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14
Interpretability logic
 Mathematical Logic, Proceedings of the 1988 Heyting Conference
, 1990
"... Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbertstyle programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength ..."
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Cited by 32 (9 self)
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Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbertstyle programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength of theories, or better to prove
Actions under presuppositions
 Logic and Information Flow
, 1994
"... vvvvv.vvvvvvvvvvvvvvvvvvvvvvvvvvv ..."
The Role of Quantifier Alternations in Cut Elimination
 NOTRE DAME JOURNAL OF FORMAL LOGIC
, 2004
"... Extending previous results from [1; 2] on the complexity of cut elimination for the sequent calculus LK, we discuss the role of quantifier alternations and develope a measure to describe the complexity of cut elimination in terms of quantifier alternations in cut formulas and contractions on such f ..."
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Cited by 2 (0 self)
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Extending previous results from [1; 2] on the complexity of cut elimination for the sequent calculus LK, we discuss the role of quantifier alternations and develope a measure to describe the complexity of cut elimination in terms of quantifier alternations in cut formulas and contractions on such formulas.
No Escape from Vardanyan’s Theorem
, 2003
"... Vardanyan’s Theorem states that the set of PAvalid principles of Quantified Modal Logic, QML, is complete Π 0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum’s Theorem. ..."
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Cited by 1 (0 self)
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Vardanyan’s Theorem states that the set of PAvalid principles of Quantified Modal Logic, QML, is complete Π 0 2. We generalize this result to a wide class of theories. The crucial step in the generalization is avoiding the use of Tennenbaum’s Theorem.
The NetherlandsNetherlands, A Modal Perspective on the Computational Complexity ofAttribute Value Grammar
, 1992
"... I 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 satisfiablity. In this paper we put this. observation to work. We study the complexity ..."
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I 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 satisfiablity. 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 Attribute Value Structures (AVSs) are probably the most widely used means of repre_ senting linguistic structure in current computational linguistics, and the process of unifying descriptions of AVSs lies at the heart of many parsers. As a number of people have recently
Key words andphrases.Provability x" Conflict resolution; TMSn the Semantics ' of Conflict Resolution in Truth Maintenance Systems
"... nthe e*ani s = Cort i esoIt on in lien systems rrutIt Catli lljn Jonker. ..."
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nthe e*ani s = Cort i esoIt on in lien systems rrutIt Catli lljn Jonker.
3584 CS Utrecht
, 1992
"... By constructing a counter, model we show that a,.appealing certain equation E has no solution in Girard's [1972] second order lambdacalculus (the socalled polymorphic, lambda " calculus). The equation E ', = E(4i) ' (with 45 a type 3 variable) is a simple functional equation in thelkiguage of Gode ..."
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By constructing a counter, model we show that a,.appealing certain equation E has no solution in Girard's [1972] second order lambdacalculus (the socalled polymorphic, lambda " calculus). The equation E ', = E(4i) ' (with 45 a type 3 variable) is a simple functional equation in thelkiguage of Godel's [1958] system of higher order primitive recursive fanctiotals and` has an easy solution in Spector"s°[1962] system of bar recursive functionals This shows that the class of bar recursive functionals differs from the class _ of functionals definable ' in the polymorphic lambda calculus."The fact that the two calculi have different classes of definable functionals (at least of type 3), contrasts the metamathematical results from 'Spector [1962] and Girard [1972] which state that the twocalculi have the same class of definable functions, 'namely, the 'provably.total recursive:.functions. of `..analysis
Logic Group Preprint Series
, 1992
"... In this essay we develop a mathematical theory of syntactic domains with special ` attention to the theory of government and binding. Starting from an intrinsic characterization of command relations as defined in [Ba 90] we determine the structure of the distributive lattice of command relations. Th ..."
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In this essay we develop a mathematical theory of syntactic domains with special ` attention to the theory of government and binding. Starting from an intrinsic characterization of command relations as defined in [Ba 90] we determine the structure of the distributive lattice of command relations. This allows to introduce implication and negation as constructors, whose logic turns out to be the intuitionistic logic of linear posets. Using what is known about intuitionistic logic we can study how domains can be defined from some basic set of command relations that are naturally supplied by the grammar. Moreover, this can be reversed. to see how the requirement that domains can be defined in a particular way constrains the syntax. This general theory will then be. applied to GB and.we will show that there is great evidence to support our claim that command relations are the basic relations from which all other syntactic domains must be defined in a clear and rigid way. *This research was supported by the project NF 102/62 356 (`Structural and Semantic Parallels
3584 CS Utrecht The NetherlandsRAMSEY'S THEOREM: AND THE PIGEONHOLE PRINCIPLE IN INTUITIONISTIC MATHEMATICS
, 1992
"... Department of PhilosophyUtrecht University Ramsey's theorem and the pigeonhole principle in intuitio flistjc mathematics ..."
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Department of PhilosophyUtrecht University Ramsey's theorem and the pigeonhole principle in intuitio flistjc mathematics
The NetherlandsA tractable algorithm for the wellfounded model
, 1992
"... A tractable algorithm ..."