More Fragments of Language

@article{PrattHartmann2006MoreFO,
  title={More Fragments of Language},
  author={Ian Pratt-Hartmann and Allan Third},
  journal={Notre Dame J. Formal Log.},
  year={2006},
  volume={47},
  pages={151-177}
}
By a fragment of a natural language, we understand a collection of sentences forming a naturally delineated subset of that language and equipped with a semantics commanding the general assent of its native speakers. By the semantic complexity of such a fragment, we understand the computational complexity of deciding whether any given set of sentences in that fragment represents a logically possible situation. In earlier papers by the first author, the semantic complexity of various fragments of… Expand
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References

SHOWING 1-10 OF 10 REFERENCES
Fragments of Language
TLDR
This paper represents a casestudy in how to approach the problem of determining the logicalcomplexity of various natural language constructions, and draws some general conclusions about the relationship between naturallanguage and formal logic. Expand
A Two-Variable Fragment of English
TLDR
This paper defines a controlled language, E2V, whose principalgrammatical resources include determiners, relative clauses, reflexives and pronouns, and provides a formal syntax and semantics for E1V, in whichanaphoric ambiguities are resolved in a linguistically natural way. Expand
Order-Based Inference in Natural Logic
TLDR
A version of Natural Logic is developed – an inference system that works directly on natural language syntactic representations, with no intermediate translation to logical formulae, and is extended for conjunctive phenomena like coordination and relative clauses. Expand
Natural Language Syntax and First-Order Inference
TLDR
This paper shows how a fragment of English syntax under Montague semantics provides the foundation of a new inference procedure that seems more effective than corresponding procedures based on either classical syntax or the previously proposed taxonomic syntax. Expand
A Logic for Natural Language
  • W. C. Purdy
  • Computer Science, Mathematics
  • Notre Dame J. Formal Log.
  • 1991
TLDR
A language called LN whose structure mirrors tilat of natural language, characterized by absence of variables and individual constants, is described, and each step of a proof in [,N has a direct counterpart in the surface language. Expand
A Variable Free Logic for Mass Terms
  • W. C. Purdy
  • Mathematics, Computer Science
  • Notre Dame J. Formal Log.
  • 1992
TLDR
This paper presents a logic appropriate for mass terms, that is, a logic that does not presuppose interpretation in discrete models, and is similar to surface English, in that the formal language and English are well-translatable, making it particularly suitable for natural language applications. Expand
Natural deduction rules for English
A system of natural deduction rules is proposed for an idealized form of English. The rules presuppose a sharp distinction between proper names and such expressions as ‘the c’, ‘a (an) c’, ‘some c’,Expand
Fluted Formulas and the Limits of Decidability
  • W. C. Purdy
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1996
TLDR
It was shown that if a fluted formula contains only homogeneous conjunction (conjoins only subformulas of equal arity), then the satisfiability of the formula is decidable, and it remained an open question whether the Satisfiability of a fluting formula without this restriction is dec formidable. Expand
Modal Languages and Bounded Fragments of Predicate Logic
TLDR
Les nouvelles directions que peuvent prendre les theoremes de Tarski dans un environnement mathematique are indique celle des contraintes structurelles speciales, des extensions infinies, de the logique modale etendue and d'une semantique dynamique. Expand
On languages with two variables
  • M. Mortimer
  • Mathematics, Computer Science
  • Math. Log. Q.
  • 1975