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A Modal Perspective on the Computational Complexity of Attribute Value Grammar
, 1992
"... Many of the formalisms; used in Attribute Value grammar are notational variants of languages of propositional modal logic,. and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiability. In this paper we put this. observation to work. We study the complexit ..."
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Cited by 43 (7 self)
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Many of the formalisms; used in Attribute Value grammar are notational variants of languages of propositional modal logic,. and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiability. In this paper we put this. observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express reeintrancy, the ability to express generalisations, and the ability to express recursive constraints. Two mail techniques axe used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted
Higman's Lemma in Type Theory
 PROCEEDINGS OF THE 1996 WORKSHOP ON TYPES FOR PROOFS AND PROGRAMS
, 1997
"... This thesis is about exploring the possibilities of a limited version of MartinLöf's type theory. This exploration consists both of metatheoretical considerations and of the actual use of that version of type theory to prove Higman's lemma. The thesis is organized in two papers, one in wh ..."
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Cited by 5 (0 self)
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This thesis is about exploring the possibilities of a limited version of MartinLöf's type theory. This exploration consists both of metatheoretical considerations and of the actual use of that version of type theory to prove Higman's lemma. The thesis is organized in two papers, one in which type theory itself is studied and one in which it is used to prove Higman's lemma. In the first paper, A Lambda Calculus Model of MartinLöf's Theory of Types with Explicit Substitution, we present the formal calculus in complete detail. It consists of MartinLof's logical framework with explicit substitution extended with some inductively defined sets, also given in complete detail. These inductively defined sets are precisely those we need in the second paper of this thesis for the formal proof of Higman's lemma. The limitations of the formalism come from the fact that we do not introduce universes. It is known that for other versions of type theory, the absence of universes implies the impossib...
Ramsey's Theorem in Type Theory
, 1993
"... We present formalizations of constructive proofs of the Intuitionistic Ramsey Theorem and Higman's Lemma in MartinLof's Type Theory. We analyze the computational content of these proofs and we compare it with programs extracted out from some classical proofs. Contents 1 Introduction 2 2 ..."
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Cited by 4 (1 self)
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We present formalizations of constructive proofs of the Intuitionistic Ramsey Theorem and Higman's Lemma in MartinLof's Type Theory. We analyze the computational content of these proofs and we compare it with programs extracted out from some classical proofs. Contents 1 Introduction 2 2 The proofs 4 2.1 An inductive formulation of almostfullness (AF ID ) : : : : : : : : : : 5 2.1.1 Intuitionistic Ramsey Theorem (IRT ID ) : : : : : : : : : : : : 7 2.1.2 Higman's Lemma (HL ID ) : : : : : : : : : : : : : : : : : : : : 12 2.2 A negationless inductive formulation of almostfullness (AF I ) : : : : : 17 2.2.1 Intuitionistic Ramsey Theorem (IRT I ) : : : : : : : : : : : : : 17 2.3 Equivalence between the various formulations of almostfullness : : : 20 3 The programs 22 3.1 A higher order program : : : : : : : : : : : : : : : : : : : : : : : : : 24 3.2 A first order program : : : : : : : : : : : : : : : : : : : : : : : : : : : 25 4 Computational content of classical proofs 28 4.1 A cl...
The NetherlandsDempster.. Belief functions and inner measures
, 1992
"... In this note we study the relation between belief functions of DempsterShafer theory and inner measures induced by probability functions. In, [3,4] Joe Halpern and Ron Fagin claim that these classes of functions are essentially the same, or, more precisely, that.theyare exactly the same in case th ..."
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Cited by 1 (0 self)
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In this note we study the relation between belief functions of DempsterShafer theory and inner measures induced by probability functions. In, [3,4] Joe Halpern and Ron Fagin claim that these classes of functions are essentially the same, or, more precisely, that.theyare exactly the same in case the functions are defined on formulas rather than sets. We show that=,when the functions are defined on sets only a proper subclass off the belief functions over aframe S corrsponds to the class of inner measures induced by a probability measurer on.somealgebra, onS. However, belief functions, over S do correspond to inner measures induced by probability measures 'defined on algebras on refinements of S. The fact that in general refinemeats of S are needed to obtain all belief functions over S is shown to be obscured;by the particular way formulas are. assigned probabilities 'or, weights in. [3]. r4 1.
A direct proof of Ramsey’s Theorem
, 2010
"... The infinite version of Ramsey’s Theorem is clearly not valid intuitionistically: even in the simple case where we color N in two colors in a recursive way, one cannot decide which color will appear infinitely often, and even less enumerate an infinite monochromatic subset. However, W. Veldman [3] f ..."
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The infinite version of Ramsey’s Theorem is clearly not valid intuitionistically: even in the simple case where we color N in two colors in a recursive way, one cannot decide which color will appear infinitely often, and even less enumerate an infinite monochromatic subset. However, W. Veldman [3] found an elegant version of Ramsey’s Theorem, directly equivalent classically to
A direct proof of Ramsey’s Theorem
, 2011
"... The infinite version of Ramsey’s Theorem is clearly not valid intuitionistically: even in the simple case where we color N in two colors in a recursive way, one cannot decide which color will appear infinitely often, and even less enumerate an infinite monochromatic subset. However, W. Veldman [5] f ..."
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The infinite version of Ramsey’s Theorem is clearly not valid intuitionistically: even in the simple case where we color N in two colors in a recursive way, one cannot decide which color will appear infinitely often, and even less enumerate an infinite monochromatic subset. However, W. Veldman [5] found an elegant version of Ramsey’s Theorem, directly equivalent classically to
The NetherlandsA tractable algorithm for the wellfounded model
, 1992
"... A tractable algorithm ..."