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A quantifier scoping algorithm without a Free Variable Constraint

1990
*
Proceedings of the 13th conference on Computational linguistics -
*
unpublished

they should not employ

doi:10.3115/991146.991180
fatcat:wfazq4wspvdjtade6uefx4chsy
*a*'*Free**Variable**Constraint*' [Pereira 1989 ]. ... The second is to ask for an*algorithm*that generates all and only the possible*scopings*of*a*sentence. ... [Pereira 1989 ] calls this 'The*Free*;*Variable**Constraint*' and complains of an appeal to logical syntax. Our own methodology avoids this. ...##
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Page 20 of Computational Linguistics Vol. 26, Issue 4
[page]

2000
*
Computational Linguistics
*

representative in

*a*company saw most samples. only the available five relative*scopings*of the*quantifiers*are produced (Hobbs and Shieber 1987, 47), but*without*the need for*a**free**variable**constraint*—the ... HOU*algorithm*will not produce any solutions in which*a*previously bound*variable*becomes*free*; the equivalences are reversible, and thus the above sentences can be generated from*scoped*logical forms ...##
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Scope Underspecification with Tree Descriptions: Theory and Practice
[chapter]

2010
*
Resource-Adaptive Cognitive Processes
*

In this paper, we outline the results of the CHORUS project on the topic of semantic underspecification, along two major lines of research: We review

doi:10.1007/978-3-540-89408-7_15
dblp:series/cogtech/KollerTP11
fatcat:bg5gl3ehbjedjh7r3jmlmvynve
*a*series of solvers for dominance*constraints*and dominance ... Parallelism*constraints*can be used to model the interaction of*scope*and ellipsis, and binding*constraints*account for*variable*binding*without*using*variable*to avoid unwanted "capturing" of*variables*... of bound object language*variables*must be in the*scope*of the*quantifier*that binds the*variable*. ...##
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A uniform approach to underspecification and parallelism

1997
*
Proceedings of the 35th annual meeting on Association for Computational Linguistics -
*

We demonstrate the use of our framework at the examples of

doi:10.3115/976909.979670
dblp:conf/acl/NiehrenPR97
fatcat:x7k4ynfwtfc63gfcggwb5x77uy
*quantifier**scope*, ellipsis, and their interaction. 1 ... The framework employs*a**constraint*language that can express equality and subtree relations between finite trees. ... Our*algorithm*proceeds on pairs consisting of*a**constraint*and*a*set of*variable*bindings. At the beginning the set of*variable*bindings is empty. ...##
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Extending the type checker of Standard ML by polymorphic recursion

1999
*
Theoretical Computer Science
*

Both the inequation

doi:10.1016/s0304-3975(98)00139-x
fatcat:p7jgpz3dzfb3nhehfcenr4tpaq
*constraints*L and their principal solutions are computed bottom-up in*a*modification of Milner's*algorithm*W. ... more restrictive criterion for introducing*quantifiers*in types of let-bound*variables*is needed. ...*without*having*a*representation of the relative*scope*of*variables*in the global term, simply by stacking the types of*A*assumptions. ...##
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Goal-Directed Reasoning for Specification-Based Data Structure Repair

2006
*
IEEE Transactions on Software Engineering
*

It then automatically generates

doi:10.1109/tse.2006.122
fatcat:ro5ftbmysjb7flcvckm4ipz7he
*a*repair*algorithm*that, during the execution of the program, detects and repairs any violations of these*constraints*. ...*Without*repair, all of the applications fail. Index Terms-Testing and debugging, language constructs and features. ... In general, each consistency*constraint*is*a*first-order logical formula consisting of*a*sequence of*quantifiers*followed by*a**quantifier*-*free*Boolean formula of atomic propositions. ...##
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Efficient Solving of Quantified Inequality Constraints over the Real Numbers
[article]

2007
*
arXiv
*
pre-print

Let

arXiv:cs/0211016v4
fatcat:p2ac55aj35bibj6f2jr72gy3bi
*a**quantified*inequality*constraint*over the reals be*a*formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. ... We ensure the practical efficiency of this*algorithm*by employing*constraint*programming techniques. ...*constraints*, but*without*branching in the universally*quantified**variables*. • The case of*quantified*systems of equations where certain*variables*occur only once, and the*quantifiers*obey certain orderings ...##
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Efficient solving of quantified inequality constraints over the real numbers

2006
*
ACM Transactions on Computational Logic
*

Let

doi:10.1145/1166109.1166113
fatcat:mfjumydf6fftzlgkoepmemrt24
*a**quantified*inequality*constraint*over the reals be*a*formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. ... We ensure the practical efficiency of this*algorithm*by employing*constraint*programming techniques. * This is*a*revised and extended version of an earlier paper [42] . ...*constraints*, but*without*branching in the universally*quantified**variables*. • The case of*quantified*systems of equations where certain*variables*occur only once, and the*quantifiers*obey certain orderings ...##
###
Efficient solving of quantified inequality constraints over the real numbers

2006
*
ACM Transactions on Computational Logic
*

Let

doi:10.1145/1183278.1183282
fatcat:ef5ep7s4vrbnzfkv7o7n5vsxxa
*a**quantified*inequality*constraint*over the reals be*a*formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are ≤ and <. ... We ensure the practical efficiency of this*algorithm*by employing*constraint*programming techniques. * This is*a*revised and extended version of an earlier paper [42] . ...*constraints*, but*without*branching in the universally*quantified**variables*. • The case of*quantified*systems of equations where certain*variables*occur only once, and the*quantifiers*obey certain orderings ...##
###
Functional Pearl: Dependent type inference via free higher-order unification
[article]

2022
*
arXiv
*
pre-print

We propose

arXiv:2204.05653v1
fatcat:xznkynhgnbgjjolho6o4eqqfpq
*a*novel approach for abstract syntax representation, which we call*free**scoped*monads. ... These constructions allow us to handle*scopes*in*a*language-agnostic way and provide generic higher-order unification*algorithms*, which serve as*a*foundation for dependent type inference. ... We have presented an approach to abstract syntax representation with*free**scoped*monads and demonstrated its effectiveness simply typed lambda calculus and Martin Löf Type Theory. ...##
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Relationships between Specified and Underspecified Quantification by the Theory of Acyclic Recursion

2016
*
Advances in Distributed Computing and Artificial Intelligence Journal
*

KEYWORD ABSTRACT Recursion; Semantics; Underspecification The paper introduces

doi:10.14201/adcaij2016541942
fatcat:mrk5hyt6mzhitoqmm4eycrrptu
*a*technique for representing*quantifier*relations that can have different*scope*order depending on context. ... The technique is demonstrated by classes of terms denoting relations, where each of the arguments of*a*relation term is bound by*a*different*quantifier*. ... Such an underspecified term has*free*recursion*variables*for*quantifiers*, that leaves the*scope*distributions open, to be specified when sufficient information is available, by context. ...##
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Solving Temporal Problems Using SMT: Strong Controllability
[chapter]

2012
*
Lecture Notes in Computer Science
*

We obtain the first practical and comprehensive solution for strong controllability: the use of

doi:10.1007/978-3-642-33558-7_20
fatcat:clvn7hj4evf7hig6piucy6hyoa
*quantifier*elimination techniques leads to*quantifier*-*free*encodings, which are in turn solved with efficient ... We provide*a*detailed experimental evaluation of our approach over*a*large set of benchmarks. ...*variables*X u satisfying the contingent*constraints*C c , the*free**constraints*C f are also satisfied. ...##
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Unification with extended patterns

1998
*
Theoretical Computer Science
*

Miller's pattern restriction is generalized by allowing repeated occurrences of

doi:10.1016/s0304-3975(97)00141-2
fatcat:panaouschzfcbf7jxiid3usrjq
*variables*to appear as arguments to*free*function*variables*, provided such*variables*are prefixed by distinct sequences of ... An extension of Miller's*algorithm*for &unification of typed L-terms is presented. ... of*a*collection of equality*constraints*between trees*without*finally solving the*constraints*which only involve "*free*"*variables*at the head. ...##
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A feature-based syntax/semantics interface

1993
*
Annals of Mathematics and Artificial Intelligence
*

These include (i)

doi:10.1007/bf02451551
fatcat:w4ociwr4trdnjc6t5rf3neh7jq
*a*more flexible relation to nonsyntactic*constraints*on semantics; (ii)*a*characterization of semantic ambiguity, which in turn provides*a*framework in which to describe disambiguation ... The last point is illustrated with an application to the notorious*scope*ambiguity problem. ...*A**variable*(occurrence) is*free*in atomic formulas, and*free*in boolean combinations under the obvious conditions, and finally*free*in*quantified*formulas where it is*free*in*a*component and not bound ...##
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Decision Procedures for Recursive Data Structures with Integer Constraints
[chapter]

2004
*
Lecture Notes in Computer Science
*

Our decision procedures for

doi:10.1007/978-3-540-25984-8_9
fatcat:3jo5hgwzanarxgbvqobjugz5bq
*quantifier*-*free*theories are based on Oppen's*algorithm*for acyclic recursive data structures with infinite atom domain. 1*A*theory is stably infinite if*a**quantifier*-*free*formula ... is not applicable to this theory, even for the*quantifier*-*free*case. ...*A*sentence is*a*formula in which no*variable*occurs*free*.*A*formula*without**quantifiers*is called*quantifier*-*free*. ...
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