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Information Structure and the SyntaxPhonology Interface
, 1998
"... The paper proposes a theory relating syntax, semantics, and intonational prosody, and covering a wide range of English intonational tunes and their semantic interpretation in terms of focus and information structure. The theory is based on a version of combinatory categorial grammar which directly p ..."
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Cited by 154 (6 self)
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The paper proposes a theory relating syntax, semantics, and intonational prosody, and covering a wide range of English intonational tunes and their semantic interpretation in terms of focus and information structure. The theory is based on a version of combinatory categorial grammar which directly pairs phonological and logical forms without intermediary representational levels.
tps: A theorem proving system for classical type theory
 Journal of Automated Reasoning
, 1996
"... This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
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Cited by 70 (6 self)
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This is a description of TPS, a theorem proving system for classical type theory (Church’s typed λcalculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems which TPS can prove completely automatically are given to illustrate certain aspects of TPS’s behavior and problems of theorem proving in higherorder logic. 7
A Finitary Version of the Calculus of Partial Inductive Definitions
 Extensions of Logic Programming
, 1992
"... The theory of partial inductive definitions is a mathematical formalism which has proved to be useful in a number of different applications. The fundamentals of the theory is shortly described. Partial inductive definitions and their associated calculi are essentially infinitary. To implement them o ..."
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Cited by 28 (1 self)
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The theory of partial inductive definitions is a mathematical formalism which has proved to be useful in a number of different applications. The fundamentals of the theory is shortly described. Partial inductive definitions and their associated calculi are essentially infinitary. To implement them on a computer, they must be given a formal finitary representation. We present such a finitary representation, and prove its soundness. The finitary representation is given in a form with and without variables. Without variables, derivations are unchanging entities. With variables, derivations can contain logical variables that can become bound by a binding environment that is extended as the derivation is constructed. The variant with variables is essentially a generalization of the pure GCLA programming language.
HigherOrder Automated Theorem Proving
, 1998
"... Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or ..."
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Cited by 6 (2 self)
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Consistency Class) Let Ñ S be a class of sets of propositions, then Ñ S is called an abstract consistency class, iff each Ñ S is closed under subsets, and satisfies conditions (1) to (8) for all sets F 2 Ñ S . If it also satisfies (9), then we call it extensional. 1. If A is atomic, then A = 2 F or :A = 2 F. 2. If A 2 F and if B is the bhnormal form of A, then B F 2 Ñ S 2 . 3. If ::A 2 F, then A F 2 Ñ S . 4. If AB2F, then F A 2 Ñ S or F B 2 Ñ S . 5. If :(AB) 2 F, then F :A :B2 Ñ S . 6. If P a A 2 F, then F AB 2 Ñ S for each closed formula B 2 wff a (S). 7. If :P a A 2 F, then F :(Aw a ) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 8. If :(A = a!b B) 2 F, then F :(Aw a = Bw) 2 Ñ S for any witness constant w a 2 W that does not occur in F. 9. If :(A = o B) 2 F, then F[fA;:Bg 2 Ñ S or F[f:A;Bg 2 Ñ S . Here, we treat equality as an abbreviation for Leibniz definition. We call an abstract consistency class saturated, iff for all F 2 Ñ S and all...
Type Classes With More HigherOrder Polymorphism
 In ACM SIGPLAN International Conference on Functional Programming
, 2002
"... We propose an extension of Haskell's type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higherorder unification. This unification procedure is more general than Haskell's kind ..."
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Cited by 5 (1 self)
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We propose an extension of Haskell's type class system with lambda abstractions in the type language. Type inference for our extension relies on a novel constrained unification procedure called guided higherorder unification. This unification procedure is more general than Haskell's kindpreserving unification but less powerful than full higherorder unification.
USING λCALCULUS TO REPRESENT MEANINGS IN LOGIC GRAMMARS
, 1983
"... This paper describes how meanings are represented in a semantic grammar for a fragment of English in the logic programming language Prolog. The conventions of Definite Clause Grammars are used. Previous work on DCGs with a semantic component has used essentially firstorder formulas for representing ..."
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Cited by 3 (0 self)
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This paper describes how meanings are represented in a semantic grammar for a fragment of English in the logic programming language Prolog. The conventions of Definite Clause Grammars are used. Previous work on DCGs with a semantic component has used essentially firstorder formulas for representing meanings. The system described here uses formulas of the typed λcalculus. The first section discusses general issues concerning the use of firstorder logic or the λcalculus to represent meanings, The second section describes how λcalculus meaning representations can be constructed and manipulated directly in Prolog. This 'programmed' representation motivates a suggestion, discussed in the third section, for an extension to Prolog so that the language itself would include a mechanism for handling the λformulas directly.
TPS: An Interactive and Automatic Tool for Proving Theorems of Type Theory
 Higher Order Logic Theorem Proving and Its Applications: 6th International Workshop, HUG '93, volume 780 of Lecture Notes in Computer Science
, 1994
"... This is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed lcalculus). TPS can be used interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduc ..."
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This is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed lcalculus). TPS can be used interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. CATEGORY: Demonstration 1. Introduction This presentation is a demonstration of TPS, a theorem proving system for classical type theory (Church's typed 3 lcalculus [14]) which has been under development at Carnegie Mellon University for a number of years. TPS is based on an approach to automated theorem proving called the mating method [2], which is essentially the same as the connection method developed independently by Bibel [13]. The mating method does not require reduction to clausal form. TPS handles two sorts of proofs, natural deduction proofs and expansion proofs. Natural deduction proofs are humanreadable formal proofs. An example of such a proof which was produced aut...