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A quantifier scoping algorithm without a Free Variable Constraint

Ian Lewin
1990 Proceedings of the 13th conference on Computational linguistics -   unpublished
they should not employ 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.  ... 
doi:10.3115/991146.991180 fatcat:wfazq4wspvdjtade6uefx4chsy

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  ... 

Scope Underspecification with Tree Descriptions: Theory and Practice [chapter]

Alexander Koller, Stefan Thater, Manfred Pinkal
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 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.  ... 
doi:10.1007/978-3-540-89408-7_15 dblp:series/cogtech/KollerTP11 fatcat:bg5gl3ehbjedjh7r3jmlmvynve

A uniform approach to underspecification and parallelism

Joachim Niehren, Manfred Pinkal, Peter Ruhrberg
1997 Proceedings of the 35th annual meeting on Association for Computational Linguistics -  
We demonstrate the use of our framework at the examples of 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.  ... 
doi:10.3115/976909.979670 dblp:conf/acl/NiehrenPR97 fatcat:x7k4ynfwtfc63gfcggwb5x77uy

Extending the type checker of Standard ML by polymorphic recursion

Martin Emms, Hans Leiβ
1999 Theoretical Computer Science  
Both the inequation 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.  ... 
doi:10.1016/s0304-3975(98)00139-x fatcat:p7jgpz3dzfb3nhehfcenr4tpaq

Goal-Directed Reasoning for Specification-Based Data Structure Repair

Brian Demsky, Martin Rinard
2006 IEEE Transactions on Software Engineering  
It then automatically generates 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.  ... 
doi:10.1109/tse.2006.122 fatcat:ro5ftbmysjb7flcvckm4ipz7he

Efficient Solving of Quantified Inequality Constraints over the Real Numbers [article]

Stefan Ratschan
2007 arXiv   pre-print
Let 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  ... 
arXiv:cs/0211016v4 fatcat:p2ac55aj35bibj6f2jr72gy3bi

Efficient solving of quantified inequality constraints over the real numbers

Stefan Ratschan
2006 ACM Transactions on Computational Logic  
Let 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  ... 
doi:10.1145/1166109.1166113 fatcat:mfjumydf6fftzlgkoepmemrt24

Efficient solving of quantified inequality constraints over the real numbers

Stefan Ratschan
2006 ACM Transactions on Computational Logic  
Let 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  ... 
doi:10.1145/1183278.1183282 fatcat:ef5ep7s4vrbnzfkv7o7n5vsxxa

Functional Pearl: Dependent type inference via free higher-order unification [article]

Nikolai Kudasov
2022 arXiv   pre-print
We propose 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.  ... 
arXiv:2204.05653v1 fatcat:xznkynhgnbgjjolho6o4eqqfpq

Relationships between Specified and Underspecified Quantification by the Theory of Acyclic Recursion

Roussanka LOUKANOVA
2016 Advances in Distributed Computing and Artificial Intelligence Journal  
KEYWORD ABSTRACT Recursion; Semantics; Underspecification The paper introduces 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.  ... 
doi:10.14201/adcaij2016541942 fatcat:mrk5hyt6mzhitoqmm4eycrrptu

Solving Temporal Problems Using SMT: Strong Controllability [chapter]

Alessandro Cimatti, Andrea Micheli, Marco Roveri
2012 Lecture Notes in Computer Science  
We obtain the first practical and comprehensive solution for strong controllability: the use of 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.  ... 
doi:10.1007/978-3-642-33558-7_20 fatcat:clvn7hj4evf7hig6piucy6hyoa

Unification with extended patterns

Dominic Duggan
1998 Theoretical Computer Science  
Miller's pattern restriction is generalized by allowing repeated occurrences of 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.  ... 
doi:10.1016/s0304-3975(97)00141-2 fatcat:panaouschzfcbf7jxiid3usrjq

A feature-based syntax/semantics interface

John Nerbonne
1993 Annals of Mathematics and Artificial Intelligence  
These include (i) 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  ... 
doi:10.1007/bf02451551 fatcat:w4ociwr4trdnjc6t5rf3neh7jq

Decision Procedures for Recursive Data Structures with Integer Constraints [chapter]

Ting Zhang, Henny B. Sipma, Zohar Manna
2004 Lecture Notes in Computer Science  
Our decision procedures for 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.  ... 
doi:10.1007/978-3-540-25984-8_9 fatcat:3jo5hgwzanarxgbvqobjugz5bq
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