Skip to main content
Log in

Logical reasoning in natural language: It is all about knowledge

  • General Articles
  • Published:
Minds and Machines Aims and scope Submit manuscript

Abstract

A formal, computational, semantically clean representation of natural language is presented. This representation captures the fact that logical inferences in natural language crucially depend on the semantic relation of entailment between sentential constituents such as determiner, noun, adjective, adverb, preposition, and verb phrases.

The representation parallels natural language in that it accounts for human intuition about entailment of sentences, it preserves its structure, it reflects the semantics of different syntactic categories, it simulates conjunction, disjunction, and negation in natural language by computable operations with provable mathematical properties, and it allows one to represent coordination on different syntactic levels.

The representation demonstrates that Boolean semantics of natural language can be successfully modeled in terms of representation and inference by knowledge representation formalisms with Boolean semantics. A novel approach to the problem of automatic inferencing in natural language is addressed. The algorithm for updating a computer knowledge base and reasoning with explicit negative, disjunctive, and conjunctive information based on computing subsumption relation between the representations of the appropriate sentential constituents is discussed with examples.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aït-Kaci, H. (1984),A Lattice-Theoretic Approach to Computation Based on a Calculus of Partially Ordered Type Structures, PhD thesis, Dept. of Computer and Info. Science, Univ. of Pennsylvania.

  • Aït-Kaci, H. (1986), An Algebraic Semantics Approach to the Effective Resolution of type Equations',Journal of Theoretic Computer Science 45, 293–251.

    Google Scholar 

  • Aït-Kaci, H. and Nasr, R. (1985), ‘LOGIN: A Logic Programming Language with Built-in Inheritance’, MCC Technical Report Number Al-068-85, Microelectronics and Computer Technology Corporation.

  • Balbes, R. and Dwinger, P. (1974),Distributive Lattices, University of Missouri Press.

  • Barwise, J. and Cooper, R. (1981), ‘Generalized Quantifiers and Natural Language’,Linguistics and Philosophy 4, 159–219.

    Google Scholar 

  • Birkhoff, G. (1979),Lattice Theory, volume 25. American Mathematical Society Colloquium Publications.

  • de Kleer, J. (1987), ‘An Assumption-based TMS’, inReadings in Nonmonotonic Reasoning, Morgan Kaufman Publishers, Inc. pp. 280–297.

  • Dowty, D.R., Wall, R.E., and Peters, S. (1981),Introduction of Montague semantics, D. Reidel Publ. Co., Dordrecht, Holland.

    Google Scholar 

  • Earley, J. (1985), ‘An Efficient Context-Free Parsing Algorithm’, InReadings in Natural Language Processing, Morgan Kaufmann Publishers, Inc. pp. 25–33.

  • Hamm, F. (1989),Naturlich-sprachliche Quantoren, Max Niemeyer Verlag.

  • Hirschberg, J.B. (1985), ‘A Theory of Scalar Implicature’, PhD thesis, Technical Report MS-CIS-85-56, Dept. of Computer and Information Science, University of Pennsylvania.

  • Horn, L.R. (1989),A Natural History of Negation, The University of Chicago Press.

  • Iwańska, Ł. (1989), Automated Processing of Narratives Written by 6–12 Grade Students: The BILING Program. Technical Report UIUCDCS-R-89-1508, Dept. of Computer Science, University of Illinois at Urbana-Champaign.

  • Iwańska, Ł. (1992a), ‘A General Semantic Model of Negation in Natural Language: Representation and Inference’, inProceedings of the Third International Conference on Knowledge Representation and Reasoning KR92),pp. 357–368.

  • Iwańska, Ł. (1992b).A General Semantic Model of Negation in Natural Language: Representation and Inference. PhD thesis. Also available as Technical Report UIUCDCS-R-92-1775 or UILU-ENG-92-1755.

  • Keenan, E.L. and Faltz, L.M. (1985),Boolean Algebra Semantics Of Natural Language, D. Reidel Publ. Co., Dordrecht, Holland.

    Google Scholar 

  • Martins, J. and Shapiro, S. (1988), ‘A Model for Belief Revision’,Artificial Intelligence 35, 25–79.

    Google Scholar 

  • Schwartz, D.G. (1989), ‘Outline of a Naive Semantics for Reasoning with Qualitative Linguistic Information’, inJCAI-89.

  • Shieber, S. (1986),An Introduction to Unification-Based Approaches to Grammar, Number 4. CLSI Lecture Notes.

  • Sterling, L. and Shapiro, E. (1986),The Art of Prolog, The MIT Press, Cambridge.

    Google Scholar 

  • Winograd, T. (1983),Language as a Cognitive Process, Addison-Wesley Publ. Comp.

  • Zadeh, L.A. (1987),Fuzzy Sets and Application: Selected Papers, John Wiley and Sons, Inc.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iwańska, L. Logical reasoning in natural language: It is all about knowledge. Mind Mach 3, 475–510 (1993). https://doi.org/10.1007/BF00974107

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00974107

Key words

Navigation