Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T20:27:07.630Z Has data issue: false hasContentIssue false
  • English
  • Français

EXPLORING THE LANDSCAPE OF RELATIONAL SYLLOGISTIC LOGICS

Part of: General logic

Published online by Cambridge University Press:  21 October 2020

ALEX KRUCKMAN  and
LAWRENCE S. MOSS
ALEX KRUCKMAN
Affiliation:
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE WESLEYAN UNIVERSITYMIDDLETOWN, CT, USA E-mail: [email protected]
LAWRENCE S. MOSS
Affiliation:
DEPARTMENT OF MATHEMATICS INDIANA UNIVERSITY BLOOMINGTONBLOOMINGTON, IN, USA E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and complexity results for a natural subfamily of relational syllogistic logics, parametrized by constructors for terms and for sentences.

Keywords

natural logicsyllogistic logicproof systemscompletenesscomputational complexity

MSC classification

Primary: 03B65: Logic of natural languages
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 3 , September 2021 , pp. 728 - 765
Check for updates
Copyright
© The Review of Symbolic Logic, 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

McAllester, D. A. (1993). Automatic recognition of tractability in inference relations. Journal of the ACM (JACM), 40(2), 284–303.CrossRefGoogle Scholar
McAllester, D. A., & Givan, R. (1992). Natural language syntax and first-order inference. Artificial Intelligence, 56, 1–20.CrossRefGoogle Scholar
Moss, L. S. (2008). Completeness theorems for syllogistic fragments. In Hamm, F., & Kepser, S., editors. Logics for Linguistic Structures. Berlin: de Gruyter Mouton, pp. 143–173.Google Scholar
Moss, L. S. (2010). Logics for two fragments beyond the syllogistic boundary. Fields of Logic and Computation: Essays Dedicated to Yuri Gurevich on the Occasion of His 70th Birthday, volume 6300 of Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, pp. 538–563.CrossRefGoogle Scholar
Moss, L. S. (2010). Syllogistic logics with verbs. Journal of Logic and Computation, 20(4), 947–967.CrossRefGoogle Scholar
Moss, L. S. (2015). Natural logic. In Handbook of Contemporary Semantic Theory (second edition, chapter 18). Hoboken, NJ: John Wiley & Sons.Google Scholar
Moss, L. S. (2020). Logic from Language. Bloomington, IN: Indiana University.Google Scholar
Moss, L. S., & Kruckman, A. (2017). All and only. In Partiality and Underspecification in Natural Language Processing. Cambridge: Cambridge Scholars Publishers.Google Scholar
Pratt-Hartmann, I. (2014). The relational syllogistic revisited. Linguistic Issues in Language Technology, 9, 195–227.CrossRefGoogle Scholar
Pratt-Hartmann, I., & Moss, L. S. (2009). Logics for the relational syllogistic. Review of Symbolic Logic, 2(4), 647–683.CrossRefGoogle Scholar
Thomas,  J. S. (1978). The complexity of satisfiability problems. Proceedings of the Tenth Annual ACM Symposium on Theory of Computing. San Diego, CA: San Diego, pp. 216–226.Google Scholar
Spaan, E. (1993). Complexity of Modal Logics. Ph.D. Thesis, ILLC, University of Amsterdam.Google Scholar