about? This course is a (non-comprehensive) introduction to topics in logic that are relevant to computer science. Unlike typical logic courses, it stresses computational metaphors: algorithmics and constructive mathematics, computational complexity, and decidability. The basic topics of the course are Propositional logic (6 lectures) First-order logic (5 lectures) Intuitionistic logic (7 lectures) Higher-order logic and realizability (4 lectures) Linear logic (7 lectures) linear logic , a so-called resource-conscious logic; we will discuss the relationship between cut-elimination (proof simplification) in linear logic, and evaluation of programs written in lambda-calculus. Required work: Work for the course will include several problem sets, and some class presentations. Even though I love grading problem sets, I'm going to try to have it done by you on a round-robin basis. Please

71. Soundness And Completeness notions of truth. These are the Soundness theorem and the Completenesstheorem for Equational Logic Recall A Boolean expression http://www.atkinson.yorku.ca/~szeptycki/classes/1090/soundcomplete.html

Soundness and Completeness There are two important theorems concerning the relationship between the semantic and syntactic notions of truth. These are the Soundness Theorem and the Completeness Theorem for Equational Logic: Recall: A Boolean expression is said to be valid (or a tautology ) if it evaluates to true in every state. A boolean expression is said to be a theorem of Equational Logic, if either 1) it is an axiom, OR 2) it is the conclusion of an inference rule all of whose premises are either axioms or previously established theorems. Validity is a semantic notion and being a theorem is a syntactic notion. Soundness Theorem : Any Boolean expression that is a theorem of Equational Logic is valid. Completeness Theorem Any Boolean expression that is valid is a theorem of Equational Logic.

72. Rybakov's Theorem In Fréchet Spaces And Completeness Of L1-spaces Rybakov's theorem in Fréchet spaces and completeness of L 1 spaces. WJ RickerSchool of Mathematics University of New South Wales Sydney, NSW 2052 Australia. http://www.austms.org.au/Publ/Jamsa/V64P2/abs/p89/

Journal of the Australian Mathematical Society - Series A Vol. Part 2 (1998) L -spaces W. J. Ricker School of Mathematics University of New South Wales Sydney, NSW 2052 Australia Abstract: We provide a simple and direct proof of the completeness of the L PDF file size: 44k TeXAdel Scientific Publishing TeXAdel Scientific Publishing

73. LICS2001 Full Abstraction/Completeness Workshop Esfandiar Haghverdi (U. Pennsylvania) A full and faithful completenesstheorem for Geometry of Interaction categories. Partially http://aix1.uottawa.ca/~scpsg/Logic/LICS01/

LICS2001 Workshop on Full Abstraction and Full Completeness: June 19-20, 2001 Organizers: S. Abramsky (Oxford) and P. Scott (Ottawa) June 19th Speaker June 20th Speaker 1:30-2:10 pm Laird 9:00-9:40 am Curien Yoshida O'Hearn Hamano Ong Haghverdi Lenisa Abramsky Hughes Mairson Pierre-Louis Curien (U. Paris) The so-called ``Full abstraction problem" for PCF and related languages: a perspective I shall survey the history of this well-known open problem that has triggered important research works of independent interest (sequentiality, logical relations, games) during a period of twenty years and more. I shall review the problem for three languages: PCF (the original problem), PCF + control, and an ALGOL-like language. The sequential algorithms and the games models have provided satisfactory (effective) solutions for the latter two languages, respectively, while the identification of the constraints that tailor the games model to just PCF was the key to a very interesting classification known as Abramsky's ``semantic cube". Esfandiar Haghverdi (U. Pennsylvania)

74. Deduction Modulo We introduce a notion of model for this logic and we prove a completenesstheorem for it. This theorem is obtained as a consequence http://www.loria.fr/~ckirchne/=tpm/TPM.html

Theorem Proving Modulo Gilles Dowek, Thérèse Hardin, Claude Kirchner Abstract: Keywords : Automated theorem proving, rewriting, resolution, narrowing, higher-order logic. Full paper available here: tpm.dvi.gz tpm.ps.gz tpm.pdf A slighly older technical report: RR-3400 Bibtex reference: tpm.bib Deduction modulo allows to give a first-order presentation of Higher-Order Logic: HOL lambda sigma: an intentional first-order expression of higher-order logic Gilles Dowek, Thérèse Hardin, Claude Kirchner Abstract: Full paper available here: holsigma.dvi.gz holsigma.ps.gz holsigma.pdf.gz Bibtex reference: Conference version: rta99.bib . Journal version: mscs2001.bib Deduction modulo also permits to prove completeness of binding logic: Binding Logic: proofs and models Gilles Dowek, Thérèse Hardin, Claude Kirchner Abstract: We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and we prove a completeness theorem for it. This theorem is obtained as a consequence of the completeness theorem of predicate logic, by encoding this logic back into predicate logic. Paper available here: binders.dvi.gz

75. Christophe Raffalli's Home Page avec René David et Karim Nour, Dunod (2001) Raf00a Simple proof of the completenesstheorem for second order classical and intuitionistic logic, avec Karim http://www.lama.univ-savoie.fr/~RAFFALLI

CHRISTOPHE RAFFALLI Table of contents Teaching Materials (supports d'enseignement) Information Research interests Publications ... Be my guest Informations Equipe de recherche : Logique Office : 21 Phone : (33) 4 79 75 81 03 Fax : (33) 4 79 75 81 42 Email : Christophe.Raffalli@univ-savoie.fr Research interests My main research topics are application of proof theory. It can be divided in four subtopics: Type systems for computer languages In and I study how the system F-eta (an extension of Girard's system F), which is undecidable, can be used as a type system in a real programming language. There are two possible approaches: In I use an incomplete algorithm which always terminates and never backtrack. Then you get clear error messages and you can always add enough type information in your program to have it type-checked. In I describe an optimized and efficient complete algorithm. This algorithm works very well (and fast) for small polymorphic programs. However, as the algorithm do backtrack, it is not clear how to get nice error messages and an interactive type-checker working like a debugger would be necessary to make this practical for larger programs. Extraction of programs from proof Using Curry-Howard isomorphism, one can extract programs from proofs, However, for a given program is not not always easy or even possible to get a proof to extract it from. It is clear now that classical logic corresponds to control operators like Felleisen Call-CC, but it is not clear how to get an exceptions mechanism similar to ML's one. In a recent forthcoming work, we propose a method to extract such program from a proof in mixed second order logic. We use three level of logic in the system: classical, intuitionnistic and non-algorithmic, and combining the three level, you can get exactly the program you want (like a search in a list using exceptions) from simple equationnal specification which do not mention exceptions.

76. Www.cs.toronto.edu/~sacook/csc2429h/problems CSC 2429S Spring, 2002. Assigned Problems. 1. Prove the Anchored CompletenessTheorem for PK, for the general case. (See Exercise http://www.cs.toronto.edu/~sacook/csc2429h/problems

77. Formal Topology Publications Algebra (ed. Ursini, Aglianò), Dekker, New York, 1996, pp. 689-702. http://www.math.unipd.it/~silvio/PublicationsFT.html

Formal topology S. Valentini Points and Co-Points in Formal Topology Bollettino dell'Unione Matematica Italiana, 7A, 1993, pp. 719. Abstract: After a short introduction on formal topology the definition of point and co-point are given. Then some methods to construct points and co-points are shown together with some applications to logic. S. Valentini Le relazioni ordinate: definizioni di base ed applicazioni, in "Atti del XV o incontro di Logica Matematica", vol. VIII, Gerla, Toffalori, Tulipani (eds), 1993. Abstract: Nel lavoro vengono introdotte le relazioni ordinate come relazioni binarie sugli elementi di una struttura algebrica ordinata che permettono di darne una rappresentazione di carattere insiemistico. Si studiano in particolare il caso dei monoidi ordinati, dei quantales e delle algebre lineari non commutative, vale a dire le strutture algebriche per la logica lineare non commutativa. Paulus Venetus (alias G. Sambin, S. Valentini), Propositum Cameriniense sive etiam itinera certaminis inter rationem insiemes aedificandi analisym situs intuitionisticamque et mathematicae artium reliquas res, in "Atti del XV o incontro di Logica Matematica", vol. VIII, Gerla, Toffalori, Tulipani (eds), 1993, pp. 115-143.

78. ¸¦µæÆâÍƤˤĤ¤¤Æ The System FL m,n for specification analysis and the completenesstheorem. Journal of Information Processing Vol. 9 (1986), pp220 http://herb.h.kobe-u.ac.jp/study.html

Top page¤Ø strongly ¦Ò-short Boolean algebras ¤Ë¤Ä¤¤¤Æ¡¢General Topology Symposium 2002,2002.12 ¡¡¡¡¹Ö±é¤Ç»ÈÍѤ·¤¿pdf¥Õ¥¡¥¤¥ë pdf ¦Ò-short complete Boolean Algebra¤Îdense subalgebras ¤Ë¤Ä¤¤¤Æ, ÆüËÜ¿ô³Ø²ñ½©µ¨Áí¹çʬ²Ê²ñ ¿ô³Ø´ðÁÏÀʬ²Ê²ñ, 2002.9 pdf ¦Ò-short Boolean algebras, ÆüËÜ¿ô³Ø²ñ½©µ¨Áí¹çʬ²Ê²ñ ¿ô³Ø´ðÁÏÀʬ²Ê²ñ, 2001.10 (with Y. Yoshinobu) pdf Banach-Mazur games on Boolean Algebras and ¦Ò-short Boolean Algebras, Set-Theory Meeting in Kasugai, 2001.7 (with Y. Yoshinobu) Positional ¤Ê winning strategy ¤Ë¤Ä¤¤¤Æ,ÆüËÜ¿ô³Ø²ñ½©µ¨Áí¹çʬ²Ê²ñ¿ô³Ø´ðÁÏÀʬ²Ê²ñ, 2000.9 pdf On extended Banach-Mazur games on Boolean algebras Completeness of Boolean Powers of Boolean Algebras The System FL ... Topological Powers and Reduced Powers to appear in Mathematical Logic Quarterly (with Y.Yoshinobu) On extended Banach-Mazur games on Boolean algebras Scientiae Mathematicae Vol. 1 No. 2 (1998), pp169-176 We extend the Banach-Mazur game on Boolean algebras so that at each stage player I can play simultaneously many elements. We introduce two games S(B) and D(B) . We show that S(B) is determined for all Boolean algebras and D(B) is determined for several Boolean algebras for which ordinary Banach-Mazur game is undetermined. Annals of Pure and applied Logic Vol. 55 (1992), pp265-284

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