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Bertrand Russell, Herbrand's theorem, and the assignment statement [chapter]

Melvin Fitting
1998 Lecture Notes in Computer Science  
And we provide formal tableau proof rules to go with the semantics, rules that are, at least in principle, automatable.  ...  In this paper we sketch a natural syntax and semantics for first-order modal logic, and show how it easily copes with well-known problems.  ...  Herbrand's Theorem In classical logic, Herbrand's theorem provides a reduction of the first-order provability problem to the propositional level, plus an open-ended search.  ... 
doi:10.1007/bfb0055899 fatcat:h33duuw2ufcfpkzpo6o3v55fya

Lectures on Jacques Herbrand as a Logician [article]

Claus-Peter Wirth, Joerg Siekmann, Christoph Benzmueller, Serge Autexier
2014 arXiv   pre-print
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  ...  We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving.  ...  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

Page 7881 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
7881 68 COMPUTER SCIENCE language for database mining (extended abstract) (1-13); Melvin Fitting, Bertrand Russell, Herbrand’s theorem, and the assign- ment statement (14-28); Richmond H.  ...  Homann, Specification and integra- tion of theorem provers and computer algebra systems (94-106); Carlos Castro, COLETTE, prototyping CSP solvers using a rule- based language (107-119); Martin Damsbo and  ... 

How Peircean was the "'Fregean' Revolution" in Logic?

И. Анеллис
2012 Logical Investigations  
are said to be the basis of what has come to be called the "Fregean revolution" in logic and which are said to constitute the elements of Frege's Begriffsschrift of 1879 as the "founding" document of  ...  The work in logic of Charles Peirce is surveyed in light of the characteristics enumerated by historian of logic J. van Heijenoort as defining the original innovations in logic of Frege and which together  ...  of the formulas of the theory and is in turn the basis for Herbrand's Fundamental Theorem [FT] which can best be understood as a strong version of LST 13 .  ... 
doi:10.21146/2074-1472-2012-18-0-239-272 fatcat:fnkk7faslff77pb3cdu25dvfl4

The Development of Mathematical Logic from Russell to Tarski, 1900–1935 [chapter]

Paolo Mancosu, Richard Zach, Calixto Badesa
2009 The Development of Modern Logic  
P is true in the canonical domain, if some substitution of elements for the free variables in H makes H true in the domain, and false otherwise. Herbrand's statement of the theorem then is: 1.  ...  The most significant contribution, of course, is Herbrand's Theorem.  ... 
doi:10.1093/acprof:oso/9780195137316.003.0029 fatcat:ygiplet5oraf7fza6fsmf5j5ly

How Peircean was the "'Fregean' Revolution" in Logic? [article]

Irving H. Anellis
2012 arXiv   pre-print
of 1879, and with Bertrand Russell (1872-1970) as its chief This position likewise understands the algebraic logic of Augustus De Morgan (1806-1871), George Boole (1815-1864), Charles Sanders Peirce (  ...  The most detailed listing and elaboration of Frege's innovations, and the characteristics that distinguish mathematical logic from Aristotelian logic, were set forth by van Heijenoort.  ...  Not dismissive, but rather oblivious, to the historical roots of the Löwenheim-Skolem Theorem, Herbrand's Fundamental Theorem, and related results in proof theory and model theory despite its strong concern  ... 
arXiv:1201.0353v1 fatcat:akg6yyefyvgszjx23qnpaolwwy

From Hilbert's program to a logic tool box

J. A. Makowsky
2008 Annals of Mathematics and Artificial Intelligence  
For Witek Marek, first mentor, then colleague and true friend, on the occasion of his 65th birthday.  ...  We discuss what the minimal toolbox of logic tools should look like for a computer scientist who is involved in designing and analyzing reliable systems.  ...  Halevy and D. Hay for stimulating discussions and suggestions about how to teach Logic to Computer Science students. I would like to thank the editors of this volume, M. Kaminski and M.  ... 
doi:10.1007/s10472-009-9115-z fatcat:5czgb6guqzb3hdq46spqz24wdy

The automation of proof: a historical and sociological exploration

D. Mackenzie
1995 IEEE Annals of the History of Computing  
to be irrelevant; and interactive theorem proving, where the proof is directly guided by a human being.  ...  has been rooted primarily in the verification of computer programs and hardware 'designs.-· · IEEE  ...  The attempt to derive mathematics from basic logical principles -thus avoiding arbitrary axioms -was also extensively pursued by Alfred North Whitehead (1861 Whitehead ( -1947 and Bertrand Russell (  ... 
doi:10.1109/85.397057 fatcat:rcaohi4jafaoxivpjmdqmhsqtq

Automation of Higher-Order Logic [chapter]

Christoph Benzmüller, Dale Miller
2014 Handbook of the History of Logic  
Besides the readers of this chapter, we thank Zakaria Chihani, Julian Röder, Leon Weber, and Max Wisnieswki for proofreading the document.  ...  The first author has been supported by the German Research Foundation under Heisenberg grant BE2501/9-1 and the second author has been supported by the ERC Advanced Grant ProofCert.  ...  Herbrand's theorem for ETT.  ... 
doi:10.1016/b978-0-444-51624-4.50005-8 fatcat:jfcztdvymjfujg3bzb2rq2qyzy


2016 Bulletin of Symbolic Logic  
Sets of assignments are called teams and the semantics is called team semantics.  ...  When one attempts to develop the model theory of a logic generalizing first order logic, one runs into the problem that model theoretic properties of the logic like compactness, Löwenheim-Skolem Theorem  ...  We prove that for some sequence of tautologies ϕn the proof steps and the proof sizes in  ... 
doi:10.1017/bsl.2016.22 fatcat:cm4a5yyvgfajzm4qvlszviblni

Page 69 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
., 99g:03015 Fitting, Melvin Bertrand Russell, Herbrand’s theorem, and the assignment statement. (English summary) (see 99k:68005) Gabbay, Dov M. Fibred semantics and the weaving of logics. II.  ...  Names and expressions. Fisher, Michael D. A normal form for temporal logics and its applications in theorem- proving and execution.  ... 

Nominal logic programming

James Cheney, Christian Urban
2008 ACM Transactions on Programming Languages and Systems  
We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs.  ...  Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we  ...  His support for me and this work has been unyielding. My other committee members, Robert Constable and Geri Gay, have also been very supportive.  ... 
doi:10.1145/1387673.1387675 fatcat:longqgnr75aktkwdy56eeyu4ne

Can Church's thesis be viewed as a Carnapian explication?

Paula Quinon
2019 Synthese  
To overcome this difficulty, I propose two possible clarifications of the pre-systematic concept of "computability" that can both be captured in recursion theory, and I show how both clarifications avoid  ...  Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent.  ...  , and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.  ... 
doi:10.1007/s11229-019-02286-7 fatcat:kckfy7ky7renvh3flf3dmfsgbu

From Hilbert's Program to a Logic Toolbox [chapter]

Johann A. Makowsky
Logic for Programming, Artificial Intelligence, and Reasoning  
For Witek Marek, first mentor, then colleague and true friend, on the occasion of his 65th birthday.  ...  We discuss what the minimal toolbox of logic tools should look like for a computer scientist who is involved in designing and analyzing reliable systems.  ...  Halevy and D. Hay for stimulating discussions and suggestions about how to teach Logic to Computer Science students. I would like to thank the editors of this volume, M. Kaminski and M.  ... 
doi:10.1007/978-3-540-75560-9_1 dblp:conf/lpar/Makowsky07 fatcat:jbt2boybbfevledq725hw3c6ga

Validating Reasoning Heuristics Using Next-Generation Theorem-Provers

2007 Proceedings of the 5th International Workshop on Modelling, Simulation, Verification and Validation of Enterprise Information Systems   unpublished
This dissertation investigates the applicability of these heuristics to next generation theorem provers.  ...  To this end a number of heuristics has been developed to aid the Otter theorem prover in finding short proofs for set-theoretic problems.  ...  Herbrand's theorem.  ... 
doi:10.5220/0002425900430052 fatcat:yuw5ooluyjf2dfapwfs6fsqcoy
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