Fragments of Language

  title={Fragments of Language},
  author={I. Pratt-Hartmann},
  journal={Journal of Logic, Language and Information},
  • I. Pratt-Hartmann
  • Published 2004
  • Mathematics, Computer Science
  • Journal of Logic, Language and Information
By a fragment of a natural language we mean a subset of thatlanguage equipped with semantics which translate its sentences intosome formal system such as first-order logic. The familiar conceptsof satisfiability and entailment can be defined for anysuch fragment in a natural way. The question therefore arises, for anygiven fragment of a natural language, as to the computational complexityof determining satisfiability and entailment within that fragment. Wepresent a series of fragments of… Expand
The Semantic Complexity of some Fragments of English
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Logics for Two Fragments beyond the Syllogistic Boundary
  • L. Moss
  • Mathematics, Computer Science
  • Fields of Logic and Computation
  • 2010
A system with the following properties is constructed: its syntax is closer to that of a natural language than is first-order logic; it can faithfully represent simple sentences with standard quantifiers, subject relative clauses, and negation on nouns and verbs. Expand
The Expressive Power of Restricted Fragments of English
This work defines four simple fragments of English based on the syntactic constructions they contain, and describes the circumstances under which an arbitrary first-order formula can be translated back into an English sentence of each fragment. Expand
Completeness Theorems for Syllogistic Fragments
Traditional syllogisms involve sentences of the following simple forms: All X are Y , Some X are Y , No X are Y ; similar sentences with proper names as subjects, and identities between names. TheseExpand
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  • J. Eijck
  • Mathematics, Computer Science
  • TbiLLC
  • 2005
This work introduces the semantic and the syntactic sides of monotonicity reasoning or `natural logic', and proposes an improvement to the Syntactic monotonic calculus, in the form of an improved algorithm for monotonicism marking. Expand
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Logical systems conceived for providing semantics/logical forms for sentences of English abound. From Montague’s original Higher-order Intensional Logic in the seventies, to Situation Theory andExpand
Complexity in Linguistics
This discussion culminates in putting forward Ristad’s Thesis, claiming that the authors' everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic (belongs to NP). Expand
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  • L. Moss
  • Computer Science
  • 2018
We discuss what is known about implementations of logical systems whose syntax is either a small fragment of natural language, or alternatively is a formal language which looks more like naturalExpand
Semantic bounds for everyday language
It is claimed that everyday language is semantically bounded by the properties expressible in the existential fragment of second-order logic, and it is shown that in both cases they are bounded by second- order existential properties. Expand


A Two-Variable Fragment of English
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A Logic for Natural Language
  • W. C. Purdy
  • Computer Science, Mathematics
  • Notre Dame J. Formal Log.
  • 1991
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
Logical inference in English: A preliminary analysis
The perfect fit of syntactic derivability and logical consequence in first-order logic is one of the most celebrated facts of modern logic. In the present flurry of attention given to the semanticsExpand
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  • E. Grädel
  • Mathematics, Computer Science
  • J. Symb. Log.
  • 1999
It is proved that the satisfiability problems for the guarded fragment and the loosely guarded fragment of first-order logic are complete for deterministic double exponential time, and a tree model property is established for both the guarded fragments and the closely guarded fragment. Expand
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Abstract This paper is a survey and systematic presentation of decidability and complexity issues for modal and non-modal two-variable logics. A classical result due to Mortimer says that theExpand
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Quantifiers have entered the Methodenstreit of contemporary linguistics in another major way, too, the idea that the structures studied in the so-called quantification theory of symbolic logic-otherwise know as first-order logic, (lower) predicate calculus, or elementary logic-can serve and suffice as semantical representations of English sentences. Expand
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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