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First Neural Conjecturing Datasets and Experiments
[article]

2020
*
arXiv
*
pre-print

We describe several datasets

arXiv:2005.14664v1
fatcat:ftafsxndqvduhkjeoiujvsmdau
*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. ...##
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Structured incremental proof planning
[chapter]

1997
*
Lecture Notes in Computer Science
*

The new meta-rule set represents a more specialized strategy better suited

doi:10.1007/3540634932_4
fatcat:cbr2x72do5bqzjlk4qbm6xbxmq
*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. ...##
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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. ...##
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Flag Algebras: An Interim Report
[chapter]

2013
*
The Mathematics of Paul Erdős II
*

But our survey is also preceded, interleaved

doi:10.1007/978-1-4614-7254-4_16
fatcat:bdpn2lvu5jcuzm5gqfdwhuufqi
*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. ...##
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Identity of Proofs Based on Normalization and Generality

2003
*
Bulletin of Symbolic Logic
*

These two proposals

doi:10.2178/bsl/1067620091
fatcat:2k56fbyssveqvfdafld4w2oovm
*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 ...##
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Does Gödel's Incompleteness Theorem Prove that Truth Transcends Proof?
[chapter]

2006
*
The Age of Alternative Logics
*

There are differences

doi:10.1007/978-1-4020-5012-7_5
fatcat:t77zyulp3rdyhlbgzldubvugzu
*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. ...##
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An Automated Theorem Proving in First-Order Predicate Calculus using Resolution

2020
*
International Journal of Engineering Research and
*

The project's focus was on the design

doi:10.17577/ijertv9is020301
fatcat:n27iauebrjeuzlvldemztsj3hm
*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. ...##
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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). ...

##
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On the notion of interestingness in automated mathematical discovery

2000
*
International Journal of Human-Computer Studies
*

We survey five mathematical discovery programs

doi:10.1006/ijhc.2000.0394
fatcat:tuhjwqyhere7xg7foozsls7fku
*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 ...##
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Real-Time Computability of Real Numbers by Chemical Reaction Networks
[chapter]

2017
*
Lecture Notes in Computer Science
*

We discuss possible implications of this

doi:10.1007/978-3-319-58187-3_3
fatcat:jpnfscnpcbhffdhp3xjducpqfa
*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 ...##
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Identity of Proofs Based on Normalization and Generality
[article]

2004
*
arXiv
*
pre-print

The second approach, which stems from Lambek, Mac Lane

arXiv:math/0208094v12
fatcat:mttiom5k25bjdiad4ld4bu6d54
*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 ...##
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Any progress in systematic design?
[chapter]

1986
*
Computer-Aided Architectural Design Futures
*

First, rules 'interpreting' deep structures into

doi:10.1016/b978-0-408-05300-6.50007-x
fatcat:zpz6brcfy5ctjmcavil3tmobuu
*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*'. ...##
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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 ...##
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Distinguished algebraic semantics for t-norm based fuzzy logics: Methods and algebraic equivalencies

2009
*
Annals of Pure and Applied Logic
*

Finally, all completeness properties

doi:10.1016/j.apal.2009.01.012
fatcat:m2jmypf4brbnpa7np4ymtae5d4
*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. ...##
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Developing Corpus-Based Translation Methods between Informal and Formal Mathematics: Project Description
[chapter]

2014
*
Lecture Notes in Computer Science
*

The goal of this project 4 is to (i) accumulate annotated informal/formal mathematical corpora suitable

doi:10.1007/978-3-319-08434-3_34
fatcat:o75tw3gz2rh7pawh355d7anlga
*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. ...
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