# Encyclopedia of Social Network Analysis and Mining

2018 Edition
| Editors: Reda Alhajj, Jon Rokne

# Automated Reasoning

Reference work entry
DOI: https://doi.org/10.1007/978-1-4939-7131-2_110188

## Glossary

Backward chaining

an inference method that searches backwards starting from the goal to be proven

Complete

a complete algorithm returns all correct answers (but may also return others)

Deduction calculus

a formal system in mathematical logic to express logical derivations, i.e., proving that a conclusion can be inferred from a given set of assumptions

Direct proof

starts from the known assumptions, and proves the desired conclusion applying rules of inference in a step-wise manner

Forward chaining

an inference method that searches for solutions applying a set of inference rules to the available data

Indirect proof

assumes that the desired conclusion is wrong, and aims at proving that this together with the known information leads to a contradiction

Resolution

a rule of inference used to show that some goal/objective is not derivable

SAT solver

program that given a propositional formula returns whether it is satisfiable

Sound

a sound algorithm...

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## Notes

### Acknowledgments

The author acknowledges the support of FCT under strategic project NOVA LINCS (UID/CEC/04516/2013) and grant SFRH/BPD/86970/2012.

## References

1. Baader F et al (eds) (2010) The description logic handbook: theory, implementation, and applications, 3rd edn. Cambridge University Press, Cambridge
2. Bibel W, Eder E (1993) Methods and calculi for deduction. In: Gabbay DM, Hogger CJ, Robinson JA (eds) Handbook of logic in artificial intelligence and logic programming, vol 1. Oxford University Press, New York, pp 68–182. http://dl.acm.org/citation.cfm?id=185728.185745
3. Davis M (1983) The prehistory and early history of automated deduction. In: Siekmann J, Wrightson G (eds) Automation of reasoning. Classical papers on computational logic. Springer, Berlin, pp 1–28Google Scholar
4. Davis M (2001) The early history of automated deduction: dedicated to the memory of Hao Wang. In: Robinson A, Voronkov A (eds) Handbook of automated reasoning. Elsevier, Amsterdam, pp 1–28
5. Dowek G (2001) Higher-order unification and matching. In: Robinson A, Voronkov A (eds) Handbook of automated reasoning. Elsevier, Amsterdam, pp 1009–1062
6. Martin U, Pease A (2013) Mathematical practice, crowdsourcing, and social machines. In: Carette J, Aspinall D, Lange C, Sojka P, Windsteiger W (eds) Proceedings of intelligent computer mathematics – MKM, calculemus, DML, and systems and projects 2013, Held as Part of CICM 2013, Bath, 8–12 July 2013, Lecture notes in computer science, vol 7961. Springer, pp 98–119Google Scholar
7. Portoraro F (2014) Automated reasoning. In: Zalta EN (ed) The stanford encyclopedia of philosophy, winter 2014 edn, http://plato.stanford.edu/archives/win2014/entries/reasoning-automated/
8. Robinson JA, Voronkov A (eds) (2001) Handbook of automated reasoning, 2 vols. Elsevier and MIT Press, AmsterdamGoogle Scholar

1. Bibel W, Eder E (1993) is a detailed overview and comparison on many of the different deduction calculiGoogle Scholar
2. Davis M (1983) presents an account on the early history of automated reasoningGoogle Scholar
3. Portoraro F (2014) also provides a rather compact overview on the topic with further pointers to the literatureGoogle Scholar
4. Robinson A, Voronkov A (2001) describes exhaustively all aspects and major approaches to automated reasoning in a detailed mannerGoogle Scholar
5. The proceedings of the International Joint Conference on Automated Reasoning (IJCAR) and of the International Joint Conference on Automated Deducation (CADE) as well as the Journal of Automated Reasoning are the main venues for publication on automated reasoningGoogle Scholar

## Authors and Affiliations

1. 1.NOVA LINCS and Dept. of Computer ScienceFaculdade de Ciências e Tecnologia, Universidade NOVA de LisboaCaparicaPortugal

## Section editors and affiliations

• Thomas Gottron
• 1
• Stefan Schlobach
• 2
• Steffen Staab
• 3
1. 1.Institute for Web Science and TechnologiesUniversität Koblenz-LandauKoblenzGermany
2. 2.YUAmsterdamThe Netherlands
3. 3.Institute for Web Science and TechnologiesUniversität Koblenz-LandauKoblenzGermany