4. Theory Reasoning in Connection Calculi

1998 ◽  
pp. 65-140
Author(s):  
Peter Baumgartner
Keyword(s):  
Theory Reasoning

scholarly journals Deep Network Guided Proof Search

10.29007/8mwc ◽  
2018 ◽  
Author(s):  
Sarah Loos ◽  
Geoffrey Irving ◽  
Christian Szegedy ◽  
Cezary Kaliszyk
Keyword(s):  
Deep Learning ◽  
Program Analysis ◽  
Network Models ◽  
Theorem Prover ◽  
Neural Network Models ◽  
Two Phase ◽  
First Order ◽  
Proof Search ◽  
System Verification ◽  
Theory Reasoning

Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.Automated first-order theorem provers can aid in the formalization and verification of mathematical theorems and play a crucial role in program analysis, theory reasoning, security, interpolation, and system verification.Here we suggest deep learning based guidance in the proof search of the theorem prover E. We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search. We give experimental evidence that with a hybrid, two-phase approach, deep learning based guidance can significantly reduce the average number of proof search steps while increasing the number of theorems proved.Using a few proof guidance strategies that leverage deep neural networks, we have found first-order proofs of 7.36% of the first-order logic translations of the Mizar Mathematical Library theorems that did not previously have ATP generated proofs. This increases the ratio of statements in the corpus with ATP generated proofs from 56% to 59%.

scholarly journals Checkable Proofs for First-Order Theorem Proving

10.29007/s6d1 ◽  
2018 ◽  
Author(s):  
Giles Reger ◽  
Martin Suda
Keyword(s):  
Theorem Proving ◽  
Critical Mass ◽  
Current Situation ◽  
Boolean Satisfiability ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Theorem Provers ◽  
Interactive Theorem Provers ◽  
Theory Reasoning

Inspired by the success of the DRAT proof format for certification of boolean satisfiability (SAT),we argue that a similar goal of having unified automatically checkable proofs should be soughtby the developers of automated first-order theorem provers (ATPs). This would not onlyhelp to further increase assurance about the correctness of prover results,but would also be indispensable for tools which rely on ATPs,such as ``hammers'' employed within interactive theorem provers.The current situation, represented by the TSTP format is unsatisfactory,because this format does not have a standardised semantics and thus cannot be checked automatically.Providing such semantics, however, is a challenging endeavour. One would ideallylike to have a proof format which covers only-satisfiability-preserving operations such as Skolemisationand is versatile enough to encompass various proving methods (i.e. not just superposition)or is perhaps even open ended towards yet to be conceived methods or at least easily extendable in principle.Going beyond pure first-order logic to theory reasoning in the style of SMT orbeyond proofs to certification of satisfiability are further interesting challenges.Although several projects have already provided partial solutions in this direction,we would like to use the opportunity of ARCADE to further promote the idea andgather critical mass needed for its satisfactory realisation.

scholarly journals Experiments with State-of-the-art Automated Provers on Problems in Tarskian Geometry

10.29007/pqh1 ◽  
2018 ◽  
Author(s):  
Josef Urban ◽  
Robert Veroff
Keyword(s):  
State Of The Art ◽  
Theorem Provers ◽  
Theory Reasoning

We describe our experiments with several state-of-the-art automated theorem provers on the problems in Tarskian Geometry created by Beeson and Wos. In comparison to the manually-guided Otter proofs by Beeson and Wos, we can solve a large number of problems fully automatically, in particular thanks to the recent large-theory reasoning methods.

Sine Qua Non for Large Theory Reasoning

2011 ◽  
pp. 299-314 ◽  
Author(s):  
Kryštof Hoder ◽  
Andrei Voronkov
Keyword(s):  
Theory Reasoning

scholarly journals The limits of conjecture: Political liberalism, counter-radicalisation and unreasonable religious views

Ethnicities ◽  
2019 ◽  
Vol 20 (2) ◽  
pp. 293-311 ◽  
Author(s):  
Gabriele Badano ◽  
Alasia Nuti
Keyword(s):  
Political Theory ◽  
Political Institutions ◽  
John Rawls ◽  
Liberal Democracy ◽  
Political Liberalism ◽  
Comprehensive Doctrine ◽  
Liberal Democratic ◽  
Theory Reasoning ◽  
The Stability

Originally proposed by John Rawls, the idea of reasoning from conjecture is popular among the proponents of political liberalism in normative political theory. Reasoning from conjecture consists in discussing with fellow citizens who are attracted to illiberal and antidemocratic ideas by focusing on their religious or otherwise comprehensive doctrines, attempting to convince them that such doctrines actually call for loyalty to liberal democracy. Our goal is to criticise reasoning from conjecture as a tool aimed at persuasion and, in turn, at improving the stability of liberal democratic institutions. To pursue this goal, we use as case study real-world efforts to counter-radicalise at-risk Muslim citizens, which, at first glance, reasoning from conjecture seems well-placed to contribute to. This case study helps us to argue that the supporters of reasoning from conjecture over-intellectualise opposition to liberal democracy and what societies can do to counter it. Specifically, they (i) underestimate how few members of society can effectively perform reasoning from conjecture; (ii) overlook that the burdens of judgement, a key notion for political liberals, highlight how dim the prospects of reasoning from conjecture are and (iii) do not pay attention to the causes of religious persons’ opposition to liberal democracy. However, not everything is lost for political liberals, provided that they redirect attention to different and under-researched resources contained in Rawls’s theory. In closing, we briefly explain how such resources are much better placed than reasoning from conjecture to provide guidance relative to counter-radicalisation in societies (i) populated by persons who do not generally hold anything close to a fully worked out and internally consistent comprehensive doctrine and (ii) where political institutions should take responsibility for at least part of the existing alienation from liberal democratic values.

scholarly journals Clingo goes linear constraints over reals and integers

2017 ◽  
Vol 17 (5-6) ◽  
pp. 872-888 ◽  
Author(s):  
TOMI JANHUNEN ◽  
ROLAND KAMINSKI ◽  
MAX OSTROWSKI ◽  
SEBASTIAN SCHELLHORN ◽  
PHILIPP WANKO ◽  
...  
Keyword(s):  
Answer Set Programming ◽  
Linear Constraints ◽  
Common Language ◽  
Theory Reasoning ◽  
Formal Properties ◽  
Answer Set

AbstractThe recent series 5 of the Answer Set Programming (ASP) systemclingoprovides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions toclingowith difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resultingclingoderivativesclingo[dl] andclingo[lp] on common language fragments and contrast them to related ASP systems.

scholarly journals PROFIL KESALAHAN PEMAHAMAN KONSEP CAHAYA PADA SISWA KELAS V SEKOLAH DASAR

2018 ◽  
Vol 9 (1) ◽  
Author(s):  
Ela Suryani
Keyword(s):  
Data Collection ◽  
Learning Process ◽  
Qualitative Data ◽  
Light Sources ◽  
Natural Phenomena ◽  
Light Refraction ◽  
Three Stages ◽  
Inaccurate Reading ◽  
Theory Reasoning

This research describes the error concept of light profile in grade V students of SD N Srondol Wetan 02. The error concept made by the students need to be analyzed further in order to get a clear and detailed description of the students' weaknesses in understanding the concept of light and used as a consideration of learning in the business improve the quality of the learning process. Subjects amounted to four students who error concept. Data collection techniques use documentation, tests, observations, and interviews. Analysis of qualitative data through three stages of data reduction, presenting data, and concluding. The results showed: (1) KP-1 students have low sample indicator but KP-2 students actually have good example indicator; 2) errors concepts occur in the concept of light sources, light-permeable objects, light refraction, light of light degradation, and objects utilizing the nature of light; (3) the factors causing error concept of students' are student only learning only the IPA textbook from the school and the notebook from the teacher, the student assumes that all the concepts derived from experience and natural phenomena are true without re-examining the correct theory, reasoning, incomplete and inaccurate reading of textbooks or problems of understanding, as well as the limitations of language in understanding the concept of light.

scholarly journals Making Theory Reasoning Simpler

2021 ◽  
Author(s):  
Johannes Schoisswohl ◽  
Giles Reger ◽  
Andrei Voronkov
Keyword(s):  
Theory Reasoning

Large theory reasoning with SUMO at CASC

2010 ◽  
Vol 23 (2-3) ◽  
pp. 137-144 ◽  
Author(s):  
Adam Pease ◽  
Geoff Sutcliffe ◽  
Nick Siegel ◽  
Steven Trac
Keyword(s):  
Theory Reasoning
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