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Comparison of Two Theorem Provers: Isabelle/HOL and Coq
[article]

2018
*
arXiv
*
pre-print

The need

arXiv:1808.09701v2
fatcat:ffesxt4esffgjottsxmwjykjri
*for**formal*definition of the very basis of mathematics arose in the last century. ...*For*this reason, it firstly gives a brief introduction to the bases of*formal**systems*and automated deduction theory, their main problems and challenges, and then provides detailed comparison of most notable ... Stavros Tripakis*for*letting me dive into the exciting world of*Logic*,*for*providing feedback on my paper at all stages of the work,*for*answering all my countless questions and supporting me. ...##
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Subject Index

2006
*
Journal of Applied Logic
*

; Supporting the

doi:10.1016/s1570-8683(06)00055-3
fatcat:yeph4llopfdgjoimxiakdzqqxm
*formal*veri- fication of mathematical texts, 592*Proof**systems*A general tableau method*for**propositional*inter- val temporal*logics*: Theory and implementa- tion, 305*Proofs*as programs ... TPS: A hybrid automatic-interactive*system**for*developing*proofs*, 367*Formal*digital libraries Innovations in computational type theory using Nuprl, 428*Formalization*of mathematics Is ZF a hack ...##
###
Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant
[chapter]

2017
*
Lecture Notes in Computer Science
*

We show how to use the

doi:10.1007/978-3-662-55947-5_5
fatcat:y2yhllvytrh7vn6rrdzzwph7xy
*proof*assistant Isabelle to*formally*prove theorems in the*logic*as well as meta-theorems about the*logic*. ... In particular, we*formalize*a meta-theorem that allows us to reduce the infinite number of truth values to a finite number of truth values,*for*a given formula, and we use this result in a*formalization*... Also thanks to Hendrik Decker and the anonymous reviewers*for*many constructive comments. ...##
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A view of automated proof checking and proving

1988
*
Annals of Operations Research
*

The main trade-off is between autonomy and flexibility in conducting

doi:10.1007/bf02283736
fatcat:gc5ifhb5vje4df3tq33jp3o3v4
*proofs*. Examples of the use of techniques and existing*systems*are given, but not attempt of an exhaustive overview is made. ... The goal is to provide the reader with an idea of what to look*for*when selecting an approach*for*his/her application. ... , or (3) submitting lemmas, i.e.,*propositions**for**proof*by the*system*. ...##
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From Logicism to Metatheory
[chapter]

2013
*
The Palgrave Centenary Companion to Principia Mathematica
*

. ii The Principia

doi:10.1057/9781137344632_4
fatcat:slpm6riocjfpxl6gsiphi2bmrm
*system*, with its explicit axiomatic approach to the fundamental principles of*logic*, was just what was needed in the early years of the 20 th century to make possible the precise formulation ... and treatment of meta-*logical*questions. ...*for**formal**systems*of*logic*. ...##
###
Constructive Formalization of Hybrid Logic with Eventualities
[chapter]

2011
*
Lecture Notes in Computer Science
*

This paper reports on the

doi:10.1007/978-3-642-25379-9_3
fatcat:mm7w4itpcfcjvb75vesju6qkzq
*formalization*of classical hybrid*logic*with eventualities in the constructive type theory of the*proof*assistant Coq. ... We present our work in three steps:*propositional**logic*, modal*logic*, and finally hybrid*logic*. ...*Proof*"⇒" Let M, w ⊨ t and S be some maximal Hintikka*system*such that H w ∈ S*for*all w ∈ |M| (*Proposition*4.4). ...##
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Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs?

2019
*
Athens Journal of Education
*

Finally, we argue that even though mathematical

doi:10.30958/aje.7-1-5
fatcat:rtox7vhbdjcelc4s7u5jovge5a
*logic*is central in mathematics, its*formal*methods are not really necessary in doing and teaching mathematical*proofs*and the role of those*formalities*... As it is already observed by mathematicians and educators, there is a discrepancy between the*formal*techniques of mathematical*logic*and the informal techniques of mathematics in regards to*proof*. ...*for*his comments on the book Mathematics B' Lyceum, and Babis Stergiou and Christos Lefkonitziatis*for*communicating to me some of the curriculum historicals related to the paper. ...##
###
Page 22 of Mathematical Reviews Vol. 58, Issue 1
[page]

1979
*
Mathematical Reviews
*

Caicedo, Xavier [Caicedo Ferrer, Xavier] 58 #129 A

*formal**system**for*the non-theorems of the*propositional*calculus. Notre Dame J.*Formal**Logic*19 (1978), no. 1, 147-151. ... The undecidability of first-order*logic*implies the nonexistence of an effective*formal**system**for*proving its nontheorems, but it*Logic*and Foundations 22 would be interesting to extend the author’s*system*...##
###
Novel Didactic Proof Assistant for First-Order Logic Natural Deduction
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/978-3-319-07482-5_42
fatcat:tloqap55g5b23dm44ysd475bli
*proof*assistant designed to help learning*formal**proof*, particularly in the*system*of Natural Deduction*for*First-Order*Logic*. ... It possesses a graphical interface presenting*proofs*as trees and handles multiple simultaneous derivations that can be dragged and dropped into one another. ... First, we shall take First-Order*Logic*as the*formal*language*for*expressing*propositions*. ...##
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Uniform provability realization of intuitionistic logic, modality and λ-terms

1999
*
Electronical Notes in Theoretical Computer Science
*

This question turned out to be a part of the more general problem of the intended realization

doi:10.1016/s1571-0661(04)00100-8
fatcat:ms423mkdgjh2lgj5oume2ouv4a
*for*G odel's modal*logic*of provability S4 which w as open since 1933. ... The problem of nding an adequate*formalization*of the provability s e m a ntics and establishing the completeness of the intuitionistic*logic*Int was rst raised by G odel in 1933. ... Heyting suggested the axiom*system*Int*for*intuitionistic*logic*( 8] ) 3 . ...##
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N.G. de Bruijn's contribution to the formalization of mathematics

2013
*
Indagationes mathematicae
*

In [McCarthy 1962] , he makes another clear case

doi:10.1016/j.indag.2013.09.003
fatcat:tgs7v5i6t5gxjl3s5c472obqje
*for*using a computer*for*checking*proofs*, especially*for*the verification of programs: It is part of the definition of*formal**system*that*proofs*be machine ... In [McCarthy 1960] , he explicitly states that Lisp was (among other things) developed*for*• Writing a program to check*proofs*in a class of*formal**logical**systems*. • Writing programs to realize various ...##
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Formalizing a Seligman-Style Tableau System for Hybrid Logic
[chapter]

2020
*
Lecture Notes in Computer Science
*

Hybrid

doi:10.1007/978-3-030-51074-9_27
fatcat:klxbbkjmwzhh7kfxm365meu4ai
*logic*is modal*logic*enriched with names*for*worlds. We*formalize*soundness and completeness*proofs**for*a Seligman-style tableau*system**for*hybrid*logic*in the*proof*assistant Isabelle/HOL. ... Moreover, the completeness*proof*we*formalize*is synthetic which suggests we can extend this work to prove a wider range of results about hybrid*logic*. ... The present work appears to be the first*proof**system**for*hybrid*logic*with a*formalized*completeness*proof*. ...##
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Isabelle/HOL as a Meta-Language for Teaching Logic

2020
*
Electronic Proceedings in Theoretical Computer Science
*

*Proof*assistants are important tools

*for*teaching

*logic*. We support this claim by discussing three

*formalizations*in Isabelle/HOL used in a recent course on automated reasoning. ... The first is a

*formalization*of

*System*W (a

*system*of classical

*propositional*

*logic*with only two primitive symbols), the second is the Natural Deduction Assistant (NaDeA), and the third is a one-sided ... Acknowledgements We thank Alexander Birch Jensen and Anders Schlichtkrull

*for*discussions. ...

##
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A formal logical framework for Cadiag-2

2009
*
Studies in Health Technology and Informatics
*

Cadiag-2-where "Cadiag" stands

pmid:19745391
fatcat:p4baxtkrubfi7mpholdjh3x5fa
*for*"computer-assisted diagnosis"- is an expert*system*based on fuzzy*logic*assisting in the differential diagnosis in internal medicine. ... The aim is to have a*formal**logical*calculus at hand which corresponds to the mode of operation of Cadiag-2 and which is among others needed to perform consistency checking of Cadiag-2's medical knowledge ... Ciabattoni et al. / A*Formal**Logical*Framework*for*Cadiag-2 650 atomic*propositions*by means of the connectives , , and ~. ...##
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Formalizing the Curry-Howard Correspondence
[article]

2019
*
arXiv
*
pre-print

We restate the tradicional correspondence between typed λ-calculi and

arXiv:1912.10961v1
fatcat:fgimqmoudbdexjfkqzsesf4q7q
*propositional**logics*inside this*formalism*, and indicate possible directions in which it could foster new and more structured generalizations ... In the current work, we introduce the*formalism*of p-institutions that could unify previous aproaches. ... From a*logical*point of view, there are multiple*formalisms**for*such*systems*, but we'll use the one in which*proofs*look like trees $ A prop A $ A true $ A prop $ B prop A $ B prop A, B $ A true A $ B ...
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