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Combining Theorem Proving with Natural Language Processing

Björn Pelzer, Ingo Glöckner
2008 Conference on Automated Deduction  
In our system we have integrated an automated theorem prover in a framework of natural language processing tools to allow for deductive reasoning over an extensive knowledge base derived from textual sources  ...  The LogAnswer system is an application of automated reasoning to the field of open domain question answering, which aims at finding answers to natural language questions regarding arbitrary topics.  ...  The fields of automated reasoning and natural language processing (NLP) differ greatly in their methodologies. A Fig. 1 . Screenshot of the LogAnswer prototype.  ... 
dblp:conf/cade/PelzerG08 fatcat:xmajl365xngyvk2wmnjarpaayy

Towards the Automatic Mathematician [chapter]

Markus N. Rabe, Christian Szegedy
2021 Lecture Notes in Computer Science  
This could prove crucial for processing natural language mathematics, which frequently contains formulas, text, and diagrams, and any model processing papers would need to understand how they relate to  ...  A new challenge arises from the use of language models for theorem proving.  ... 
doi:10.1007/978-3-030-79876-5_2 fatcat:w6hmshg5gzbabdfkyj5om3yeme

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 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.  ...  The process model used in this project is a hybrid of the "waterfall" model and the evolutionary development model. The program was implemented using the Python programming language.  ...  The procedure for proving a conjecture in a theorem is to replace the conjecture with its negation, combine this with the axioms and place in CNF to form a set of clauses.  ... 
doi:10.17577/ijertv9is020301 fatcat:n27iauebrjeuzlvldemztsj3hm

Integrating WS1S with PVS [chapter]

Sam Owre, Harald Rueß
2000 Lecture Notes in Computer Science  
There is a growing trend to integrate theorem proving systems with specialized decision procedures and model checking systems.  ...  In this way, a theorem proving system like PVS provides a common front-end and specification language for a variety of specialized tools.  ...  There is a growing trend to integrate theorem proving systems with specialized decision procedures and model checking systems.  ... 
doi:10.1007/10722167_42 fatcat:obik2mf2fvdvle5hetcievhhb4

Natural Language Premise Selection: Finding Supporting Statements for Mathematical Text [article]

Deborah Ferreira, Andre Freitas
2020 arXiv   pre-print
This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of mathematical discourse.  ...  Mathematical text is written using a combination of words and mathematical expressions.  ...  and natural language processing.  ... 
arXiv:2004.14959v1 fatcat:z35xxglfyrfbliu322kdzul3lm

CoCEC: An Automatic Combinational Circuit Equivalence Checker Based on the Interactive Theorem Prover

Wilayat Khan, Farrukh Aslam Khan, Abdelouahid Derhab, Adi Alhudhaif, Huihua Chen
2021 Complexity  
It automatically proves, in few seconds, the equivalence of circuits with as many as 45 variables (3.5 × 10 13 states).  ...  In this paper, we (1) define two simple, one formal and the other informal, gate-level hardware description languages, (2) design and develop a formal automatic combinational circuit equivalence checker  ...  CoCEC, on the contrary, is based on interactive theorem proving with additional advantages [14] and accepts the input in a natural style without requiring any programming skills.  ... 
doi:10.1155/2021/5525539 fatcat:6hlteqwfoff5ppeo342edfxydq

Six issues concerning future directions in concurrency research

Jos C. M. Baeten, Jan A. Bergstra
1996 ACM Computing Surveys  
A challenging but promising route is therefore to combine model-checking and theorem-proving techniques.  ...  The starting point is diverse: specification languages like LOTOS and PSF combine algebraically specified datatypes with process algebra syntax by having processes, actions and conditional constructs depending  ... 
doi:10.1145/242224.242272 fatcat:4vjmqlfg5zh67nduawzpzvbcfm

The Isabelle/Naproche Natural Language Proof Assistant [chapter]

Adrian De Lon, Peter Koepke, Anton Lorenzen, Adrian Marti, Marcel Schütz, Makarius Wenzel
2021 Lecture Notes in Computer Science  
Abstract"Image missing" is an emerging natural proof assistant that accepts input in the controlled natural language ForTheL.  ...  The dialect of ForTheL can be typeset by "Image missing" into documents that approximate the language and appearance of ordinary mathematical texts.  ...  The system uses the dedicated input language ForTheL (Formula Theory Language), natural language processing for texts with symbolic material, strong automatic theorem proving (ATP) for filling in implicit  ... 
doi:10.1007/978-3-030-79876-5_36 fatcat:2ox6tmqltvelpppwkrpketx46m

The PROSPER toolkit

Louise A. Dennis, Graham Collins, Michael Norrish, Richard J. Boulton, Konrad Slind, Thomas F. Melham
2003 International Journal on Software Tools for Technology Transfer (STTT)  
The nature of communication between components is specified in a languageindependent way.  ...  It is implemented in several common programming languages to allow a wide variety of tools to have access to the toolkit.  ...  There has also been a great deal of recent work in combining decision procedures (in particular model checkers) with automated theorem proving to increase the size of design that can be dealt with [1,  ... 
doi:10.1007/s100090200076 fatcat:bc4pffbyuzda5ejbxtdsrvp4y4

Is Strategic Programming a Viable Paradigm?

Paul Klint
2001 Electronical Notes in Theoretical Computer Science  
proving and programming-in-the-large.  ...  paper for the Workshop on Reduction Strategies in Programming and Rewriting (WRS'01) speculates on the viability of strategic programming in mainstream programming and in two selected application areas: theorem  ...  Theorem proving In the case of theorem proving axioms and proof rules are given and the problem is to prove or refute a potential theorem.  ... 
doi:10.1016/s1571-0661(04)00275-0 fatcat:bhzh73djrfcj7g5gtv3scbmkou

PROSPER An Investigation into Software Architecture for Embedded Proof Engines [chapter]

Thomas F. Melham
2002 Lecture Notes in Computer Science  
Combining Proof Tools. There is now a fairly large literature on combining decision procedures, and in particular model checkers, with theorem proving.  ...  A useful summary of other recent work on combining model checking with theorem proving is given in Tomás Uribe's invited talk at FroCoS 2000 [54] . Integration Architectures.  ... 
doi:10.1007/3-540-45988-x_16 fatcat:w6w7lbt2zbczlljouwu3a7nzce

A Vernacular for Coherent Logic [article]

Sana Stojanovic, Julien Narboux (INRIA Nancy - Grand Est / LSIIT, ICube), Marc Bezem, Predrag Janicic
2014 arXiv   pre-print
Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.  ...  language form (formatted in LATEX or in HTML).  ...  Conclusions and Further Work Over the last years a lot of effort has been invested in combining the power of automated and interactive theorem proving: interactive theorem provers are now equipped with  ... 
arXiv:1405.3391v1 fatcat:dthpav7c2rgbvdfckkmcd4b2rq

A Vernacular for Coherent Logic [chapter]

Sana Stojanović, Julien Narboux, Marc Bezem, Predrag Janičić
2014 Lecture Notes in Computer Science  
Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.  ...  language form (formatted in L A T E X or in HTML).  ...  Conclusions and Further Work Over the last years a lot of effort has been invested in combining the power of automated and interactive theorem proving: interactive theorem provers are now equipped with  ... 
doi:10.1007/978-3-319-08434-3_28 fatcat:jffyus6dlrhfdeaemyy46zkgba

Deductive software verification

Jean-Christophe Filliâtre
2011 International Journal on Software Tools for Technology Transfer (STTT)  
They are then discharged using either automated or interactive theorem provers. We briefly review this research area, with an emphasis on tools.  ...  Deductive software verification, also known as program proving, expresses the correctness of a program as a set of mathematical statements, called verification conditions.  ...  In this wide soup of tools, some natural selection process is taking place: tools are created, modified, abandoned, combined into new ones, etc.  ... 
doi:10.1007/s10009-011-0211-0 fatcat:cx7iofeyqraxhdrw4mx7uamo6y

A Survey of Languages for Formalizing Mathematics [article]

Cezary Kaliszyk, Florian Rabe
2020 arXiv   pre-print
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages.  ...  These goals are challenging to combine and state-of-the-art tools typically have to make difficult compromises.  ...  Controlled Natural Language These approaches combine formal grammars for fragments of natural language with formal languages for formulas.  ... 
arXiv:2005.12876v1 fatcat:lwpxnq4wdjexxar3ocod3ncdvy
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