Results 11  20
of
129
Higher Type Recursion, Ramification and Polynomial Time
 Annals of Pure and Applied Logic
, 1999
"... It is shown how to restrict recursion on notation in all finite types so as to characterize the polynomial time computable functions. The restrictions are obtained by enriching the type structure with the formation of types !oe, and by adding linear concepts to the lambda calculus. 1 Introduction ..."
Abstract

Cited by 22 (3 self)
 Add to MetaCart
It is shown how to restrict recursion on notation in all finite types so as to characterize the polynomial time computable functions. The restrictions are obtained by enriching the type structure with the formation of types !oe, and by adding linear concepts to the lambda calculus. 1 Introduction Recursion in all finite types was introduced by Hilbert [9] and later became known as the essential part of Godel's system T [8]. This system has long been viewed as a powerful scheme unsuitable for describing small complexity classes such as polynomial time. Simmons [16] showed that ramification can be used to characterize the primitive recursive functions by higher type recursion, and Leivant and Marion [14] showed that another form of ramification can be used to restrict higher type recursion to PSPACE. However, to characterize the much smaller class of polynomialtime computable functions by higher type recursion, it seems that an additional principle is required. By introducing linear...
A generalization of the linzhao theorem
 Annals of Mathematics and Artificial Intelligence
, 2006
"... The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program’s stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definiti ..."
Abstract

Cited by 21 (7 self)
 Add to MetaCart
The theorem on loop formulas due to Fangzhen Lin and Yuting Zhao shows how to turn a logic program into a propositional formula that describes the program’s stable models. In this paper we simplify and generalize the statement of this theorem. The simplification is achieved by modifying the definition of a loop in such a way that a program is turned into the corresponding propositional formula by adding loop formulas directly to the conjunction of its rules, without the intermediate step of forming the program’s completion. The generalization makes the idea of a loop formula applicable to stable models in the sense of a very general definition that covers disjunctive programs, programs with nested expressions, and more. 1
Alpaca: extensible authorization for distributed services
 In 14th ACM Conference on Computer and Communications Security
, 2007
"... Traditional Public Key Infrastructures (PKI) have not lived up to their promise because there are too many ways to define PKIs, too many cryptographic primitives to build them with, and too many administrative domains with incompatible roots of trust. Alpaca is an authentication and authorization fr ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
Traditional Public Key Infrastructures (PKI) have not lived up to their promise because there are too many ways to define PKIs, too many cryptographic primitives to build them with, and too many administrative domains with incompatible roots of trust. Alpaca is an authentication and authorization framework that embraces PKI diversity by enabling one PKI to “plug in ” another PKI’s credentials and cryptographic algorithms, allowing users of the latter to authenticate themselves to services using the former using their existing, unmodified certificates. Alpaca builds on ProofCarrying Authorization (PCA) [8], expressing a credential as an explicit proof of a logical claim. Alpaca generalizes PCA to express not only delegation policies but also the cryptographic primitives, credential formats, and namespace structure needed to use foreign credentials directly. To achieve this goal, Alpaca introduces a method of creating and naming new principals which behave according to arbitrary rules, a modular approach to logical axioms, and a domainspecific language specialized for reasoning about authentication. We have implemented Alpaca as a Python module that assists applications in generating proofs (e.g., in a client requesting access to a resource), and in verifying those proofs via a compact 800line TCB (e.g., in a server providing that resource). We present examples demonstrating Alpaca’s extensibility in scenarios involving interorganization PKI interoperability and secure remote PKI upgrade.
The maximality of the typed lambda calculus and of cartesian closed categories
 Publ. Inst. Math. (N.S
"... From the analogue of Böhm’s Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
From the analogue of Böhm’s Theorem proved for the typed lambda calculus, without product types and with them, it is inferred that every cartesian closed category that satisfies an equality between arrows not satisfied in free cartesian closed categories must be a preorder. A new proof is given here of these results, which were obtained previously by Richard Statman and Alex K. Simpson.
Comparing Control Constructs by Doublebarrelled CPS
 Higherorder and Symbolic Computation
, 2002
"... We investigate callbyvalue continuationpassing style transforms that pass two continuations. Altering a single variable in the translation of #abstraction gives rise to di#erent control operators: firstclass continuations; dynamic control; and (depending on a further choice of a variable) eithe ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
We investigate callbyvalue continuationpassing style transforms that pass two continuations. Altering a single variable in the translation of #abstraction gives rise to di#erent control operators: firstclass continuations; dynamic control; and (depending on a further choice of a variable) either the return statement of C; or Landin's Joperator. In each case there is an associated simple typing. For those constructs that allow upward continuations, the typing is classical, for the others it remains intuitionistic, giving a clean distinction independent of syntactic details. Moreover, those constructs that make the typing classical in the source of the CPS transform break the linearity of continuation use in the target.
Labelled Modal Logics: Quantifiers
, 1998
"... . In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4:2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logic ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
. In previous work we gave an approach, based on labelled natural deduction, for formalizing proof systems for a large class of propositional modal logics that includes K, D, T, B, S4, S4:2, KD45, and S5. Here we extend this approach to quantified modal logics, providing formalizations for logics with varying, increasing, decreasing, or constant domains. The result is modular with respect to both properties of the accessibility relation in the Kripke frame and the way domains of individuals change between worlds. Our approach has a modular metatheory too; soundness, completeness and normalization are proved uniformly for every logic in our class. Finally, our work leads to a simple implementation of a modal logic theorem prover in a standard logical framework. 1 Introduction Motivation Modal logic is an active area of research in computer science and artificial intelligence: a large number of modal logics have been studied and new ones are frequently proposed. Each new log...
A Deterministic Terminating Sequent Calculus for GödelDummett logic
, 1999
"... We give a short prooftheoretic treatment of a terminating contractionfree calculus G4LC for the zeroorder GödelDummett logic LC. This calculus is a slight variant of a calculus given by Avellone et al, who show its completeness by modeltheoretic techniques. In our calculus, all the rules of G4 ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
We give a short prooftheoretic treatment of a terminating contractionfree calculus G4LC for the zeroorder GödelDummett logic LC. This calculus is a slight variant of a calculus given by Avellone et al, who show its completeness by modeltheoretic techniques. In our calculus, all the rules of G4LC are invertible, thus allowing a deterministic proofsearch procedure.
Fibring Labelled Deduction Systems
 Journal of Logic and Computation
, 2002
"... We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial ..."
Abstract

Cited by 13 (9 self)
 Add to MetaCart
We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial characterization of fibring of models. Based on this, we establish the conditions under which our systems are sound and complete with respect to the general semantics for the corresponding logics, and establish requirements on logics and systems so that completeness is preserved by both forms of fibring.
A system of interaction and structure II: the need for deep inference
 Logical Methods in Computer Science
, 2006
"... Vol. 2 (2:4) 2006, pp. 1–24 ..."
A New Method for Bounding the Complexity of Modal Logics
, 1997
"... . We present a new prooftheoretic approach to bounding the complexity of the decision problem for propositional modal logics. We formalize logics in a uniform way as sequent systems and then restrict the structural rules for particular systems. This, combined with an analysis of the accessibility r ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
. We present a new prooftheoretic approach to bounding the complexity of the decision problem for propositional modal logics. We formalize logics in a uniform way as sequent systems and then restrict the structural rules for particular systems. This, combined with an analysis of the accessibility relation of the corresponding Kripke structures, yields decision procedures with bounded space requirements. As examples we give O(n log n) space procedures for the modal logics K and T. 1 Introduction We present a new prooftheoretic approach to bounding the complexity of the decision problem for propositional modal logics. We formalize logics in a uniform way as cutfree labelled sequent systems and then restrict the structural rules for particular systems. This, combined with an analysis of the accessibility relation of the corresponding Kripke structures, yields decision procedures with space requirements that are easily bounded. As examples we give O(n log n) space decision procedures f...