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Page 5453 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
1-MAL-C; Lowell, MA) An extended joint consistency theorem for a nonconstructive logic of partial terms with definite descriptions.  ...  The present paper utilizes the tableaux system in establishing an extended joint consistency theorem for LPD that incorporates the Robinson joint consistency theorem and the Craig-Lyndon interpolation  ... 

Logic Blog 2017 [article]

Andre Nies
2018 arXiv   pre-print
The blog is somewhat shorter than in previous years, It contains new insights in a variety of areas, including computability, quantum algorithmic version of the SMB theorem, descriptions of groups (both  ...  There are also lots of open questions in computability, randomness, and computable model theory.  ...  A generic description of g is a partial description of g with domain of density 1.  ... 
arXiv:1804.05331v1 fatcat:jd2h4ucvlbgmfcuhhx3ggj575u

Toward useful type-free theories. I

Solomon Feferman
1984 Journal of Symbolic Logic (JSL)  
There are a number of compelling reasons for maintaining this separation but, as we shall see, there are also many close parallels from the logical point of view.The initial solutions to the paradoxes  ...  Those falling under the first heading have to do with such notions astruth, assertion(orproposition), definition, etc., while those falling under the second have to do withmembership, class, relation,  ...  ,yn] for the term q~(~)[fi,,. . . ,yn]. The fixed-model theorem thus provides us with a partial structure llJZ* = (m0,. ..,E , ...) such that for each cp with the appropriate free variables.  ... 
doi:10.2307/2274093 fatcat:b5p3wvxykbfodnbkjkfi6br7du

A logic of nonmonotone inductive definitions

Marc Denecker, Eugenia Ternovska
2008 ACM Transactions on Computational Logic  
in a new logic for Non-Monotone Inductive Definitions (ID-logic).  ...  The logic formally extends Logic Programming, Abductive Logic Programming and Datalog, and thus formalizes the view on these formalisms as logics of (generalized) inductive definitions.  ...  Also description logics have been extended with such fixpoint constructs.  ... 
doi:10.1145/1342991.1342998 fatcat:265gngzzhnealdwfqk6v3mjqre

History of Interactive Theorem Proving [chapter]

John Harrison, Josef Urban, Freek Wiedijk
2014 Handbook of the History of Logic  
ACKNOWLEDGEMENTS The authors are grateful to Jörg Siekmann for inviting them to prepare this chapter and for his patience in the face of our lengthy delays.  ...  The helpful review of the official reader Larry Paulson as well as useful comments from Mike Gordon, Tom Hales and J Moore, have significantly improved the eventual form of the chapter.  ...  A formalization in this system essentially consists of a long list of definitions, in which a sequence of constants are defined as abbreviations of typed lambda terms.  ... 
doi:10.1016/b978-0-444-51624-4.50004-6 fatcat:sngnxnl3ivectj5taj3dgsaa7m

Lectures on Jacques Herbrand as a Logician [article]

Claus-Peter Wirth, Joerg Siekmann, Christoph Benzmueller, Serge Autexier
2014 arXiv   pre-print
We sketch Herbrand's two proofs of the consistency of arithmetic and his notion of a recursive function, and last but not least, present the correct original text of his unification algorithm with a new  ...  Besides Herbrand's Fundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we carefully investigate Herbrand's notion of intuitionism in connection with his notion of falsehood in an infinite  ...  Paulson -the second readers of our previous handbook article ] on the same subject -for their numerous, extensive, deep, and most valuable and helpful suggestions for improvement of previous versions  ... 
arXiv:0902.4682v5 fatcat:pgxxo7vjcbeyvhjej4svsv6lqe

Mini-Workshop: Constructive Homological Algebra with Applications to Coherent Sheaves and Control Theory

Mohamed Barakat, Thierry Coquand, Alban Quadrat
2013 Oberwolfach Reports  
Surprisingly, these apparently remote fields share a considerable amount of common constructive methods.  ...  There, the current state already reached a level of generality which allows simultaneous application to diverse fields of applied and theoretical mathematics.  ...  For smooth toric varieties there is a global description when a sheaf is zero. Theorem.  ... 
doi:10.4171/owr/2013/25 fatcat:rxgxeg667fcrfg74vx4qvrrqee

Automated deduction for verification

Natarajan Shankar
2009 ACM Computing Surveys  
A logic consists of a formal language, a formal semantics, and a formal proof system.  ...  First-order logic extends propositional logic to predicates and terms built from variables and function symbols, and serves as a formal foundation for arithmetic and set theory.  ...  ACKNOWLEDGMENTS Tony Hoare and Jayadev Misra suggested the idea for this survey article and shepherded it through many revisions with copious feedback, advice, and encouragement.  ... 
doi:10.1145/1592434.1592437 fatcat:satgicglyneqvl2nw5pjnr3d3a


Wilfried Sieg
2009 Philosophy of Mathematics  
Before we can start copying, we have to discover at least partially the nature of the residue, with an emphasis on "partially", through some restricted proposals for finding proofs in mathematics.  ...  Gödel discusses then a theorem of Herbrand's, which he considers to be the most far-reaching among interesting partial results in the pursuit of Hilbert's consistency program.  ... 
doi:10.1016/b978-0-444-51555-1.50017-1 fatcat:7fjtsyt6izeizbzm4zgoastvuy

Dimension spectra of random subfractals of self-similar fractals

Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo, Philippe Moser
2014 Annals of Pure and Applied Logic  
The dimension spectrum of a set X in Euclidean space is the subset of [0, n] consisting of the dimensions of all points in X.  ...  Our proof techniques include van Lambalgen's theorem on independent random sequences, measure preserving transformations, an application of network flow theory, a Kolmogorov complexity lower bound argument  ...  We start with a description of constructive dimension on Σ ∞ m . For the rest of this section let π denote a positive probability measure on Σ m , extended by product to Σ * m . Definition.  ... 
doi:10.1016/j.apal.2014.07.001 fatcat:ofgifuwcyfae5mup6qtkx7obsa

Formal Methods and their Role in the Certification of Critical Systems [chapter]

John Rushby
1997 Safety and Reliability of Software Based Systems  
Its purpose is to outline the technical basis for formal methods in computer science, to explain the use of formal methods in the specification and verification of software and hardware requirements, designs  ...  This report was prepared to supplement a forthcoming chapter on formal methods in the FAA Digital Systems Validation Handbook 1 .  ...  and argue their points of view with me.  ... 
doi:10.1007/978-1-4471-0921-1_1 fatcat:33n3af7ssbfkbiy6o6vj462idi

Formal specification languages in knowledge and software engineering

Dieter Fensel
1995 Knowledge engineering review (Print)  
Characteristics of such systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem. Languages for kbs have to cover both these aspects.  ...  Therefore it seems quite natural to compare formal languages for specifying kbs with formal languages which were developed by the software engineering community for specifying software systems.  ...  very helpful comments on drafts of the paper.  ... 
doi:10.1017/s0269888900007566 fatcat:gvexdbifpvagpasu7mgpon7qsa

Rough Sets and Rough Logic: A KDD Perspective [chapter]

Zdzisław Pawlak, Lech Polkowski, Andrzej Skowron
2000 Studies in Fuzziness and Soft Computing  
This main goal is motivated by the basic fact, constituting also the main problem of KDD, that languages we may choose for knowledge description are incomplete.  ...  logic, propositional logic, predicate logic, modal logic, belief and belief revision logics, default logic, para-consistent logic, non-monotonic logic, fuzzy logic, rough logic. their negations) such  ...  To give a formal description of first order logical calculi on lines of deductive systems, we begin with an alphabet which in general case consists of few types of symbols: First we define the set of terms  ... 
doi:10.1007/978-3-7908-1840-6_13 fatcat:vy35ujzaszcwvevywvjcms4wzy

A survey of languages for specifying dynamics: a knowledge engineering perspective

P. van Eck, J. Engelfriet, D. Fensel, F. van Harmelen, Y. Venema, M. Willems
2001 IEEE Transactions on Knowledge and Data Engineering  
Characteristics for knowledge-based systems are a complex knowledge base and an inference engine which uses this knowledge to solve a given problem.  ...  In fact, we have taken approaches for the specification of information systems (Language for Conceptual Modeling and TROLL), approaches for the specification of database updates and logic programming (  ...  Wieringa for their comments on an earlier version of this paper. The anonymous reviewers of this paper provided valuable suggestions for improvements.  ... 
doi:10.1109/69.929903 fatcat:tq623ya3qfhnhhqssjdjfu7jl4

Toposes of Monoid Actions [article]

Morgan Rogers
2021 arXiv   pre-print
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize.  ...  As groundwork for considering topological monoids, we branch out into a study of supercompactly generated toposes (a class strictly larger than presheaf toposes).  ...  Given a topology on S, we may extend it to a topology on S 1 with an equivalent category of actions by making the singleton consisting of the adjoined unit an open subset, and extending this to a topology  ... 
arXiv:2112.10198v1 fatcat:vs2uzbr5lbb7jeotjqawnlc2ym
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