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First Neural Conjecturing Datasets and Experiments [article]

Josef Urban, Jan Jakubův
2020 arXiv   pre-print
We describe several datasets and first experiments with creating conjectures by neural methods.  ...  The datasets are based on the Mizar Mathematical Library processed in several forms and the problems extracted from it by the MPTP system and proved by the E prover using the ENIGMA guidance.  ...  There are many interesting conjectures generated during the unconditioned sampling. The trained models can be directly used by Mizar users for autocompletion of their texts.  ... 
arXiv:2005.14664v1 fatcat:ftafsxndqvduhkjeoiujvsmdau

Structured incremental proof planning [chapter]

Stefan Gerberding, Brigitte Pientka
1997 Lecture Notes in Computer Science  
The new meta-rule set represents a more specialized strategy better suited for the current situation. We de ne the semantics of our framework by an inference system.  ...  By employing nested sets of meta-rules the formulation of strategies may be structured. By switching to another meta-rule set the planner can adjust to a new situation within the proof.  ...  The data structure bool is freely generated by the constructors true and false. list is generated by nil and add, hd and tl are destructor functions for add.  ... 
doi:10.1007/3540634932_4 fatcat:cbr2x72do5bqzjlk4qbm6xbxmq

Page 8104 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
; Grenoble) ; Peltier, Nicolas (F-CNRS-IM; Grenoble) Semantic generalizations for proving and disproving conjectures by analogy.  ...  The paper investigates the problem of model checking for knowl- edge formulae in the S5,, Kripke semantic structures generated by finite state environments.  ... 

Flag Algebras: An Interim Report [chapter]

Alexander A. Razborov
2013 The Mathematics of Paul Erdős II  
But our survey is also preceded, interleaved and concluded with a few general digressions about the method itself.  ...  For the most part, this article is a survey of concrete results in extremal combinatorics obtained with the method of flag algebras.  ...  Acknowledgment I am grateful to Rahil Baber, Victor Falgas-Ravry, Ron Graham, Sergey Norin and Christian Reiher for useful remarks.  ... 
doi:10.1007/978-1-4614-7254-4_16 fatcat:bdpn2lvu5jcuzm5gqfdwhuufqi

Identity of Proofs Based on Normalization and Generality

Kosta Došen
2003 Bulletin of Symbolic Logic  
These two proposals proved to be extensionally equivalent only for limited fragments of logic.  ...  This proposal seems more promising than the other one for the general proof theory of classical logic.  ...  The writing of the paper was financed by the Ministry of Science, Technology and Development of Serbia through grant 1630 (Representation of proofs with applications, classification of structures and infinite  ... 
doi:10.2178/bsl/1067620091 fatcat:2k56fbyssveqvfdafld4w2oovm

Does Gödel's Incompleteness Theorem Prove that Truth Transcends Proof? [chapter]

Joseph Vidal-Rosset
2006 The Age of Alternative Logics  
There are differences and analogy between Fermat conjecture and G-sentences. First, Fermat's conjecture is intuitevely clear and simple, when the Gödel sentence is weird.  ...  , I refer only to the Disquotational Theory (DT) described by Ketland and to the result he has proved: DT added to any (non-semantical) theory S is conservative over S.  ... 
doi:10.1007/978-1-4020-5012-7_5 fatcat:t77zyulp3rdyhlbgzldubvugzu

An Automated Theorem Proving in First-Order Predicate Calculus using Resolution

Moko Anasuodei, James Godbless Tamaraebi, Federal University Otuoke
2020 International Journal of Engineering Research and  
The project's focus was on the design and implementation of a program for automated theorem proving in first-order logic using the resolution proof procedure for first-order logic.  ...  The justification for implementing such a program using logic is that, proofs derived by humans in natural languages are ambiguous and vague but with logic the ambiguity can be eliminated.  ...  ACKNOWLEDGMENT All gratitude goes to God almighty for his infinite provisions, guidance and inspiration.  ... 
doi:10.17577/ijertv9is020301 fatcat:n27iauebrjeuzlvldemztsj3hm

Page 7267 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
and Nicolas Peltier, Semantic generalizations for prov- ing and disproving conjectures by analogy (27-45); Anatoli Degtyarev [Anatolii Degtyarév] and Andrei Voronkov, What you always wanted to know about  ...  Paulson, Tool support for logics of programs (461 498); N. Shankar, Machine-assisted verification using theorem proving and model checking (499-528).  ... 

On the notion of interestingness in automated mathematical discovery

SIMON COLTON, ALAN BUNDY, TOBY WALSH
2000 International Journal of Human-Computer Studies  
We survey five mathematical discovery programs by looking in detail at the discovery processes they illustrate and the success they've had.  ...  We also look at the ways in which the programs assess how surprising and complex a conjecture statement is, and the different ways in which the applicability of a concept or conjecture is used.  ...  We would also like to thank Susan Epstein for her comments explaining aspects of the GT program, JanŻytkow for his comments on the system by Bagai et al and Craig Larson for helping us understand the Graffiti  ... 
doi:10.1006/ijhc.2000.0394 fatcat:tuhjwqyhere7xg7foozsls7fku

Real-Time Computability of Real Numbers by Chemical Reaction Networks [chapter]

Xiang Huang, Titus H. Klinge, James I. Lathrop, Xiaoyuan Li, Jack H. Lutz
2017 Lecture Notes in Computer Science  
We discuss possible implications of this for the 1965 Hartmanis-Stearns conjecture, which says that no irrational algebraic number is real time computable by a Turing machine.  ...  We show that every algebraic number and some transcendental numbers are real time computable by chemical reaction networks in this sense.  ...  We thank Wolfgang Kliemann, James Hanson, Jonathan Smith, and Matthew Riley for useful discussions, we thank Kendal Gast for useful suggestions on the exposition, and we thank Sergey Verlan for additional  ... 
doi:10.1007/978-3-319-58187-3_3 fatcat:jpnfscnpcbhffdhp3xjducpqfa

Identity of Proofs Based on Normalization and Generality [article]

K. Dosen
2004 arXiv   pre-print
The second approach, which stems from Lambek, Mac Lane and Kelly, and is inspired by the generality of proofs, seems to be more promissing in classical logic.  ...  In general proof theory there are two approaches to the question of identity criteria for proofs.  ...  I am grateful to the organizers for inviting me to deliver this talk. I am also grateful to the Alexander von Humboldt Foundation for supporting my participation at the colloquium. The writing of the  ... 
arXiv:math/0208094v12 fatcat:mttiom5k25bjdiad4ld4bu6d54

Any progress in systematic design? [chapter]

A.H. Bridges
1986 Computer-Aided Architectural Design Futures  
First, rules 'interpreting' deep structures into semantic structures will be superfluous: if all meaning is accounted for in deep structures, and these are isomorphic with semantic structures, then semantic  ...  Second, if deep structure is semantic structure, then the function of transformations will be to interpret semantic structures into surface structures: hence 'generative semantics'.  ... 
doi:10.1016/b978-0-408-05300-6.50007-x fatcat:zpz6brcfy5ctjmcavil3tmobuu

Page 3986 of Mathematical Reviews Vol. , Issue 83j [page]

1983 Mathematical Reviews  
The author’s conjecture is a semantic technique, albeit that he concedes the extant “evidence” to be scant (p. 8). He adapts Lukasiewicz’s form of Aristotle’s “ecthesis” [J.  ...  The “proving in a circle” in II.5—7 iterates the procedure in II.8-10, to prove that the conclusion of a syllogism and one of its premisses with an exchange of the subject and predicate yield the other  ... 

Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies

Petr Cintula, Francesc Esteva, Joan Gispert, Lluís Godo, Franco Montagna, Carles Noguera
2009 Annals of Pure and Applied Logic  
Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved.  ...  In the general framework of propositional core and ∆-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras.  ...  Acknowlegdements: We are grateful to Félix Bou for his reading and useful comments to Section 5 and to Mauro Di Nasso for discussion about ultrapowers of [0, 1] and measurable cardinals.  ... 
doi:10.1016/j.apal.2009.01.012 fatcat:m2jmypf4brbnpa7np4ymtae5d4

Developing Corpus-Based Translation Methods between Informal and Formal Mathematics: Project Description [chapter]

Cezary Kaliszyk, Josef Urban, Jiří Vyskočil, Herman Geuvers
2014 Lecture Notes in Computer Science  
The goal of this project 4 is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machinetranslation  ...  methods, (ii) to develop such methods oriented at the formalization task, and in particular (iii) to combine such methods with learning-assisted automated reasoning that will serve as a strong semantic  ...  Analogously, strong semantic ARLT methods are likely to be useful in the formalization field also for complementing the statistical methods that learn formalization.  ... 
doi:10.1007/978-3-319-08434-3_34 fatcat:o75tw3gz2rh7pawh355d7anlga
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