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Natural Deduction and the Isabelle Proof Assistant

Jørgen Villadsen, Andreas Halkjær From, Anders Schlichtkrull
2018 Electronic Proceedings in Theoretical Computer Science  
We describe our Natural Deduction Assistant (NaDeA) and the interfaces between the Isabelle proof assistant and NaDeA.  ...  In particular, we explain how NaDeA, using a generated prover that has been verified in Isabelle, provides feedback to the student, and also how NaDeA, for each formula proved by the student, provides  ...  Alexander Birch Jensen was the lead programmer for earlier versions of NaDeA and ProofJudge.  ... 
doi:10.4204/eptcs.267.9 fatcat:ehv2tosmcff2fnqer3frtc4toy

Computational logic and the social

Ursula Martin
2014 Journal of Logic and Computation  
verification research, computational logic and Roy Dyckhoff's pioneering work on computer proof.  ...  This paper outlines a research agenda for a new vision of a mathematics social machine, a combination of people, computers, and archives to create and apply mathematics, and places it in the context of  ...  Natural deduction proofs in the style of books like Lemmon [42] , while convenient for meta-logical reasoning about proof, are hard to understand and construct, even for very short proofs.  ... 
doi:10.1093/logcom/exu036 fatcat:pdcsxxhabfaejmqx2ocsnkcuhm

Review: Eckart Menzler-Trott's — Logic's Lost Genius: The Life of Gerhard Gentzen

John N. Crossley
2008 The Australasian Journal of Logic  
 Natural deduction now features in virtually every first course in formal logic.  ...  The scope of the journal includes all areas of logic, both pure and applied to topics in philosophy, mathematics, computation, linguistics and the other sciences.  ... 
doi:10.26686/ajl.v6i0.1795 fatcat:vsa3jkuvcjd3rgtw3o52oevy2q

Gentzen-Prawitz Natural Deduction as a Teaching Tool [article]

Jean-François Monin, Cristian Ene (VERIMAG - Imag), Michaël Périn
2009 arXiv   pre-print
We argue that this pedagogical approach is a good alternative to the use of Boolean algebra for teaching reasoning, especially for computer scientists and formal methods practionners.  ...  We report a four-years experiment in teaching reasoning to undergraduate students, ranging from weak to gifted, using Gentzen-Prawitz's style natural deduction.  ...  This rule has a special interest for computer scientists, as it illustrates the notion of scope, which is here applied on hypotheses : the scope of an hypothesis is its availibility domain.  ... 
arXiv:0907.3599v1 fatcat:bhqrcd5mlve5bi4vlqxfmklh3u

An introduction to mechanized reasoning

Manfred Kerber, Christoph Lange, Colin Rowat
2016 Journal of Mathematical Economics  
Mechanized reasoning uses computers to verify proofs and to help discover new theorems.  ...  Computer scientists have applied mechanized reasoning to economic problems but -- to date -- this work has not yet been properly presented in economics journals.  ...  The development of formal logic from 1850 to 1930, the advent of the computer, and the inception of artificial intelligence (AI) as a research field at the Dartmouth decade or so, computer scientists have  ... 
doi:10.1016/j.jmateco.2016.06.005 fatcat:out6y5pgjrcrhc4yq4lk55yrhy

From constructivism to computer science

A.S. Troelstra
1999 Theoretical Computer Science  
Preamble My field is mathematical logic, with a special interest in constructivism, and I would not dare to call myself a computer scientist.  ...  But some computer scientists regard my work as a contribution to their field; and in this text I shall try to explain how this is possible, by taking a look at the history of ideas.  ...  Preamble My field is mathematical logic, with a special interest in constructivism, and I would not dare to call myself a computer scientist.  ... 
doi:10.1016/s0304-3975(97)00172-2 fatcat:zb4sklb2a5crfk5bnfmkslb2j4

My Continuing Journey from Logic to Computational Argumentation

Douglas Walton
2019 Felsefe Arkivi - Archives of Philosophy  
The story ends by leading to recent collaborations with three young logicians and computer scientists who are continuing on the path of my journey.  ...  The exposition moves on to relate how my interests shifted to the study of argumentation in informal logic, and from there to computational systems combining defeasible argumentation schemes with argument  ...  Panisson, has applied argumentation tools to widely interesting problems and issues that arise not only in computer science, but are also logical in nature and that have important applications to argumentation  ... 
doi:10.26650/arcp2019-5123 fatcat:p3heewoxrrgxfek6buzkkryeny

Is Mathematical Logic Really Necessary in Teaching Mathematical Proofs?

Michael Aristidou
2019 Athens Journal of Education  
Finally, we argue that even though mathematical 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.  ... 
doi:10.30958/aje.7-1-5 fatcat:rtox7vhbdjcelc4s7u5jovge5a

Special issue on 'Logical frameworks and metalanguages'

GÉRARD HUET
2003 Journal of functional programming  
Meanwhile, computer modelling developed a need for concrete uses of logic, first for the design of computer circuits, then more widely for increasing the reliability of sofware through the use of formal  ...  specifications and proofs of correctness of computer programs.  ...  Editorial The year 1989 was a turning point for the constitution of a research community around this paradigm, grouping proof theorists from mathematical logic with computer scientists both from the denotational  ... 
doi:10.1017/s0956796802004549 fatcat:zkmf6ncdjnhbvfhmshmsevmvt4

Intelligent Systems and Formal Methods in Software Engineering

Bernhard Beckert, Tony Hoare, Reiner Hahnle, Douglas Smith, Cordell Green, Silvio Ranise, Cesare Tinelli, Thomas Ball, Sriram Rajamani
2006 IEEE Intelligent Systems  
Confidence in the correctness of the proof is very high because it has been generated and checked automatically by computer.  ...  Our understanding of the concept of a proof goes back to the Greek philosophers Pythagoras and Aristotle.  ...  Second, it proves validity by deduction in a logic calculus. Third, it uses computer assistance for proof search and bookkeeping.  ... 
doi:10.1109/mis.2006.117 fatcat:e3gffxrewbhubelnmkv7rvrf7i

About the Chasm Separating the Goals of Hilbert's Consistency Program from the Second Incompletess Theorem [article]

Dan E. Willard
2018 arXiv   pre-print
The current paper will review some of our prior results and also introduce an 'enriched' refinement of semantic tableaux deduction.  ...  We have published several articles about generalizations and boundary-case exceptions to the Second Incompleteness Theorem during the last 25 years.  ...  Acknowledgment: I thank Seth Chaiken for several comments about how to improve the style of presentation.  ... 
arXiv:1807.04717v2 fatcat:hel52u2mgbc5tk2uobkgef2i6q

Mathematical Logic in Computer Science [article]

Assaf Kfoury
2018 arXiv   pre-print
The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.  ...  I corrected several wrong dates and wrong attributions, and made several adjustments, some minor and some significant, after communicating with Martin Davis, Peter Gacs, Michael Harris, Roger Hindley,  ...  Aki Kanamori, Phokion Kolaitis, Leonid Levin, Pawel Urzyczyn, and Moshe Vardi.  ... 
arXiv:1802.03292v1 fatcat:bqajf55ih5aw3mxxo6tt5tjzkq

The computational value of debate in defeasible reasoning

Gerard A. W. Vreeswijk
1995 Argumentation: an international journal on reasoning  
How they apply in a theory of formal argument, will be shown in this article.  ...  Defeasible reasoning is concerned with the logics of non-deductive argument.  ...  Except for chapters on propositional logic and predicate logic, the discussion is not tied to a specific formalism, and is more concerned with practical aspects of reasoning (argument, debate, and resolution  ... 
doi:10.1007/bf00721964 fatcat:x6od4r3jf5er7pzu5sh3sbdmzi

NOTICES

2019 Bulletin of Symbolic Logic  
research involving formal logic, computing and programming theory, and natural language and reasoning.  ...  ) • The program of the Summer School will consist of seven courses, given by leading scientists: Proof Theory in Logic, by R.  ... 
doi:10.1017/bsl.2019.29 fatcat:jedzposqqbbotnc2rcfydzp33a

Logicism and the Development of Computer Science [chapter]

Donald Gillies
2002 Lecture Notes in Computer Science  
The formal language of logic is suitable for humans trying to communicate with computers.  ...  In particular, logicism, the view that mathematics can be reduced to logic, was developed by Frege and Russell, long before computers were invented, and yet many of the ideas of logicism have been central  ...  Non-monotonic logic has been developed by computer scientists since the early 1980's, and is an example of an entirely new kind of logic which was introduced as the result of applying logic to computer  ... 
doi:10.1007/3-540-45632-5_23 fatcat:k2ew5lygf5bglbqaxdfqxceuvq
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