Encyclopedia of Social Network Analysis and Mining

2014 Edition
| Editors: Reda Alhajj, Jon Rokne

Reasoning

  • Cong Wang
  • Pascal Hitzler
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6170-8_115

Glossary

First-order Logic

A formal logic system in mathematics distinguished from propositional logic by its use of quantified variables

Deductive Reasoning

The process of reasoning from one or more general statements (premises) to reach a logic conclusion

Tableaux

A proof procedure for formulas of first-order logic based on tree expansion

Resolution

A proof procedure for formulas of first-order logic based on a set of inference rules for clauses

Definition

When considering logical reasoning, it is often divided into three basic paradigms: deductive, inductive, and abductive reasoning. Deductive reasoning concerns what follows necessarily from the given premises (if α, then β) in a top-down approach, while inductive reasoning, the opposite of deductive reasoning, tries to derive a reliable generalization from observations in a bottom-up approach. Abductive reasoning is seeking the explanation for given rules and conclusions (if αβ and β, then perhaps α.) For each of them, there...

This is a preview of subscription content, log in to check access.

Notes

Acknowledgment

This work was supported by the National Science Foundation under award 1017225 “III: Small: TROn—Tractable Reasoning with Ontologies.”

References

  1. Baader F, Calvanese D, McGuinness D, Nardi D, Patel-Schneider P (2007) The description logic handbook. Cambridge University Press, CambridgeMATHGoogle Scholar
  2. Baumgartner P, Furbach U, Niemel I (1996) Hyper tableaux. JELIA 1126:1–17Google Scholar
  3. Johnson-Laird P (2011) Mental models and human reasoning. PNAS 108(50):19862–19864Google Scholar
  4. Motik B (2006) Reasoning in description logics using resolution and deductive databases. Karlsruhe Institute of Technology, pp 1–249Google Scholar
  5. Ray O, Broda K, Russo A (2003) Hybrid abductive inductive learning: a generalisation of progol. ILP 2835:311–328Google Scholar
  6. Robinson J, Voronkov A (2001) Handbook of automated reasoning (in 2 volumes). MIT, BostonGoogle Scholar

Recommended Reading

  1. Gabbay D, Hogger C, Robinson, J (1994) Handbook of logic in artificial intelligence and logic programming. Oxford University Press, OxfordGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Cong Wang
    • 1
  • Pascal Hitzler
    • 1
  1. 1.Department of Computer Science and Engineering, Wright State UniversityDaytonUSA