Geometry.Net - Theorems_And_Conjectures: Completeness Theorem

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

Extractions: 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. Philosophical and critical 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.
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

Extractions: 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)
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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
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
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

Extractions: October 9, 2002 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. 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: 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.
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

Extractions: 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
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

Extractions: 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.
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

Extractions: 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! 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.
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

Extractions: 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.
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

Extractions: 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 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
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

Extractions: 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.
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/
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/

Extractions: 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)
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

Extractions: Bibtex reference: Deduction modulo also permits to prove completeness of binding logic: 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
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

Extractions: My main research topics are application of proof theory. It can be divided in four subtopics: 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: 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.
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
Formal Topology Publications
Algebra (ed. Ursini, Aglianò), Dekker, New York, 1996, pp. 689-702.
http://www.math.unipd.it/~silvio/PublicationsFT.html

Extractions: 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.
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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

Extractions: 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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